Perspectives for obtaining large amounts of nuclear energy

AstroNuclPhysics ® Nuclear Physics - Astrophysics - Cosmology - Philosophy Physics and nuclear medicine

1. Nuclear and radiation physics
1.0. Physics - fundamental natural science
1.1. Atoms and atomic nuclei
1.2. Radioactivity
1.3. Nuclear reactions and nuclear energy

1.4. Radionuclides
1.5. Elementary particle and accelerators
1.6. Ionizing radiation

1.3. Nuclear reactions and nuclear energy

Spontaneous decay or transformation of nuclei, ie radioactivity, is only one of the nuclear processes leading to the transmutation of nuclei and the emission of ionizing radiation. Here we will briefly discuss other nuclear processes associated with the transformation of nuclei - nuclear reaction, including the possibility of obtaining energy from atomic nuclei.
Terminological note:
The nuclear reactions discussed in this chapter are, in a sense, a special case of "reactions" or interactions of microworld particles. At least in the sense that they are due to the interactions of the elementary particles - protons, neutrons, electrons, photons, possibly also mesons and hyperons. The category of nuclear reactions also sometimes includes spontaneous decay or transformation of nuclei, ie radioactivity, or the interaction of protons and neutrons with each other or with other particles. In our explanation, we have devoted a separate §1.2 "
Radioactivity" to radioactivity and we deal with the interaction of particles in §1.5 "Elementary particles". In the text of this chapter we will deal with nuclear reactions in the true sense of the word, ie processes in atomic nuclei caused by interactions with other particles or nuclei, mostly reactions in binary collisions of nuclei and particles, including fission of heavy atomic nuclei and fusion light cores to heavier cores.
   In the school literature, nuclear reactions are sometimes divided, according to the number of nuclei and reacting particles involved, into two groups :

Mononuclear reactions involving a single atomic nucleus that transforms to form a new nucleus and emitted particles (corpuscular alpha, beta, or photons gamma). This includes radioactivity.
Binuclear reactions, where the target nucleus, after interacting with a bombardment particle or another nucleus, transforms into a new nucleus and emitted particles (corpuscular or gamma photons).
We do not use this division and terminology here.

Chemical <- versus -> nuclear reactions

In chemical reactions, the electron shells of atoms interact
(§1.1, passage "Interactions of atoms") , in which atoms can combine into molecules or, conversely, molecules can decompose. In nuclear reactions, atomic nuclei interact with other nuclei or particles to form new nuclei and emitted particles. The course of specific types of nuclear reactions will be discussed below. Analogies and differences between chemical and nuclear reactions will also be discussed in several places.

   Under nuclear reactions in nuclear physics generally refers to the process whereby two nucleons or two cores or nucleon or other particles and core approach each other at a distance of the order of 10-13 cm, enters the field of action of strong interactions, causing the nuclei changes in the number, energies and configurations of nucleons that may lead to the emission of other particles. The result is the transmutation of the nucleus - either to another isotope of the same element (change in the number of neutrons), or to the nucleus of another element (change in the number of protons). A new nucleus is almost always formed in the excited state, during its deexcitation g radiation is emitted. Cores transformed with nuclear reactions are often radioactive (mostly b- or b+); nuclear reactions are therefore the most important way of producing artificial radionuclides (see §1.4 "Radionuclides", section "Production of artificial radionuclides").

Fig.1.3.1. Basic scheme of a nuclear reaction caused by a particle bombarding a nucleus.

   Most nuclear reactions involve the target nucleus being bombarded by a particle. which by its interaction causes the change in the nucleus and emission of new particles; such a reaction can be written by a simple scheme *)
         a + X ® Y + b + Q ,
where a denotes the arriving particle, X the target nucleus, Y the nucleus formed in the reaction, b the emitted particle (it can also be a photon, or there can be emitted even several particles), Q expresses the energy balance, ie the energy released in an exothermic reaction or the energy delivered in an endothermic reaction. This scheme is abbreviated as X(a,b)Y, or even just (a,b), as far as the reaction itself is concerned and not its products.

*) Slightly different schemes govern the reactions of
nuclear fission and nuclear fusion, which will be discussed in detail below in separate sections of this chapter.
   The nuclei and particles involved are provided with the indices N - number of nucleons and Z - number of protons in the equations of nuclear reactions. Due to the conservation laws
(see below), the condition for the formal correctness of the reaction equation is that the sum of the proton and neutron numbers of the individual nuclei and particles on both sides of the equation is the same.
   Nuclear reactions are very diverse. The same input situation - bombarding the same nuclei with the same particles, often leads to different exit situations - different interactions, in which different nuclei and various particles are formed, with different probabilities.

Technical and natural-scientific importance of nuclear reactions
Transmutation of elements - nuclear "alchemy"

A remarkable feature of nuclear reactions is that, in principle, they make it possible to realize the ancient dream of alchemists - the transmutation of elements *). E.g. even that magic gold
197Au79 can be created from mercury 198Hg80 (content 10% in natural mercury) by bombarding high-energy gamma radiation with photons in the photonuclear reaction - either directly in the reaction 198Hg80(g, p)197Au79, or in reaction 198Hg80(g,n)197Hg80, followed by radioactive transformation of the mercury-197 nucleus by electron capture 197Hg80+e-(EC)®197Au79 (T1/2=2.7 days) into the resulting stable isotope gold-197. From the isotope of mercury 196Hg80 (which, however, is contained in natural mercury only in 0.15%), gold can be prepared by neutron fusion 196Hg80(n,g)197Hg80, again with subsequent radioactive transformation by electron capture into the resulting stable isotope of gold. Similarly, other elements can be created by nuclear reactions from neighboring elements of the Mendeleean table. More laboriously, a series of successive neutron fusions with subsequent b- decays can create a number of heavier elements from lighter elements, similar to the supernova explosion (§4.2 "Final stages of stellar evolution. Gravitational collapse" of the book "Gravitation, black holes and physics of space-time" and the syllabus "Cosmic Alchemy") .
*) However, alchemists had no idea not only about atoms and their nuclei, but also did not recognize elements and compounds. They judged the substances according to their external manifestations and a few simple chemical reactions that they were able to carry out (cf. the passage "Quackery versus science" in the above-mentioned monograph).
   A common disadvantage of artificial transmutation is the low yield, many orders of magnitude lower than in the formation of compounds by chemical reactions. In addition, the target material, or the final product, usually needs to be purified by complex methods, including mass spectrometry - isotope separation. In practice, therefore, only a very small amount of the resulting element can be prepared on accelerators, only on the order of picograms. Even for the rarest elements (gold, platinum), their production by nuclear transmutations would be many millions of times more expensive than their extraction from natural sources
(where a large number of them were left by nuclear reactions during a supernova explosion) . A somewhat more favorable situation in the yield is in nuclear reactors, where a massive neutron flux can produce, for example, light transurans (such as plutonium) also in kilogram quantities (see "Nuclear reactors", "Transurans" below); uranium fission also produces a large number of medium-heavy elements, mostly in the form of b- -radioactive isotopes.
Preparation of artificial radionuclides
The creation of elements by nuclear transmutations is important in nuclear research, for elements (or their isotopes) that do not occur in terrestrial nature, or in the preparation of special targets for accelerators. Nuclear transmutations are most often used for the production of artificial radionuclides
(§1.4., Section "Production of artificial radionuclides"), used in many areas of science, technology, medicine.
  Newly formed atoms just after the nuclear reaction of the original nucleus are sometimes called nascent atoms
(lat. nascendi = birth). They have an initially deformed and excited electron shell, they have a non-zero electric charge - they are in the state of a positive or negative ion, they have a high kinetic energy due to the transmitted kinetic energy during the interaction ("hot atoms"). It leads to high chemical reactivity of nascent atoms after a nuclear reaction.
Nuclear energy
In nuclear reactions, part of the binding energy of nucleons in atomic nuclei may be released and converted into the kinetic-thermal energy of the substance. This occurs in two processes :
1. Combining (fusion) of light nuclei into heavier ones - eg hydrogen nuclei into helium. These thermonuclear reactions are a source of radiant energy of stars - it is described in §4.1, section "Thermonuclear reactions inside stars" of the monograph "Gravity, black holes and space-time physics". Efforts to carry out thermonuclear reactions for the technical recovery of nuclear energy are described below in the section "Fusion of atomic nuclei. Thermonuclear reactions.".
2. Fission of heavy nuclei into lighter ones - eg uranium nuclei. This technology is used in current nuclear power plants, it is discussed below in the section "Fission of atomic nuclei".
Cosmic nucleosynthesis
The enormous natural-scientific significance of nuclear reactions lies in the nuclear nucleosynthesis of all elements (heavier than hydrogen) in space. This cosmic nucleosynthesis took place in two phases :
- Primordial cosmological nucleosynthesis of light elements at the beginning of the universe - in addition to light hydrogen, it was deuterium, temporarily tritium, especially helium and smaller amounts of lithium, beryllium, boron. It is analyzed in more detail in §5.4, section "Lepton era. Initial nucleosynthesis" monograph "Gravity, black holes and space-time physics".
- Thermonuclear synthesis of heavier elements in stars - §4.1, part "Thermonuclear reactions inside stars" in the same book.
  For the creation of elements in the universe, see also §1.1, passage "Cosmic alchemy" and syllabus "Cosmic Alchemy". Thanks nuclear reactions are in the universe heavier elements, that make produce a diverse structure and later life.

Conservation laws and energy balance of nuclear reactions
An important common aspect of nuclear reactions are conservation laws - it is mainly the law of conservation of electric charge, number of nucleons, energy (kinetic energy and rest energy in connection with Einstein's relation E = mc2 equivalence of mass and energy), then momentum, angular momentum, or parity and isospin. The fact that these laws must be complied with in nuclear reactions has some basic consequences, such as the ways ("channels") in which a given reaction can take place and which it cannot.
   Their energy balance is of great importance for the implementation, course and use of nuclear reactions. Essencialy important is the balance of the kinetic energy of nuclear reaction Q = [E
k(Y)+Ek(b)] - [Ek(X)+Ek(a)], which is the difference of the total kinetic energy Ek of particles after the reaction and before the reaction (here there are only two components, generally it would be the sum over all incoming and outgoing particles). It is thus the kinetic energy released or consumed in the reaction. According to the law of conservation of energy and Einstein's relation of equivalence of mass and energy, this energy of a nuclear reaction is also given by the difference of the sums of rest masses of all particles before the reaction and after the reaction Q = {[m0(X)+m0(a)] - [m0(Y)+m0(b)]}.c2. For atomic nuclei, this is the difference in the so-called mass defect given by the binding energy of the nucleus.
   According to the energy of a nuclear reaction, these reactions are divided into two groups :
¨ Endothermic (endoenergetic) reactions Q < 0 ,
where the kinetic energy of interacting nuclei and particles is "consumed" to change the internal state of nuclei or to release or produce new particles.
¨ Exothermic (exoenergic) reactions Q > 0 ,
where there is a "release" and gain of kinetic energy, which is drawn from the binding energy of nuclei.
  Most nuclear interactions have endoenergetic character. Important exoenergetic interactions between light nuclear fusion and heavy nuclear fission will be discussed below in the "
Nuclear Energy" section. In order to carry out most nuclear reactions, it is necessary for the incident particles to have a relatively high kinetic energy of the order of a few MeV. This energy is needed both to overcome the Coulomb electrostatic repulsion (if the particle is positively charged; this does not apply to neutrons) and to introduce the energy needed for the relevant changes in the nuclear structure. Therefore, most nuclear reactions are performed with particles accelerated to high energies on accelerators - see §1.5, section "Charged particle accelerators".

General mechanisms of particle interactions with atomic nuclei
If a flying particle (situation according to Fig.3.1.1 bottom left) comes close to the atomic nucleus, there can be several ways of its interaction with the nucleus, depending on the type of particle and nucleus (including their charge), the kinetic energy of the particle, on the impact factor :

Mechanisms of nuclear reactions
Nuclear reactions are usually very complex processes in which "come into play" a number of factors of properties of incident particles (especially their electric charge and other reported interactions - strong, weak), their energy, momentum - impact factor, as well as structure of bombarded atomic nuclei. If the shelling particle penetrates the area of the target nucleus, the interaction can take place in basically two ways (at least according to our model ideas) :

Effective cross-section of nuclear reactions
As with chemical reactions, nuclear reactions take place differently "willingly" - with different efficiencies or probabilities, depending on the type of reaction and the energy of the particles. The probability of nuclear reactions can be clearly expressed in a geometric way using the so-called effective cross section of the reaction. The effective cross section expresses the probability that the bombardment particle will interact with the target core in a given specific way.
   The concept of the effective cross-section is based on the illustrative idea that the target core behaves as an "absorbing body" with a radius r with respect to the incident particle, which the particle either hits and the required reaction occurs, or does not hit them (passes them, flies around) and the reaction does not occur - Fig.1.3.2. The larger the radius r of this body, resp. its effective area
s = p .r2 - effective cross section, the greater the probability of interaction (probability that the particle "hits").

Fig.1.3.2 Expression of the probability of a nuclear reaction using an effective cross section

   The cross section may, but need not be directly related to the "geometric radius" of the target nucleus rgeom or its "geometrical cross section" sgeom = p .r2geom. For "attracting" particles (eg neutrons) s > sgeom, for repelling particles (eg protons) is s < sgeom - Fig.1.3.2 on the right. In addition, the same firing particle can cause different nuclear reactions on the same core , the various probabilities of which are described by different effective cross sections. These effective cross-sections no longer have anything to do with the geometric dimensions of the core - they are the result of the internal mechanisms of specific types of reactions.
   The so-called impact parameter b is important for the course of a specific interaction of nuclei: it is the geometric distance of the centers of effective "disks" of interacting particles (nuclei and particles), in which they fly around each other or they intersect. In the case of a small impact parameter b << r
geom it is a central collision, in the case of larger values b it is a peripheral collision. If the impact parameter is greater than rgeom , resp. greater than the sum of the effective radii of booth nuclei, there are no longer strong interactions between nucleons, but nuclei can interact through their electric fields (such a collision is sometimes called ultraperipheral).
   The unit of effective cross-section in the SI system would be m
2, which is, however, inadequately large, and therefore in practice the unit barn (bn) is used: 1 bn = 10-28 m2, which has the order of magnitude of the geometric cross-section of heavy atomic nuclei such as uranium nuclei.
Note: The slang name "barn" originated in the early nuclear technology in the 1940s from the humorous comparison that neutrons hits "nuclei as big as a barn" - uranium 235 nuclei.
   The effective cross section s indicates the probability that the bombardment particle will interact with the target core in a give specific way. If we were bombard a target substance, that has the number of SN of the given atomic nuclei per unit area, by the total number no of particles that can enter nuclear reactions, then the number of particles n which actually cause a given nuclear reaction will be: n = no .SN .s. This can be rewritten as s = (n/no). (1/SN) - cross section is given by the ratio of the realized nuclear reactions to the number of particles needed to induce them, multiplied by the inverse of the number of nuclei per unit area substance.

Energy dependence of nuclear reactions
The actual course and efficiency (effective cross-section) of nuclear reactions depends in a complex way not only on the type of target nucleus and the bombardment particle, but also on the kinetic energy of this particle, more precisely on the energy in the center of gravity system [nucleus + particles]. With the exception of neutron capture, there is an energy threshold for most nuclear reactions *); below this value the reaction does not occur
(or it can occur with low probability, due to the quantum tunneling phenomenon). With increasing energy, different types of reactions then occur first with an increasing effective cross-section, but then the effective cross-section often decreases and one type of reaction is replaced by other types. By a suitable setting of the energy of the bombarded particles, the optimal effective cross-section can be achieved for the specific nuclear reaction required. However, even with the same energy, different types of reactions often occur (albeit with different effective cross sections).
*) For positively charged particles (protons, deuterons, a) the energy threshold is given mainly by the need to overcome the repulsive electric (Coulomb) forces of a positively charged nucleus. For photons, the energy threshold of photonuclear reactions is given by the binding energy of nucleons in specific nuclei.

Types of nuclear reactions
Nuclear reactions are usually classified according to the cause of their origin, ie what particles they were caused by :

Neutron-induced reactions
The easiest way to induce nuclear reactions is to use neutrons that do not have an electric charge, are not repelled by nuclei, and therefore usually willingly enter nuclei even when they are slow *). The simplest neutron reaction is a ordinary capture of a neutron by the nucleus X - neutron fusion, which already remains in the nucleus:
1n0 + NXZ ® N+1YZ + g, while the newly formed composite nucleus Y is in an excited state and deexcited by photon radiation g. Therefore, this reaction is also called neutron radiation capture, and X(n,g)Y, or just (n,g), is abbreviated. The newly formed nucleus Y is an isotope of the same element, enriched in one neutron; often shows b- radioactivity.
*) The slower the neutrons fly on, the more likely they are to penetrate the nucleus (they have "more time" to do so). The effective neutron capture cross section is therefore largest for very slow "thermal" neutrons. With increasing kinetic energy of neutrons En (ie velocity of neutrons nn), the effective cross section first decreases monotonically (due to the shorter residence time of the neutron in the nucleus), approximately according to the law 1/vn. In the region of slow neutrons around about tens of keV, the energy dependence of the effective cross section shows a number of sharp resonant maxima and minima (related to the occupancy of discrete energy levels of nucleons in the nucleus; for heavy nuclei resonant maxima and minima are more pronounced and very condensed), after which, for higher neutron energies, the effective neutron capture cross section decreases significantly. A typical energy dependence of the effective cross section of neutron capture by the nucleus is in the left part of the figure below.
   Neutrons can also induce other reactions in the nucleus associated with particle radiation, especially at higher kinetic energies. Such reactions are (n, p), (n, d), (n, a ), resp. at higher energies, more particles can be emitted, such as (n, 2p), etc. Production of radionuclides by neutron reactions is mentioned in §1.4 "Radionuclides", part "Production of artificial radionuclides". Nuclear reactions induced by neutrons are further used in neutron activation analysis (§3.4, section "Activation analysis").
   For heavy uranium and transuranic nuclei, neutrons induce specific fission reactions, which will be discussed in detail below in the "
Nuclear Fission" section.

Typical dependence of the effective cross section of nuclear reactions on the energy of bombarding neutrons (left) and protons (right).

Nuclear reactions induced by neutrons and protons are of great importance in nuclear astrophysics - in primordial cosmological nucleosynthesis (§5.4, part "Lepton era. Initial nucleosynthesis" monograph "Gravity, black holes and space-time physics") and nucleosynthesis inside stars, nova explosions and especially supernovae (it is discussed in §4.1, part "Evolution of stars" and in §4.2, part " Supernova explosion. Neutron star. Pulsars.", passage "Types of supernovae and their astronomical classification" in the same book).
Reactions induced by protons

In order for the proton p
+ penetrated into the nucleus and could cause a nuclear reaction there, it must be accelerated *) to relatively high kinetic energy (at least hundreds of keV to MeV units) to overcome the repulsive electrical (Coulomb) forces of a positively charged nucleus. Depending on the energy of the protons, a number of reactions can take place. The simplest of these is the radiation capture of a proton (p, g): p+ + NXZ ® N+1YZ+1 + g, but also occur reactions of the type (p, p), (p, n), (p, d), (p, a), at higher energies more particles can be emitted, eg (p, 2n), (p, pn), (p, 3n). The resulting Y core often exhibits b+ -radioactivity (the nucleus is usually enriched in proton); the production of radionuclides by proton reactions is mentioned in §1.4 "Radionuclides", part "Production of artificial radionuclides"
*) Acceleration of protons and other charged particles (heavier ions) is most often performed in a cyclotron, or in a linear accelerator - it is discussed in more detail in §1.5 "Elementary particles", part "Charged particle accelerators").
   To carry out a nuclear reaction, a proton must have a certain threshold energy to overcome the repulsive electrical force of the core, in co-production with the tunneling phenomenon. Thus, with proton energy, the effective cross-section of the reaction first increases sharply from zero to a certain maximum value, and then decreases monotonically again at higher energies, as high-velocity protons shorten their residence time inside the nucleus
(reducing the likelihood of a nuclear reaction).
   At the highest proton energies (hundreds of MeVs and more), fragmentation reactions occur, in which the nucleus is more or less "broken" - a larger number of protons and neutrons of different energies are ejected from it; or other particles are produced, most often
p- mesons. In addition to accelerators, we encounter these effects during the impact of cosmic radiation (§1.6 "Ionizing radiation", part "Cosmic radiation"); the interesting use of the fragmentation reaction for so-called accelerator - controlled transmutation technology (ADTT) is mentioned below.

Reactions induced by deuterons, a-particles, heavier nuclei (positive ions) :
- Deuterons
Anther relatively heavy particles can cause nuclear reactions, are the ions-nuclei of deuterium
2H1, or deuterons d formed by a pair of coupled protons and neutrons. The most common reactions of deuterons with target nuclei are (d, p) and (d, n), which take place mainly by direct processes of "entrainment" of nucleons. Such direct processes take place by tearing off and absorbing a neutron or proton from the deuteron in the field of the atomic nucleus. This is due to the relatively large distance » 4.10-13 cm between a proton and a neutron in a deuteron and their lower binding force (corresponding to a binding energy of 2.226 MeV). By reaction with cyclotron-accelerated deuterons, it is often used to prepare radionuclides, rarely as neutron sources.
Deuterium-tritium neutron generators

It is enough to accelerate the deuterons to an energy of about 100-200keV and let them fall on a target containing tritium to cause a nuclear reaction
2D1 + 3T1 ® 1n0 + 4He2 (+17,6MeV), in which neutrons are released. A fairly small accelerator or just a tube is enough for this (see §1.5, section "Accelerators", pasage "Accelerators as neutron generators"). Such neutron generators are used in a number of applications, especially in neutron activation analysis (§3.4, section "Neutron activation analysis"), in some radiation technologies, experimentally also in radiotherapy (§3.6, section "Hadron radiotherapy").
- Alpha particles

a, which are the nuclei of helium 4He2 induce during bombardment of target nuclei most reactions of type (a, n) and (a, p), with event. emissions of quantum g; both of these types of reactions occur with roughly the same probability. In light nuclei, these reactions can also take place with the energies of particles a the order of MeV units, which occur in some natural radionuclides from the uranium and thorium decay series. With reactions of type (a, p) already in 1919 E.Rutheford carried out the first artificial transformation of elements, reactions (a, n) led to the discovery of the neutron by J.Chadwick in 1932 during the bombardment of beryllium nuclei by alpha particles. Alpha particles from the radionuclides of reactions (a, n) are still used as neutron sources. Otherwise, however, particles a artificially accelerated in accelerators, are now used for nuclear reactions and the production of radionuclide, where nuclear reactions can be performed for all elements of Mendeleev's periodic table.
- Nuclear reactions in collisions of heavier nuclei
Heavier nuclei, also referred to as multiple-charged ions (eg lithium
7Li3 , ..., carbon 12C6, nitrogen 14N7, oxygen 16O8, ..., neon 20N10, and others), due to the high Coulomb repulsive barrier, it is necessary to accelerate to considerably high kinetic energies in order to carry out a nuclear reaction (> »100 MeV, the heavier the core, the higher). At lower energies, only electromagnetic (Coulomb) excitation of the nucleus occurs, usually with a higher angular momentum. At energies only slightly above the threshold energy, there is usually a peripheral direct interaction of the ion with the nucleus, in which one nucleon (neutron or proton) is transferred ("torn down") from the ion to the nucleus. At higher energies, an excited composite nucleus is formed with subsequent "evaporative" emission of particles (nucleons, a-particles). Multiple charged ions with sufficiently high energy can further cause the heavier nuclei to split into two lighter nuclei, event. fragmentation and breakage, mostly with neutron emission and quantum g-radiation. Alternatively, bombarding heavy nuclei with other heavy multiple-charged ions, at the appropriate energy, can lead to their composition to form new superheavy nuclei, as will be described in more detail below in the "Transurans" section.
   In addition to energy, the result of a nuclear reaction depends on the collision parameter b of nuclei. With a collision parameter of several tens of femtometers, a distant collision occurs, the nuclei flying around each other deviated by elastic (Rutheford) scattering, and their Coulomb excitation can occur. With the impact parameter of the fm units, a peripheral collision occurs, accompanied by scattering, with the possibility of direct reactions of peripheral nucleons (such as nucleon entrainment). At b
»1 fm there is a tight "sliding" collision, with deeply inelastic scattering of the cores, with the possibility of partial fusion or fragmentation. At almost central collision, b <1 fm, at suitable energy the nuclei may fuse, at high energies their fragmentation or breakage, at very high energies even form a quark-gluon plasma, the hadronization of which produces a large number of secondary particles (see below).

Nuclear reactions in collisions of two heavy atomic nuclei.
When two nuclei collide at low or medium energies, their electrical (Coulombic) scattering, inelastic scattering with direct interactions by nucleon transfer or ejection, fragmentation or composition (fusion) of the nuclei can occur to form a new heavy nucleus.
Bottom: During a high-energy collision of two nuclei, a quark-gluon plasma is formed for a short time, followed by hadronization.

High-energy collisions of heavier atomic nuclei. Quark-gluon plasma.
We have shown above how nuclear reactions leading to the formation of new nuclei - nuclear transmutations, accompanied by the emission of nucleons, gamma photons, or a -particles. At energies of hundreds of MeVs to units of GeV, the nuclei then fragment into individual nucleons or nuclear fragments, often with the formation of p- mesons in nucleon-nucleon interactions.
   If atomic nuclei collide with the very high kinetic energies of many GeVs or TeVs - these are ultrarelativistic nuclear collisions, nuclei is not enough time to enter into a nuclear reaction or fragment, but fundamentally new phenomena occur. The nucleons in the colliding nuclei penetrate each other and "melt" into a mixture of free-moving quarks and gluons *): the so-called quark-gluon plasma is formed. This state lasts only a small moment, about 10-22 seconds, because when the energy of quarks and gluons decreases (during "cooling" due to thermodynamic expansion), free quarks under the action of gluons "connect" again to hadrons - nucleons and mesons, quark-gluon plasma will be hadronized. A spray of a large number of p- mesons, protons and neutrons, K-mesons and other particles, as well as their antiparticles, then flies out of the interaction site.
*) Under normal conditions, quarks are perfectly "trapped" in hadrons, here in protons and neutrons, under the action of gluons. When the energy density exceeds about 1 GeV/fm3, which corresponds to a temperature higher than about 2.1012 °K (temperature one hundred thousand times higher than inside the Sun!) and occurs at energy higher than 170 MeV, however, there is a local release of quarks from hadrons. The quarks and gluons then move freely for a short time in a mixture called quark-gluon plasma.
   In the case of high-energy (ultrarelativistic) collisions of atomic nuclei, the kinematic and dynamic effects of the special theory of relativity are significantly manifested . An interesting phenomenon is the relativistic contraction, in which the longitudinal dimension of the cores moving at velocity v is effectively shortened by the Lorentz factor g = (1-v2/c2) -1/2. At high energies, where the velocities are very close to the speed of light, the longitudinal dimensions of the heavy core relative to the observer at rest can be shortened more than 1000 times! The interaction of the two nuclei then resembles the collision of two thin disks rather than two spheres. At these high energies, the effective wavelengths of the nucleons forming the nucleus are also shortened. This increases the influence of the details of the structure of the nucleus and the structure of nucleons - the density distribution of gluons and quarks. In frontal collisions (central, b »0 fm) most nucleons in both nuclei succumb to this process, in non-central collisions only a certain part that collides; the other nucleons continue to fly as nuclear fragments.
   Due to high instability we cannot analyze the quark-gluon plasma directly, but only additionally using particles emitted after its hadronization. Thus, the detectors surrounding the site of the heavy nucleus collision register only "ordinary" hadrons and other common particles (photons, electrons, positrons, muons), regardless of whether or not the quark-gluon plasma was formed during the collision. To demonstrate the formation of a quark-gluon plasma, a careful analysis of the number of different species of flying hadrons and their momentum spectrum needs to be performed, that could be explained by the presence of free-moving quarks in the initial phase of the interaction.
   The formation of quark-gluon plasma can be studied on large accelerators using heavy nuclei ("ions"), accelerated to energies of hundreds of GeV and higher, especially in the opposite direction beams (§1.5, part "Charged Particle Accelerators", section "Colliders"). The observation of quark-gluon plasma was first reported at the CERN SPS in 2000. However, its properties were analyzed latter at the RHIC (Relativistic Heavy Ion Collider) accelerator. Research is now continuing at the LHC large accelerator at CERN, where collisions of lead nuclei with energies greater than 2 TeV/(nucleon pair) are detected by the ALICE detection system (see §1.5, section "Large accelerators"). It turns out that quark-gluon plasma immediately after its formation behaves as an almost ideal liquid with low viscosity. From the point of view of particle physics, the quark-gluon plasma is discussed in §1.5, passage "Quark-gluon plasma - "5th state of matter"".
Electron- induced reactions
Electrons do not carry a strong interaction, so that in general their interaction with nuclei is not significant
(of course with the exception of the electrical bonding of the envelope electrons, forming the structure of the atoms). Under normal circumstances, the nucleus is part of the atom. At lower energies of the incident electrons, the nucleus is relatively effectively shielded from them by the repulsive electrical forces of the electrons of the atomic shell, so that the bombarding electrons are usually scattered and do not penetrate the nucleus. When bombarding atomic nuclei with accelerated electrons, their elastic and inelastic scattering (with the formation of bremsstrahlung radiation) and Coulomb excitation of atomic nuclei occur. At high energies in the order of hundreds of MeV to GeV, the Broglie wavelength of electrons is less than the effective dimensions of the nucleons, and such fast electrons penetrate the nuclei, where they can induce nuclear reactions. ..........
   Interesting reaction that may occur during bombardment of nuclei with accelerated electrons, is called inverse b -decay - electron penetrates into the core and then is combined with a proton to form a neutron and emit a neutrino: e- + p+ ® no + n'e. From the point of view of the bombarded core, this manifests itself as a reaction: e+ + NXZ ® NYZ-1+ n + g. This process takes place through a weak interaction and its effective cross section is very small, so it is practically not used in laboratory conditions. However, it has important astrophysical significance in the final stages of the life of material stars, where it leads to a supernova explosion and the formation of a neutron star - see §4.2 "Final stages of stellar evolution. Gravitational collapse", section "Supernova explosion, neutron stars, pulsars" book "Gravity, Black Holes and the Physics of Spacetime").

Reactions induced by g -radiation - photonuclear reactions
g- radiation does not show a strong interaction, so it interacts with atomic nuclei indirectly, through electromagnetic action. At low and medium energies of the order of MeV units, elastic scattering (classical Thomson or Compton scattering) of photons g on nuclei occurs and inelastic scattering causing an excited state of the target nucleus (followed by deexcitation of gamma radiation emissions). A special case is the resonant nuclear fluorescence of gamma radiation - the Mösbauer effect (described in more detail in §1.6 "Ionizing radiation", passage "Interaction of gamma radiation").
   If the quantum radiation g has a sufficiently high energy, greater than the binding energy of the nucleons in the target nucleus (at least about 2.5 MeV), they can be absorbed and induce a nuclear reaction in the nucleus, in which a neutron or proton is ejected from the nucleus: photonuclear reactions (g, n), (g, p); at sufficiently high energies g or even more particles: (g, 2n), (g, np), (g, 2p), (g, a). The simplest photonuclear reaction is the ejection of a neutron from the deuterium nucleus g + 2H1 ® p + n (ie its fission into a proton and neutron), which has a threshold energy of 2.23 MeV. For heavier nuclei, a substantially higher radiation energy g is usually required to produce a photonuclear reaction. The resulting nucleus after the photonuclear reaction can be radioactive - we say that the so-called gamma-activation occurs.
   If the energy of the radiation g causing the photonuclear reaction is only slightly higher than the threshold energy (given by the binding energy of the nucleons), the reaction proceeds through a compound nucleus, and at higher energies by a direct process.
   When irradiating heavy nuclei in the uranium and transuranic region (such as 235,238U) with hard radiation g of energy higher than 15MeV, may cause photofission such nuclei into two fragments - medium-heavy nuclei from the middle of the Mendeleev table, similar to their fission by spontaneous or neutron action.
   At very high energies of gamma radiation, exceeding
»150 MeV, new elementary particles, such as p -mesons , are already produced, at even higher energies also K-mesons and hyperons (as mentioned in more detail in §1.5 "Elementary particles and accelerators", section "Interaction of elementary particles", passage Formation of new particles during interactions").

Fission and fusion of atomic nuclei. Nuclear energy.
General possibilities of obtaining energy from matter

Energy is contained in mass - substance in nature. The maximum amount of energy E that can in principle be obtained from matter is given by the Einstein relation of the equivalence of mass and energy E = m.c2, where m is the mass and c is the speed of light. However, the actual practically available amount of energy is many times (by many orders of magnitude) smaller. The following figure shows the ways in which energy can be obtained from matter :

Chemical reactions
Here on Earth, the most common way to obtain energy from matter is through chemical reactions between atoms, in which part of the electrical binding energy of the envelope electrons in the atoms is released . Besides the energy recovered by living organisms from food, it is often burning - combining a suitable fuel with oxygen. However, the binding energy of electrons in atoms is relatively low, so the efficiency is only 0.000 000 01 % m.c
2 (from the maximum possible energy by Einstein relation E = mc2). Suitable chemical fuels containing carbon and hydrogen - and atmospheric oxygen however, there is enough, so that even this negligible efficiency was until recently sufficient to cover common needs. However, with industrial development, energy consumption increases, fossil fuels are depleted and the chemical method will no longer be sufficient (cf. also below the reflection "Energy-life-society").
Nuclear reactions
The perspective here is nuclear reactions, in which part of the binding energy of a strong interaction of nucleons in atomic nuclei is released. This nuclear energy is many orders of magnitude larger than chemical energy. During the fission of heavy nuclei (eg uranium) about 0.1% mc
2 is released, during merging (fusion) of light nuclei then even higher energy approx. 1% mc2. Both of these methods will be discussed in detail below.
Gravity, antimatter ?

Theoretically, there are two other more efficient ways that are, however, in the foreseeable future
(and perphas forever?) only at the level of science fiction :
1. Gravity - the release of the gravitational binding energy of matter in the field very strongly graviting object, black holes where theoretically it can reach a maximum efficiency of up to 42%
( Gravity4-8.htm ). However, we have no available black hole; even if we had it, we will not have technologies in the foreseeable future that would be able to release and use this energy.
2. Annihilation of electrons with positrons, in which 100% of their mass is converted into gamma radiation
(it is discussed in §1.5, passage "Antiparticles, antimatter, antisworlds"). However, we do not have available the antimatter and the energy from annihilation is almost impossible to effectively exploit (discussed in the passage "Antimatter - a potential source of energy?" §1.5).
   Most technologies for obtaining energy from matter are based on the consumption of fossil fuels that originated on Earth in the distant past and are not renewed, either at all, or much slower than their consumption. They are therefore in danger of being exhausted. This applies in particular to coal, oil and natural gas reserves; these fuels are also ecologically problematic - they contaminate the environment with compounds of sulfur, nitrogen, carbon dioxide...

Energy of atomic nuclei
Nucleons in atomic nuclei are strongly bound by nuclear forces, which is associated with considerable potential binding energy E
b. It is the energy needed to completely "break down" the nucleus into individual nucleons, or vice versa, the energy that is released when the nucleus is "assembled" from these nucleons. Due to the equivalence of mass and energy (expressed by the known Einstein relation E = mc2) results in the total mass of the nucleus mZ, N being less than the sum of the masses of its free nucleons Z.m p + (N.Z).mn. This difference between the mass of free nucleons and the actual mass of the nucleus: Dm = + (N.Z).mn - mZ,N is called the mass defect and is related to the total binding energy of the nucleus by the relation Eb = Dm.c2. The total binding energy of the nucleus Eb increases with the number of nucleons, but for the stability of the nucleus and the energy balance in nuclear transmutation, it is more important the mean binding energy per one nucleon: Eb/N (characterize also sometimes called. packing factor, mentioned in §1.1 passage "binding energy of the nucleus") . For different atomic nuclei, this binding energy per nucleon is different, as can be seen from Fig.1.3.3. For light elements, this binding energy increases with the nucleon number, with a few fluctuations for the lightest elements, nuclei with an even number of protons and neutrons show higher stability. The combination of two protons and twoo neutrons forming the nucleus of helium 4He is significantly more stable. Above N »20 the growth slows down and a slow maximum is reached for the elements of the iron group (chromium, manganese, iron, nickel, copper). For nuclei heavier than iron, the binding energy of the nucleon gradually decreases again; this is due to the fact that for large nuclei, in addition to the attractive short-range nuclear forces, an electric repulsive force between protons is increasingly being applied.
   In small nuclei, nucleons bind by nuclear forces to a small number of "neighbors", so they have a relatively low binding energy per nucleon. As the volume of the nucleus increases, the inner nucleons bind efficiently to about 12 surrounding "neighbors", the proportion of surface nucleons decreases, and the binding energy is established at about 8 MeV/nucleon. The maximum of 8.8 MeV/nucleon is for the iron nucleus 56Fe, for larger nuclei, the binding energy per nucleon decreases slightly due to increasing electrostatic repulsion of protons.

Fig.1.3.3. Dependence of the mean binding energy E
b/one nucleon on the nucleon number N of the nucleus. In the initial part of the graph, the scale on the horizontal axis is slightly stretched to better see the differences in binding energy for the lightest nuclei. The right part schematically shows both ways of releasing the binding energy: the splitting of the heavy nucleus and the merging of the two light nuclei.

By nuclear energy we mean the binding energy of nucleons in nuclei. From the shape of the binding energy curve in Fig.1.3.3 it follows that there are two basic possibilities of effective energy release during nuclear transformations :

  1. By joining ,
    or by synthesis or fusions lightest nuclei (hydrogen, helium ...) into the heavier nuclei, with a larger number of protons. In the resulting heavier nucleus, the nucleons will be bound more strongly than in the two original lighter nuclei, so that up to 5MeV of energy per nucleon will be released
    (for fusion of deuterium with tritium in total about 17MeV). This very promising method, which is still in the research and development stage, will be discussed in more detail below in the section "Fusion of atomic nuclei. Thermonuclear reactions.".
  2. By splitting ,
    or by fissions the heaviest nuclei (especially uranium) into lighter nuclei, with about half the proton numbers. With such fission of, for example, uranium nuclei, the nucleons will be more strongly bound in the two resulting lighter nuclei; about 1 MeV of energy is thus released per nucleon (a total of about 200 MeV). We will first describe this now widely used method (in the section "Fission of atomic nuclei").

In both of these processes, the nucleons in the resulting nuclei have a greater binding energy than in the initial nuclei, and the difference between these binding energies is released - we obtain nuclear energy.
   The third way of releasing nuclear energy is nuclear decay, where a nucleus with a slightly different proton number is spontaneously formed from the original nucleus - by radioactive transformation of nuclei. However, the amount of energy released here is relatively small. Nevertheless, this method can be advantageously used where low energy output is sufficient, especially in low-current electronics. A device that uses energy from the decay of radioactive isotopes to produce electricity is called nuclear battery, radioisotope generator, or radionuclide volta cell :
Radionuclide Volta Cells ("Atomic" Batteries)
As will be discussed in detail below, on a macroscopic scale, we commonly obtain electrical energy from nuclear energy through thermal energy. It would certainly be advantageous to convert nuclear energy into electrical energy directly. We cannot do this in the process of fission or fusion, but in the case of nuclear radioactive transformations we can do it in part. Electrically charged particles, which are formed during the transformation of radioactive nuclei and which fly out of them, actually represent an electric current. Although this electric current is very weak, electric voltage and current can be excited by suitable capture of flying particles - an electric source can be created on the power of the order of milliwatts to watts (depending on the activity of the radionuclide and the performance of electrical conversion). A device in which electrical energy is generated or accumulated by the action of radiation from radioactive substances is called a radioisotope battery (inaccurately also an "atomic battery"), or a nuclear battery. Since beta electrons are the most suitable for direct excitation of electricity (alpha-particles have a short range in matter), we also encounter the name beta-volta cells. Tritium 3H currently appears to be the most suitable excitation radionuclide (§1.4, passage "Hydrogen - 3H"), strontium-yttrium-90, promethuim 147Pm, plutonium 238Pu or americium 141Am are also used. Radionuclides with low-energy beta- -radiation have the advantage that no shielding is required (radiation is absorbed inside and in the battery case) and there is no radiation in the vicinity.
  In principle, it is possible to construct four types of radionuclide electric batteries, which use different mechanisms of interaction of nuclear radiation with matter, in which electric voltage and current are generated :
¨ Direct excitation
of electric voltage by charged particles emitted during radioactive transformations. Charged beta or alpha particles are captured on suitably modified electrodes, where they transmit their charge and kinetic energy; these electrodes are thus a source of electrical voltage and current that can flow through the external circuit. If the electrodes are perfectly insulated, they function as a capacitor and can generate high voltages of many kV
(due to the high kinetic energy of charged particles b, a emitted during radioactive conversion), but they are able to supply only a very small current and el. power - depending on the activity of the radiator.
¨ Ionisation radioisop batteries ,
with a gas filling in which nuclear radiation causes ionization. Between two electrodes with different contact potential is a gas charge in which ionizing radiation of an exciting radionuclide causes the formation of oppositely charged ions. Due to the different contact potential of the electrodes, the ions move to the opposite electrodes, where they discharge and drive an electric current in the outer circuit between the two electrodes. Argon with the addition of the excitation radioisotope tritium
3H is suitable as a gas filling.
Semiconductor radionuclide batteries ,
using the action of ionizing radiation on the transitions p-n of a suitable semiconductor. Charged particles emitted by a radionuclide are not direct carriers of electricity here, but only their energy is used to create el. current in the semiconductor material. Due to the action of ionizing radiation, electron-hole pairs are formed in the semiconductor. An electromotive force then arises at the p-n junction. The desired effect can also be achieved by combining a emitter and a semiconductor with a suitable scintillator: nuclear radiation first interacts with the scintillator material in which it induces light radiation, and only then excites the p-n transition; it is similar to a conventional photovoltaic cell. Semiconductor beta-volta cells excited by tritium
3H appear to be the most promising.
¨ Thermoelectric radioisotope batteries
(also called radioisotope thermoelectric generators - abbreviation RTG ) are made up of common thermocouples heated by heat *) generated by radioactivity (incl. absorption of nuclear radiation). This creates an electromotive force, providing an electric current to the external circuit. It is possible to use beta and alpha (or gamma) radioactivity here, but the efficiency is relatively low (approx. 0.2%). In practice, the plutonium isotope 238Pu is often used for long-term thermoelectric batteries (eg pacemakers, space probes), (a -radioaktivity, half-life 87.7 years, has a heat capacity of 0.54 W per 1 gram).
*) This type of nuclear battery actually gives electricity through thermal energy, only in a different way than nuclear power plants.
Radionuclide electric batteries have
(unlike nuclear reactors) only very little power. Their energy efficiency or profitability cannot be spoken of at all: many times ( many millions of times!) more energy is used to produce the relevant radioactive preparation than a radioisotope battery supplies during its entire operation.
   However, their advantages are small (often miniature) dimensions, long service life, mechanical and temperature resistance. Unlike electrochemical batteries, they work even at very low temperatures, so they can be used to advantage in rockets and artificial satellites launched into space.

Fission of atomic nuclei
In §1.1, the section on the structure of the atomic nucleus
("Structure of the nucleus"), we mentioned the strong nuclear interactions holding the nucleus together against repulsive electrical forces between protons. An important feature of these strong interactions is their short range of only »10-13 cm. Nuclear forces appear to be saturated consisting in that each nucleon attracts strongly only with its nearest neighbors. This property means that it is not possible to "fold" a stable nucleus with an arbitrarily large number of nucleons - in large nuclei, the strong interaction "no longer" reaches sufficiently from the inside of the nucleus to the peripheral parts. All nuclei heavier than bismuth are radioactive, mostly alpha...
   This reduced stability of heavy atomic nuclei is manifested in a specific way by the interaction of neutrons with these nuclei, which are significantly different from the usual reactions (n,
g), (n, p) , (n, a), etc., occurring in lighter nuclei: often a new phenomenon occurs for slow neutrons - the fission of atomic nuclei.

Fissionable and fissile nuclides
From a purely theoretical point of view, each larger atomic nucleus can in principle be split into two lighter nuclei by means of suitable nuclear reactions - by bombarding particles accelerated to the required energies.
   However, only such heavy nuclei (N>230) are interesting for nuclear technology, which can be cleaved by neutron absorption (fast or slow), while nuclear energy is released - the difference in binding energy / 1 nucleon between lighter and heavier nuclei. Such nuclei are called fissionable here. These are, for example, cores
232Th, 233,235,238U, 239Pu, event. heavier transurans, which are, however, difficult to obtain in larger quantities.
   Among these fissionable nuclei, such nuclei occupy a prominent position, which cleaves "very willingly" by absorbing even a slow neutron, and during fission, at least two more neutrons are released, capable of initiating the fission of other nuclei. They are called fissile nuclides. In a sufficiently large so-called critical amount in a suitable configuration, these fissile nuclides are able to self-sustain a chain fission reaction. The most commonly used nuclides of this species are uranium
235U and plutonium 239Pu. Whether a fissionable nuclide will also behave as fissile at the same time, it decides energy balance of binding energy during neutron capture, as discussed below in the section"Fission by slow and fast neutrons".
   In fields other than nuclear technology, in general nuclear physics, the names "fissionable - fissile" are usually not recognized.

The course of nuclear fission
We will show the fission of atomic nuclei on a typical example of
235U. When a slow neutron enters this nucleus, the uranium nucleus splits into two medium-heavy fragments F1 and F2 *), emitting 2 or 3 neutrons: 235U + no ® F1 + F2 + (2 -3) no + Q (energy, includes g). The energy balance of fission and the properties of the fragments will be mentioned below.
*) In addition to the usual binary fission, there is also a relatively rare type - the so-called ternary fission (0.2-0.3% of cases), in which the heavy nucleus splits into three fragments. Two of these fragments are medium-heavy nuclei from the middle of the periodic table, the third may be a very light nucleus - helium
4He, tritium 3H, 5He is also observed (which decays to 6 Li with a half-life of about 0.8 s.).
   We imagine the mechanism of fission according to the drop model of the nucleus in the following stages: By capturing the neutron in the 235U nucleus, its excitation occurs - for a short time, the 236U* core is formed, which is brought into oscillation. As a result of these oscillations, the originally spherical shape of the core deforms to an elliptical, at the ends of which repulsive protons collect. The repulsive electrical force of the protons overcomes the strong short-range interaction, the nucleus narrows and constricts in the middle, until the binding energy is overcome and the nucleus splits into two fragments, that will fly away by repulsive Coulomb forces and take about 90% of the energy released. Each of these fragments sends a "surplus" neutron *) very quickly, sometimes 2 neutrons - these are neutrons that remain in a "strangled" place and after the nucleus ruptures, they explode into the environment. Upon deexcitation of their excited levels, fission fragments also emit gamma radiation (referred to as "instantaneous", because it occurs during the fission process - in contrast to the subsequent radiation g, generated latter during the radioactive transformations of fission products; this radiation can be "delayed" in very different ways, from microseconds to millions of years, depending on the half-lives of the radioactive fission products).
*) Neutrons released immediately during fission are called instantaneous neutrons; there are about 99% of them and their energy ranges from 0.025 eV to about 10 MeV. However, during fission reactions, so-called delayed neutrons are also formed in an amount of about 1% (with energies in the range of about 0.2-0.6 MeV), originating in radioactive fragments of fission with an excess of neutrons, which are removed either by b decay or, especially when in a highly excited state, neutron emission. These neutrons are emitted with a delay of up to a few seconds (the mean time of this neutron delay is about 0.1 s). An example is the fission of a uranium nucleus 235U ® 87Br + 147La + 2n, while the bromine nucleus 87 remains in a state with high excitation energy after fission, by b -decay is transformed into a highly excited 87Kr* nucleus , which changes to a stable neutron emission core 86Kr (the competitive reaction is its b -conversion to 87Sr). Another cause of delayed neutrons is, for example, the isotope iodine 137I. Delayed neutrons are of great practical importance for the dynamics and control of the fission reaction in nuclear reactors, as will be mentioned below.
   Heavy nuclei (such as 235U) have a higher neutron to proton ratio for their (relative) stability than stable medium-heavy nuclei. Thus, the medium - heavy nuclei that are formed during fission have a significant excess of neutrons, which are "removed" by several b- -radioactive transformations until stable nuclei are formed. This produces "beta" electrons and electron (anti) neutrinos, and gamma radiation during deexcitation of nuclear levels. This subsequent radiation a and b it can be "delayed" very differently from the act of fission, from microseconds to millions of years, depending on the half-lives of radioactive fission products.

Fission by slow and fast neutrons
As mentioned above, the initial phase of the mechanism of fission of a heavy nucleus is its excitation, for which the necessary activation energy must be supplied to the nucleus *). The magnitude of this energy (and the appropriate mechanism for its delivery) depends on the size of the nucleus and the configuration of the energy levels of the nucleons in the nucleus; this is explained by the shell and drip model of the nucleus
(in the equation for the binding energy, the even-odd target nuclei 235U92, 233U92, 239Pu94 have a spin element equal to zero, while the even-even nuclei 232Th90, 238U92 have a positive spin member and the threshold energy must be exceeded to perform the fission).
*) A certain exception is the spontaneous fission of heavy nuclei without the participation of neutrons, which can be caused by internal quantum fluctuations of oscillations in the nucleus. Here too, however, it appears that excited heavy nuclei are much more easily subject to spontaneous cleavage (this is a serious problem in the formation and detection of the heaviest transurans, as will be discussed below - the "Transurans" section).
  For odd isotopes of heavy nuclei (such as 235U, 233U, 239Pu), it is sufficient to capture a slow neutron whose binding energy itself on a shell with an odd neutron is sufficient to vibrate the nucleus and split it. When a sufficient number of such nuclei is collected in a certain compact volume, the so-called critical amount, a chain fission reaction can be triggered - see below. Such nuclides are called fissile.
  For even isotopes (
232Th, 238U, 240Pu), the absorbed new odd neutron is only weakly bound. The binding energy of a captured neutron is thus not in itself sufficient for the necessary oscillation and fission of the nucleus - in order for a neutron to split such a nucleus, it must also bring a certain kinetic energy: such nuclei are fissile only by fast neutrons, are referred to as fissionable. These nuclei do not undergo a chain fission reaction, most of the emitted fast neutrons leave the space rapidly without interaction. In order for these even isotopes 232Th and 238U to be used as nuclear fuel, they must first be converted to odd-numbered neutron isotopes that are fissile in a chain reaction. However, the capture of slow neutrons in 238 U and 232 Th - the so-called propagating nuclides - causes nuclear reactions which, after a series of radioactive transformations, eventually result in the formation of odd plutonium nuclei 239Pu and 233U, which are cleavable by slow neutrons and allow the formation of a chain fission reaction - see "Propagation reactors" below.

The efficiency of some neutron nuclear reactions, important for fission nuclear energy, depending on the kinetic energy of neutrons.
Left: Effective cross section of fission of three important heavy nuclides depending on the energy of bombarding neutrons. Right: Effective cross section of the formation of fission nuclides
239Pu and 233U by bombarding propagating materials 238U and 232Th with neutrons of different energies.
Note: The complex course of the effective cross section in the resonance region was measured using highly sophisticated and demanding experimental methods. However, in the actual course of nuclear chain reactions, where fission neutrons have a continuous spectrum with a wide range of energies, these details do not manifest themselves. Here, a smooth (strongly smoothed) curve of effective cross sections is applied.

For each nuclear reaction, the dependence of its effective cross section (defined above in the section "Effective cross section of nuclear reactions") on the energy of the bombardment particles is important. From the left part of the figure we see that the effective cross section for neutrons induced fission is the largest for all three basic fission nuclides 235U, 233U, 239Pu for very slow "thermal" neutrons (about 104 barn) - the slower the neutrons fly, the they are more likely to penetrate the nuclei. With increasing kinetic energy of neutrons En (ie neutron velocity vn) the effective cross section first decreases monotonically, approximately according to the law 1/vn (faster neutrons remain in the field of nuclear forces for a shorter time, so the probability of a nuclear reaction taking place decreases). In the region of slow neutrons of about 10-6 -10-3 keV, the energy dependence of the effective cross section shows a large number of sharp resonant maxima and minima (related to the occupancy of discrete energy levels of nucleons in the nucleus), after which for higher neutron energies the effective fission cross section stabilizes on the geometric cross section of core approx. 1 barn. For the 238U and thorium 232Th, a "reasonable" effective fission cross section appears only for neutrons with energies > 1MeV - these nuclei are fissile only by fast neutrons.
238U and 232Th nuclei can transmute to 239U and 233Th by neutron absorption - by reaction (n, g) with effective cross sections according to the right part of the figure, followed by double beta-radioactive conversion to fission nuclides 239Pu and 233U. This is used by the so-called "Propagation reactors" described below.

Energy balance of fission
The energy Q released during the fission of heavy uranium nuclei is about 200 MeV. This relatively large released energy is due to the fact that the binding energy per nucleon in the region of medium-heavy F1,2 fragments is about 8.4 MeV/nucleon, while in the uranium nucleus it is about 7.5 MeV/nucleon, ie about 0.9 MeV/nucleon smaller; by multiplying this difference by the number of uranium nucleons, we get a total released energy Q » 0.9 . 235 @ 212 MeV. The actual value of the energy released is given by the statistical average of about 30 cleavage procedures, that occur with varying probabilities. Most of the released energy Q is carried away by the nuclei (fragments) F1,2 , whose kinetic energy averages about 165 MeV. Another part of energy - about 20 MeV - carries g radiation (of which a smaller part of immediate gamma radiation, a larger part of gamma radiation caused by deexcitation of excited levels during radioactivity of chips), then radiation b (approx. 8MeV), neutrons (approx. 6MeV) and flying away neutrinos (approx. 6MeV - but they will fly away without use...).
   By nuclear fission we can get about 3,000,000 times more energy per unit of mass than by burning fossil fuels (to produce 100 GJ of thermal energy we have to burn about 3 tons of coal, or to split about 1 gram of uranium). This high energy efficiency is the main reason for the development of nuclear energy using
fission nuclear reactors. Even higher energy efficiency is expected from thermonuclear fusion, which is discussed in more detail below in the section "Fusion of atomic nuclei. Thermonuclear reactions".

Fission Products
In the general description of the atomic nucleus fission reaction, we have not yet specifically specified the resulting F
1 and F2 nuclei (called fragments, slags, chips, or fission products) to which the 235U nucleus cleaves. Here are two typical examples: 235U92 + 1n0 ® 137Ba56 + 97Kr36 + 21n0 + Q, or 235U92 + 1n0 ® 97Sr38 + 137Xe54 + 21n0 + Q, which is just an example of about 30 other more common combinations of F1 and F2 fragments. Combinations of F1 fragments with nucleon numbers 80 to 110 (centered around N = 95) and F2 fragments with nucleon numbers 125 to 155 (centered around N = 137) give the most probable cases of cleavage. The most common cleavage products of F1,2 are: 137Cs, 93Zr, 99Tc, 90Sr, 131I, 137Xe, .... The curve of the dependence of the occurrence of fission products on the nucleon number has a characteristic two-peak shape with the centers of the peaks in the values of nucleon numbers 95 and 137. From the physical balance of fission it follows, that the total sum of the yields for all fission radionuclides (over all nucleon numbers N of fragments) is equal to 200% .

Graphical plot of the dependence of the proportion of fission products (% yield per 1 fission) on the nucleon number in the fission of uranium-235, plutonium-239 and uranium-233 nuclei with the participation of thermal neutrons. Some of the more important nuclides formed by fission are indicated by red circles at positions corresponding to the cleavage yield of the most common
235U fissile material .

   For other fissile materials, 239Pu and 233U, the two-peak dependence of the yield of fission products on the nucleon number differs only slightly from 235U. The peak yield for heavier element isotopes (N = 125-155) is practically the same, while the peak yield of lighter isotopes (N = 80-110) is shifts slightly to the left for 233-uranium and slightly to the right for 239-plutonium.
   Because the nuclei formed by fission are substantially smaller than the original heavy nucleus, the ratio of the number of neutrons and protons required for the stability of the nucleus is smaller than in the original nuclear mass of the heavy nucleus. Thus, fission products have an excess of neutrons. Most fission products are therefore radioactive (most often
b-, due to an excess of neutrons) and further decays on average into 2 to 3 additional daughter isotopes. Some of the more important fission products resulting from the fission of 235-uranium, 239-plutonium and 233-uranium nuclei and their daughter nuclides are listed in the following table :

Nuclides Yield [% / cleavage]
U        239 Pu 233 U       
Half-time Radioactive transformations b -
134 Cs 6.8% ....... ....... 2.06 years 134 Cs (2.06r) ® 134 Ba (stable)
135 I 6.3% ....... ....... 6.57 hrs. 135I(6,7hod.)® 135Xe(9,2hod.)® 135Cs(2,6.106let)® 135Ba(stab.)
93 Zr 6.4% 3.9%. 6.9% 1.5 . 10 6 y 93 Zr (1.5.10 6 r) ® 93 Nb (stable)
137 Cs 6.1% ....... ....... 30.17 years 137 Cs (30r) ® 137 Ba (stable)
99 Tc 6.1% 6.2% 5.0% 211 000 y 99 Tc (2,1.10 5 r) ® 99 Ru (stable)
90 Sr 5.7% 2.0% 6.6% 28.8 years 90 Sr (28.8r) ® 90 Y (2.66d) ® 90 Zr (stable)
131 I 2.8% ....... ....... 8.02 d 131 I (8d) ® 131 Xe (stable)
147 Pm 2.3% .fill in.. ....... 2.62 years .........
149 Sm 1.1% ...... ....... stable -
129 I 0.7% 1.4% 1.6% 15.7 . 10 6 y 129 I (15.7 . 10 6 r) ® 129 Xe (stable)
151 Sm 0.42% 0.8% 0.3% 90 years .........
106 Ru 0.39% ....... ....... 376.3 d .........
85 Cr 0.27% ....... ....... 10.8 y .....fill in....
......... ........ ....... .......   .........
......... ........ ....... .......   .........
......... ........ ....... .......   .........
......... ........ ....... .......   .........
......... ........ ....... .......   ....fill in.....
......... ........ ....... .......   .........

Note: Numerical values from the nuclear tables "Lederer, Hollander, Perlman: Table of Isotopes" and from the tables "IAEA: Nuclear Data for Safeguards" were used to draw graphs and create a table. It will be specified according to other data ...
   The summary of nuclides formed by fission is called a mixture of fission products. About 60 isobars of various types of nuclei (mostly with an excess of neutrons) are formed directly during fission, most of which decay into 2-3 more daughter radioisotopes. In the fresh fission mixture we can find almost 1300 different radionuclides, most of which have short half-lives (eg the mentioned 137Xe has a half-life of only 4 minutes, with which it changes to 137Cs); more important are about 180 radionuclides. Short-term radionuclides are not listed in the graph or table, we consider only half-lives of the order of hours, days, years and longer. The isotopic composition of the fission mixture changes significantly over time. Initially, the specific activity is very high due to radioactive transformations of short-term radionuclides. Short-term radionuclides decay rapidly, the specific activity decreases significantly and after a few days 131I, later 137Cs, 90Sr and others dominate. After many decades, long-lived radionuclides such as 99Tc, 93Zr, 135Cs persist and smaller amounts of some others. These radionuclides form a difficult and long-term dangerous component of spent nuclear fuel, which must therefore be stored for a long time. An alternative possibility of nuclear transmutation of long-lived radionuclides is discussed below ("Nuclear waste", transmutation technology).

Chain Fission Reaction
When a nucleus is split, the neutron that caused the fission reaction is "consumed", but during the reaction two more (or three) "2nd generation" neutrons are emitted, which are in principle capable of inducing the fission of other nuclei. If this happens, these new neutrons will cause the fission of two more nuclei to form a total of 4 neutrons, these will cause further fission, etc. - the number of neutrons in each "generation" is rapidly multiplied by a geometric series and the rate of branching nuclear fission reaction increases avalanche - occurs nuclear chain reaction. The usability of neutrons for fission is reduced by two competing processes :
- Neutron capture in the nuclei of the environment. This can be either radiation trapping in the fissile material, which leads to a different nuclear reaction than fission, or neutron trapping in the non-fissile material of the fuel mixture (especially in the so-called "neutron poison" - see below).
- Leakage of neutrons from the reaction volume into the surrounding space.
Nuclides for Chain Reactions - Fissile and Propagating Materials

In order to maintain a chain fission reaction, it is necessary that, on average, at least one neutron released during fission "survives" in the reaction space, enters into the nucleus of fissile material and induces a new fission reaction. This can only be done if the nuclides used can be cleaved by very slow neutrons; this is because most fast neutrons soon leave the reaction space and are not sufficient to cause fission
(discussed above in the section "Fission by fast and slow neutrons"). These nuclides are called fissile materials (....) and only four are available *) : uranium 235U , plutonium 239Pu , uranium 233U and possibly plutonium 241Pu.
*) Some higher transurans, such as americium or californium, also have this property (and even more effectively - less critical amounts) however, due to the complex preparation, they are only available in small quantities, which does not allow the chain reaction to operate.
   The only fission material occurring in nature, is uranium 235U. The other three mentioned fission nuclides must be obtained by bombarding the so-called propagating materials (....) of uranium 238U and thorium 232Th by neutrons (theoretically analyzed above in the section "Fission of atomic nuclei", passage "Fission by slow and fast neutrons", practical use is described below in the section "Propagation reactors"). After neutron absorption, two subsequent beta transformations take place here, resulting in the cleavable nuclei of plutonium-239 or uranium-233.
Chain reaction dynamics
The so-called multiplication factor k is important for the chain reaction dynamics, which is the ratio of the number of neutrons of the next generation to the number of neutrons in the previous generation, and the mean lifetime of neutrons
tn in the reaction medium, also called the mean neutron cycle time; it is the time between the next two succesive generations of neutrons. If at a certain moment n neutrons are present in the fissile material, then after the time tn their number will be k.n, so the increase in neutrons during the time tn is k.n-n = n. (k-1). Thus, the equation dn/dt = n .(k-1)/tn will apply to the rate of change of the number of neutrons. The solution of this differential equation is the exponential dependence
                 n(t) = n
o .e [(k-1) / tn] .t   ,
where n
o is the number of neutrons in the initial time t = 0. The dynamics of the increase or decrease in the number of neutrons, and thus the running away or slowing down of the fission reaction, is sharper the more the multiplication factor k is greater than or less than 1 and the shorter is the mean time of the neutron cycle tn . For k> 1 the reaction increases, for k <1 the reaction stops, in the special case k = 1 the reaction is kept constant.
Note: A chain nuclear reaction can be compared to a chemical chain reaction - see §1.1, section "Interaction of atoms".
Critical amount of fissile material
In order for such a chain reaction to occur, it is necessary to have a sufficient amount of fissile material concentrated in a certain volume - at least the so-called critical amount (weight); with a smaller amount, the vast majority of neutrons it escape from the substance (or it is absorbed in another way), before it is enough to split another nucleus. The critical amount of fissile material in specific situations depends mainly on three factors :
w Type of fissile material and its concentration
These must be nuclei cleavable by slow neutrons (
235,233U; 239Pu and other transurans) with a high effective cross section of the interaction with slow neutrons. The higher the effective neutron capture cross section, the smaller the critical amount. The critical amount is inversely proportional to the square of the density of the fissile material.
Dimensions and geometric arrangement of the area containing fissile material
The more compact the geometric arrangement, the smaller the critical mass. It is the lowest for the arrangement of fissile material in a spherical volume, where the highest ratio of volume to surface size (through which neutrons can escape) is.

Presence of other substances and materials capable of absorbing, reflecting or slowing down neutrons
Substances with a high effective neutron absorption cross-section significantly increase the value of critical mass. The presence of substances capable of reflecting flying neutrons (and thus returning them to the reaction) reduces critical mass, as do light nuclei capable of slowing down (moderating) neutrons during elastic reflections - see below "Nuclear Reactors".
   For individual types of fissile materials, their critical mass m
crit is given for a spherical homogeneous arrangement (of radius Rcrit) of pure material, eg :
235 U: m crit = 48 kg, R crit = 9 cm ;
          239Pu: m crit = 17 kg, R crit = 6 cm ;
233 U: m crit = 16 kg, R crit = 6 cm ;
for some other transurans the critical amount is even smaller
(eg 245-curium 12kg, 246-curium 7kg, 251-californium 9kg). Of interest is transuranic americium 242mAm, which of all fissile materials has the highest effective cross-section of fission by slow neutrons (thousands of barns) and a low critical mass (approx. 0.1 uranium) - it is considered promising for rocket propulsion in the future - see below "Nuclear propulsion of cosmic rocket".
   If the fissile material is surrounded by a substance that reflects neutrons (so-called reflector or neutron shell), the critical amount decreases 2-3 times. If the concentration of the fissile material is less than 100%, the critical mass increases significantly, especially when neutron absorbers are present. For low concentrations of fissile material, there is usally no critical amount exists and the chain fission reaction cannot arise spontaneously; the possibilities of fission reactions even in such cases, using neutron moderation or ADTT technologies, will be discussed below.
   Storage the supercritical amount of fissile material is a very delicate matter. This is because the critical amount for a given (used) configuration may be exceeded, which would lead to an avalanche-like chain fission reaction (k> 1) with very dangerous radiation consequences. Persons at the scene of an accident would receive very high, often lethal, doses of radiation
(see §5.2 "Biological effects of ionizing radiation"), followed by significant contamination of the environment with radioactive fission products.
   To prevent this, it is necessary to store the fissile material in an arrangement or containers with the so-called safety geometry - with the largest possible surface area in relation to the volume (unlike to a spherical arrangement, where the opposite is the case), so that most neutrons easily escape outside the volume of the fissile material and thus cannot cause further fission.

Preparation of fissile material
The material capable of a chain fission reaction can be of natural origin or produced artificially. There is only one nuclide in nature, directly usable for the chain fission reaction - uranium
235U. It is contained in uranium ore, which has the following representation of individual uranium isotopes: 238U 99.284%, 235U 0.711% and trace amounts 234U (0.005%). The amount of 0.7% fissible 235U in most technologies is not sufficient to start and maintain a chain fission reaction. Therefore, it is necessary to artificially increase its occupancy - to perform the so-called enrichment of uranium with the isotope 235U.
Uranium enrichment
Uranium enrichment is a technologically very demanding and expensive process. It cannot be done purely chemically (all uranium isotopes have almost the same chemical properties), but it is necessary to use slightly different physical properties of different uranium isotopes *). In the first phase, uranium is chemically combined with fluorine to form hexafluoride gas UF6, which is then separated by repeated diffusion separation in special separation columns (isotope diffusion of UF6 gas through porous baffles) or in high-speed ulracentrifuges (mechanical-gravity separation), which are arranged in cascades. Slightly different molecular weights of compounds 235UF6 and 238UF6 are used. The fluoride fraction with a correspondingly increased content of 235U is then again chemically converted into other suitable compounds, or metallic enriched uranium.
*) Isotopes of the same element are characterized by small differences in nuclear, chemical, physical and partly also chemical properties. These "isotope phenomena" are due to the different masses of nuclei and atoms of individual isotopes, which are manifested by subtle differences in the kinetics of atoms and molecules in mechanical motion and chemical fusion. They can be used for chemical-isotope separation of elements and their isotopes.
   The laser method of uranium enrichment is interesting at the stage of development . It is based on the principle of selective excitation of atoms in the gaseous state by means of light radiation of such a wavelength that excitation occurs only in the atoms of one isotope of the element, while the atoms of the other isotopes remain in the ground state. The excited atoms can then be separated electromagnetically or by a suitable chemical reaction. The mixture of uranium 235 and 238 in the gaseous state is irradiated with precisely tuned lasers, which excite only molecules with
235U, which allows their subsequent separation.
   Another fissile material, plutonium 239Pu, is practically non-existent in nature *), as it has a significantly shorter half-life than uranium isotopes. However, it can be produced artificially from uranium 238U by neutron fusion in a nuclear reactor (see below "Other fissile materials. Transurans. Propagating reactors.").
*) However, a very small trace amount (<10-14) of plutonium occurs in uranium ores, where it is formed from 238U by neutrons emitted from nuclear reactions (a, n), caused by particles a from the radioactivity of uranium and its daughter products (decay series), in light elements contained in uranium ores.
   The fissile material, properly enriched, is then converted into the final chemical and material form suitable for use in the fuel cells of nuclear reactors (see below).

Uncontrolled Chain Reaction - Nuclear Explosion
The nuclear chain reaction can take place either in a controlled - regulated manner
(this will be discussed below in the "Nuclear Reactors" section) or in an uncontrolled - avalanche, which can result in a nuclear explosion.
Fission Nuclear Weapons  
An explosive nuclear chain reaction is the essence of the criminal misuse of nuclear energy for war purposes in a nuclear bomb
(often also called the "atomic bomb"), at which explosion releases a large amount of energy, from a relatively small amount of nuclear material. Fissile material - uranium 235U or plutonium 239Pu - is divided into two or more parts (segments) in the bomb at rest, each of which has a subcritical amount with its volume. A nuclear explosion is triggered by these segments rapidly approaching each other by the explosion of a suitable chemical explosive ("shot" into each other - "cannon" method in the picture on the top left), creating a geometry of the supercritical quantity. In newer types, the supercritical amount is achieved by compressing the circularly arranged fissile material by chemical explosion of the outer spherical shell ("implosive" method, bottom left in the figure).

Basic principles of construction and operation of fissile and thermonuclear nuclear weapons
Left: Fission nuclear bomb (two different constructions)                            Right: Thermonuclear bomb

When a critical amount is reached quickly, a nuclear explosion occurs immediately, as a small amount of neutrons, which are always present in the material (formed by spontaneous fission of nuclei and cosmic radiation) initiates an avalanche-like chain reaction *), which in about 10-6 seconds it splits almost all the nuclei and a large amount of energy is explosively released (about 1.107 kJ of energy is released from 1 kg of uranium, which corresponds to the explosion of about 20,000 tons of the classic trinitrotoluene explosive). In a nuclear bomb, the fission material is surrounded by a massive envelope, which serves both as a neutron reflector and, with its mechanical strength, keeps the fission material together as long as possible so that it is possible to split as much material as possible at once. During an explosion, the remainder of the fissile material disperses to a subcritical amount, thereby stopping the chain fission reaction itself.
*) In pure fissile material, the mean time of the neutron cycle is very short, tn »10-8 s, so that even at a slightly supercritical ratio (eg k = 1.2) according to the above exponential dependence, a single initial neutron will cause in only 4 ms the emergence of about 1025 neutrons and the same number of nuclear fission, which corresponds to the fission of about 50 kg of uranium in 4 microseconds! The rate of increase of the chain reaction is therefore extremely high - it has the character of a violent explosion.
   Due to the compression caused by the (chemical) explosion, the density of the material increases and the sufficient critical amount of fissile material is slightly less than the above values for uranium or plutonium under normal conditions. This required minimum amount can be further reduced by a suitable envelope serving as a neutron reflector and by the use of a neutron initiator - an additional radioisotope source of neutrons (eg
210Po-beryllium) located in the center of the charge. By compression, the a-emitter (210Po) and the target material (beryllium) come into close contact, and the released neutrons serve as a "igniter" of the fission reaction. The neutron initiator accelerates the dynamics of the chain reaction, which does not have to start from a few initial neutrons, but a large number of neutrons causing a chain reaction are rapidly delivered throughout the volume of the fissile material. The critical amount is also reduced by the moderating effect of substances capable of retarding neutrons (see "Nuclear reactors" below). By combining different methods, the smallest critical amount can be achieved for uranium, about 15 kg, for plutonium, about 5 kg.
   The explosion temperature reaches the order of 107 °C and the explosion is accompanied by intense ionizing radiation and extensive radioactive contamination with fission products, which multiplies the destructive and deadly effects of the explosion itself. "Improvements" to fission nuclear bombs are thermonuclear weapons (on the right-hand side of the figure), which use fission as a "detonator" to trigger an explosive fusion reaction of deuterium and tritium, releasing significantly more energy (see "Merging atomic nuclei - thermonuclear fusion" below, passage "Explosive thermonuclear reactions").
The first fission nuclear bomb was developed in 1942-45 in the nuclear laboratories in Los Alamos by a group led by R.Oppenheimer *), was completed and tested in the spring of 1945 as part of the "Manhattan" project. The legitimate reason for the accelerated realization of a nuclear weapon was the threat of Hitler's fascist Germany. However, at the end of World War II, on August 6 and 9, 1945, two atomic bombs, uranium and plutonium, were dropped on the Japanese cities of Hiroshima and Nagasaki. More than 130,000 people, the vast majority of civilians, died in this war crime (from a military point of view already nonsensical), and the consequences of the exposure in tens of thousands of other people caused later deaths or permanent damage to their health. Fortunately, nuclear weapons have not been used since then, they only served as a "deterrent"- perhaps paradoxically, they contributed to peacekeeping during the "Cold War" (fissile weapons in 1949 and thermonuclear weapons in 1953, the Soviet Union also developed).
*) J.R.Oppenheimer, often referred to as the "father of the atomic bomb", along with others prominent physics and co-workers, but after 1945 began to publicly highlight the threat of nuclear weapons (and crime of their use) and called for control over the development and manufacture of such weapons of mass destruction and killing. For these peaceful activities, Oppenheimer was persecuted by the then US regime (where Cold War activist R.S.Truman ruled) and was expelled from all leadership positions. He was rehabilitated only after the accesion of democratic president J.F.Kennedy in 1961.

Nuclear reactors
These are complex devices in which a purposefully regulated chain fission reaction takes place. In order for a nuclear fission chain reaction to proceed in an equilibrium controlled manner, three things must be ensured in principle :
a) Collect a supercritical amount of nuclear fission material for a given configuration.
b) Ensure control of the number of neutrons by means of suitable absorbers and moderation of neutron energy so that the fission reaction proceeds with the required intensity. This regulation of the neutron balance controls the power of the nuclear reactor.
 And, of course, it is necessary to ensure the dissipation of released energy, which is mainly converted into heat, or :
c) Ensure cooling of the reaction zone - removal of heat generated by a suitable cooling medium (usually water, sometimes inert gases, occasionally molten salts or metals; these methods will be specifically discussed below).
   The dynamics of cleavage reaction determines the ratio between the average number of new neutrons and the number of neutrons consumed for cleaving (or the ratio between the number of neutrons following generations and the number of neutrons of the previous generation) - called neutron multiplication factor k, also called multiplication factor neutron
(has already been used above in the general analysis of chain fission reaction dynamics). When the multiplication factor k is less than 1, the reaction ceases, at k = 1 it is maintained in equilibrium, at k greater than 1 the number of fissioning nuclei increases avalanche, until for some reason the factor k acquires values k <1 (mainly regulation by neutron absorption); if this does not happen in time, the reaction will become explosive.

The controlled chain reaction
of nuclear fission (especially
235U) takes place in a complex device called a nuclear reactor *). First, we present a general description of the reactor, relating mainly to the classical reactor splitting 235U with slowed neutrons (Fig.1.3.4); alternative solutions will be listed below.
*) Note: The first experimental nuclear reactor, the "atomic milestone" CT-1 composed of uranium, a graphite moderator and cadmium control rods manually shifted, was built by E.Fermi and his colleagues in 1942 in the basement under the stands of the stadium in Chicago.
   The control of the number of neutrons maintaining the fission reaction is carried out in two stages in a conventional reactor
(a minor third option is mentioned below - "3. Reactor control by controlled moderation") :

Simplified schematic diagram of a fission nuclear reactor.
For the sake of clarity, the structure of the active zone (fuel cells) is not shown in the figure.

   The part of the reactor in which the fissile material is located and in which the chain fission reaction takes place is called the active zone - core. The fissile material (which is mostly enriched uranium) is stored in the reactor in the form of a large number of separate and independent so-called fuel cells, where the fissile material is encapsulated in a package protected by a suitable surface layer. In water-cooled reactors, zirconium (niobium-alloyed) is used for encapsulation, characterized by low neutron absorption (less uranium enrichment is sufficient); for fast reactors, the coating tubes are made of stainless steel (alloyed with nickel, chromium, niobium). There is a moderator between the fuel cells and regulating absorption rods are also inserted between them (in the pictures, the fuel cells, moderator and cooling are only sketchily drawn for simplicity, the fissile material is marked as a granular volume). The core of the reactor is further surrounded by a so-called reflector - a layer of suitable material that reflects the escaping neutrons and returns them partially back to the reaction volume of the reactor, which somewhat increases the yield of the reaction. In the reflector, basically the same materials are used as in the moderator - graphite, heavy water. The inner part, the primary circuit, of the reactor is stored in a solid reinforced concrete protective envelope with a hermetic steel lining, so-called containment (in sense of : contain , container = closed vessel, box, case; containment = control, restriction ).
Release and utilization of nuclear energy from fission reactions
During the chain fission reaction, a considerable amount of energy is released
- nuclei fragments, flying out with high kinetic energy, quickly slowed down by the impacts on surrounding atoms and thus transfer their energy to the material in the form of heat. The fissile material is therefore heated and must be intensively cooled by a suitable cooling material (eg water *) flowing directly around the fuel cells - this is the so-called primary cooling circuit. In two-circuit systems, the heat from the primary cooling circuit in the heat exchanger is transferred to the water of the secondary cooling circuit; in a nuclear power plant the secondary cooling circuit is a steam generator, the steam of which rotates the turbine blades driving the generator producing the electric current (again, for simplicity, the primary and secondary circuits are not distinguished in Figures 1.3.4 and 1.3.5).
*) Note: Water can be advantageously used both as a moderator and a refrigerant. The use of water as both a refrigerant and a moderator leads to a negative reactivity temperature coefficient : as the temperature increases, the density of water and thus the proton density decreases, which reduces the moderating effect and the intensity of the fission reaction. In the event of water leakage from the primary circuit, the moderating effects are lost and the fission reaction stops itself ® greater safety against accident in case of failure. In two-circuit systems, the primary cooling circuit is hermetically sealed so that its radioactive water does not mix with the water in the secondary circuit.
   Water for cooling and moderation in the primary circuit of a nuclear reactor should be demineralized for two reasons: 1. Minerals are excreted from the water and precipitate on the walls of the cooling tubes, which reduces the efficiency of heat exchange; chemical reactions with metal surfaces can cause corrosion. 2. Intense neutron flux can induce radioactive isotopes by nuclear reactions with the nuclei of mineral atoms. Boron (boric acid, approx. 12 g /liter of water) is sometimes added to the cooling water as a neutron absorber, the concentration of which is gradually reduced by dilution for better control during fuel combustion (see below).
   Thus, a nuclear reactor for energy use serves only as a mere "steam boiler" and further conversion into electrical energy takes place "old-fashioned" via a turbine and an electric alternator. Unfortunately, we cannot directly convert the released nuclear energy into electricity. Certain hypothetical possibilities for the direct conversion of particle energy into electrical energy are outlined below in the passage "Neutron-free fusion reactions - direct conversion to electricity?" (however, this is not usable in a fission nuclear reactor, but perhaps only in future thermonuclear reactors..?..).

Dynamics of fission reaction and regulation of a nuclear reactor
For the dynamics of fission reaction control in a nuclear reactor, the speed with which the increase or decrease in the number of neutrons in individual generations (and thus the intensity of the fission reaction) reacts to the change of the multiplication factor k is important. The time dynamics of the instantaneous neutron flux
F, and thus the reaction rate and the instantaneous reactor power, is given by the exponential dependence F(t) = Fo.e [(k-1)/tn].t (as derived above in the general analysis chain reaction), which can be written as F(t) = Fo.e t/T. The time constant (also called the period ) of the reaction T, which is the time during which the number of neutrons changes e-times (ie 2.718 times), is approximately given by the relation T = tn/(k-1), where tn is average lifetime (or residence, diffusion) of a thermal neutron in the reaction medium; in larger reactors it is of the order of 10-3 s. To change the multiplication factor by eg one hundredth (| k-1 | = 10-2), the decrease or increase of the reaction would react with a time constant of approx. T = 10-3/10-2 = 0.1 seconds. With such a small time constant, the changes in neutron flux would be so abrupt that it would be very difficult to control the reactor. However, this dynamic applies to the so-called instantaneous neutrons, released immediately during fission. However, during fission reactions, so-called delayed neutrons are also formed, originating in radioactive fragments of fission with an excess of neutrons, which they get rid of by b conversion or neutron emission. These neutrons are emitted with a delay of up to a few seconds (the mean time of this neutron delay is about 0.1 s). This phenomenon causes the average lifetime of one generation of neutrons to be significantly longer than the diffusion time of thermal neutrons, which extends the effective time constant of the reactor to values of the order of 10 sec.
   In conventional reactor designs, the regulation of the instantaneous reaction rate and thus the reactor power takes place by means of neutron-absorbing control rods, driven by electronically controlled servomotors in feedback with detectors neutron flux. The so-called emergency rods, which are released by an emergency accident signal and automatically fall into the active zone by their own weight, serve for a quick emergency stop of the fission reaction and thus shutdown of the reactor.
Gradual fuel combustion
In addition to the mechanisms of immediate regulation of the fission reaction, certain changes of a longer-term nature take place in the active zone during longer operation of the reactor, affecting (mostly reducing) the yield of the reaction. Above all, it is clear that during fission the number of atoms of fissile material gradually decreases, the fuel "burns out". This reduces the multiplication factor and in order to maintain the equilibrium operation of the reaction, the control circuits must gradually eject the neutron absorbers - the so-called compensating rods. Another possibility for long-term control and compensation of fuel combustion is to change the concentration of a suitable neutron-absorbing substance, such as boron, dissolved in the refrigerant. This is used in some water-cooled reactors, where about 1% boric acid is added to the cooling water and then during operation and fuel combustion, its concentration is gradually reduced (by dilution with clean water fed to the primary circuit) to virtually zero before changing the fuel.. When more enriched uranium is used, gadolinium is sometimes added to the nuclear fuel itself, which serves as a temporary "combustible neutron poison" (absorbs neutrons similar to cadmium) - a "burning" neutron absorber. During operation, it is gradually degraded by transmutation in the neutron flux
(by neutron absorption it changes to various Gd and Tb isotopes, which already have a low effective neutron capture cross section), so that as the uranium-235 content decreases, the gadolinium content also decreases, so that in the fuel cell it absorbs fewer neutrons in the absorber and more in the fuel - longer operation time of the enriched fuel with easier regulation.
Absorption of neutrons by fission products, neutron "poison" - "poisoning" of the reactor
Furthermore, during fission, new nuclei are formed, fission products
(detailed above), some of which strongly absorb neutrons - accumulation of fission products in fuel cells can also reduce reactivity. If such neutrons absorbing waste products in larger quantities are formed, they disturb the neutron balance in the reactor (reduce k) - we say that the so-called poisoning of the reactor with neutron poison occurs. Reactor poisoning is quantified by the ratio of the thermal neutrons absorbed in the fission product ("poison") to the number of neutrons absorbed in the fuel. Most important thing for reactor poisoning is the nuclide 135Xe, "xenon poisoning", partly also 149Sm. During the cleavage of 235U this 135Xe namely is formed directly in only a small amounts (0.3%), but a larger quantity of about 6% of a fission product 135Te and 135I, whose decay b follows the series :
                135Te (30 sec.) ® 135I (6.7 hours) ® 135Xe (9.2 hours) ® 135Cs (2.6.10 6 years) ® 135Ba (stab.) .
135Xe has an extremely high effective cross sectionfor neutron absorption 3.5.106 barn (almost perfect neutron absorber!). During normal operation of the reactor, the occurrence of 135Xe and 135I is in equilibrium, the ongoing fission reaction constantly produces new 135I, which partially changes to 135Xe and then to 135Cs, but more often changes by neutron absorption to stable 136Xe (neutron transmutation combustion 135Xe). 135Cs or 136Xe neutrons almost do not absorb and do not affect the dynamics of the fission reaction. However, when the reactor power is significantly reduced or shut down, the equilibrium is disturbed and 135Xe begins to accumulate in the reactor, to which the already formed 135I is constantly converted with a half-life of 6.7 hours. This "xenon poisoning" causes that the reactor to be unable to start operating again for several hours before 135Xe disintegrates *). This time, during which it is not possible to restart the reactor, is sometimes called the "iodine pit" - after stopping the fission reaction, no more 135I are formed in the reactor, but this iodine gradually decreases with decomposition to xenon; the concentration of neutron poison 135Xe first increases and then gradually decreases by radioactive decay until a state is reached in which the reactor can be restarted, operated and regulated.
*) If we still wanted to restart the reactor in this situation, we would have to eject the amount of control absorption rods out of the core corresponding to the absorption capacity of the accumulated xenon 135. If this were possible at all (for design reasons), it would be very dangerous - after the start of the chain fission reaction, the neutron flux would quickly "burn" the inhibiting 135-xenon and the reaction could start uncontrollably until the crash. It is worth noting that this very situation of "xenon poisoning" during the decommissioning of the Chernobyl reactor played an important disorientation role in the case of operator errors which ultimately resulted in a fatal reactor accident, as described below ("Nuclear Reactor Accident").
   The degree of xenon poisoning of a reactor and its time dynamics can vary widely, depending on a number of factors. It depends on the rate of time changes in the intensity of the fission reaction (rate of shutdown or start-up of the reactor), the degree of nuclear fuel burn-up, the dimensions and the geometric arrangement of the core. As mentioned above, xenon poisoning is significant ("iodine pit") when the power is suddenly reduced or the reactor is shut down. When the reactor is shut down slowly, 135I still form and 135Xe "burns" by neutron transmutation; there is a limit to the shutdown rate of the reactor at which significant xenon poisoning does not yet occur and the reactor does not fall into the "iodine pit". This rate value depends on the fuel supply in the cells (their degree of combustion) as well as the power of the reactor from which the change in reactivity is made.
   In reactors with a larger core and a high neutron flux, an inhomogeneous distribution of the neutron flux can occur - inhomogeneities in reactivity arise. A random increase in neutron flux density at some point leads to an increased degradation of
135Xe, thereby reducing neutron absorption at that point and leading to a further local increase in neutron flux. However, this will also increase production 135I, it decays into 135Xe, which thus accumulates somewhat locally and reduces the neutron flux with its increased absorption. This process can be repeated periodically - so-called xenon oscillations of the intensity of the fission reaction occur in various places in the reactor. Under normal circumstances, such periodic fluctuations in neutron flux in the core do not significantly affect the overall performance of the reactor and its stability. However, with a large core volume, autonomous regions can form, whose xenon inhomogeneities can get into positive feedback, which can cause an increase in the amplitude of the xenon oscillations and a violation of the reactor stability.
Reactor "slagging"

Another nuclide that can affect the neutron balance in the reactor is
149Sm, which has an effective neutron absorption cross section of about 4.104 b. It is formed in fission products in the amount of 1.13% as a decay product of the series: 149Nd (2 hours) ® 149Pm (51 hours) ® 149Sm. Due to the smaller effective cross-section and lower yield compared to xenon, reactor poisoning by samarium is usually low; since the 149-samarium is stable, it has the character of a kind of "slag" or "cinders" which accumulates in the nuclear fuel and prevents its more perfect combustion.
Even less important are the neutron poisons 157,155Gd and 155Eu, which are formed only in very small amounts.
Neutron balance; reactivity reserve
The neutron balance, which is the proportion of the number of neutrons in successive generations, is therefore crucial for the proper operation of the reactor. The core of the reactor must be designed so that the proportion of neutrons in successive generations is only slightly higher than 1. A certain potential excess of neutrons, called the reactivity reserve, is needed as the amount of fuel decreases and neutron absorption gradually increases during operation, mainly due to the formation of fission products. During reactor operation, the excess neutrons are compensated by absorbers, which are gradually take out from the reactor. The stable and safe operation of the reactor is due to the reliable control of the balance between the excess neutrons needed for operation and the uncontrolled excess, which could lead to an accident.
Replacement of spent fuel cells
When the concentration of fissile material decreases to such an extent that the fission reaction would no longer be maintained even with the absorbent rods sufficiently displaced, such spent fuel cells must be replaced with new ones. This is usually after 12-36 months of reactor operation (depending on the type of reactor and fuel enrichment); this period is called the "reactor campaign". For most types, the reactor must be shut down for this change ("campaign exchange"), but some types allow for a continuous stepwise exchange of fuel during operation. Replacing fuel cells is a very demanding job. In contrast to new (fresh, unused) fuel cells, whose activity is relatively low (long half-life of
a-decay of uranium), spent fuel cells are highly radioactive (they contain radionuclides with significantly shorter half-lives; the activity is inversely proportional to T1/2, as derived in §1.2 "Radioactivity") and no one is allowed to approach them! The cells are pulled out of the reactor core by means of remotely controlled manipulators and are immediately inserted into strong shielding containers. The radioactive decay of fission products in spent fuel cells is initially so intense that heat is released and the material is heated - freshly spent fuel cells must be cooled. The most common way of their initial storage is placement in a water pool near the reactor; water provides not only cooling, but also relatively effective shielding from radiation. Another way is "dry" cooling, where the fuel cells are placed in special containers filled with helium, the containers are cooled by air from the outside. After about 5 years, when the activity of the material decreases sufficiently, the fuel cells are placed in intermediate storage and only after many years they are stored in the final central repository (unless, of course, their appropriate further processing is taken, see below).
The problem of cooling nuclear reactors 
Nuclear energy in a fission reactor is released in the form of kinetic energy of nuclei-fragments and neutrons, which are converted into heat by their braking in matter. With the chain fission reaction triggered, it goes without saying that this large amount of heat must be dissipated by the cooling medium for further energy use
(described below). However, even after stopping the chain fission reaction - "shutting down" the reactor - the heat output does not immediately drop to zero, but residual heat continues to develop in the reactor. The fuel cells heat up for some time to come: they contain a large amount of highly radioactive fission products, whose intense radioactive transformations heat these partially or completely spent fuel cells with their energy *). It is therefore necessary to cool - aftercool the reactor and fuel cells even after the reactor has been shut down, otherwise they may be thermally damaged (even melted). Cooling failure can thus cause serious and difficult-to-repair damage, in extreme cases even an accident and destruction of the reactor! - as happened at the Fukushima nuclear power plant (see "Accidents at the Fukushima nuclear power plant"). The residual heat output is highest immediately after stopping the reactor; decreases significantly with increasing downtime **).
*) The residual heat output of a nuclear reactor depends on the degree of combustion fuel cells. If we shut down the reactor soon after it is started with new (fresh) fuel cells, the residual heat output will be small. However, with the increasing degree of fuel cell burnout, the concentration of highly radioactive fission products increases (initially it rises rapidly, but later more slowly: the most active fission products with a short half-life just disintegrate - saturation is reached). Thus, when shutting down a reactor with an advanced degree of combustion, the residual heat output will be relatively large (it may initially reach up to 10% of the nominal fission power).
**) After the reactor is shut down, the fission products in the fuel cells decay radioactively with different half-lives - the activity and the residual heat output produced by it decreases (multi)exponentially with time. Immediately after shutdown of the reactor, the largest radioactivity in fresh decomposition products in fuel cells consists of short-lived radionuclides, which decompose rapidly, so that the heat output initially decreases rapidly exponentially (one hour after shutdown, residual heat output is less than 2% of operating fission power). As short-lived radionuclides "dying out" in fission products, the rate of decrease in residual heat output slows down constantly - in the first few days it decreases with a half-life of about 4 days, after a week with T1/2 about 8 days (radioiodine
131I). After a long time, long-lived radionuclides with half-lives of hundreds of days to several years survive in fuel cells in fission products, so that the heat output is already low, but decreases only very slowly.
Temperature coefficient of reactivity, cavity effect in the reactor
At low temperatures of the order of hundreds to thousands of °C, the physical process of fission of heavy nuclei does not depend on temperature. However, in such a complex mechanical and hydrodynamic system as a nuclear reactor, temperature changes are necessarily reflected in geometric proportions, neutron absorption and moderation, as a result of which the rate of fission reaction - reactivity, energy or thermal performance - may depend on temperature. The dependence of energy output on temperature (with unchanged other parameters) is expressed by the temperature coefficient of reactivity, which can be either negative (as the temperature increases the rate of fission reaction decreases) or positive (as the temperature increases, the intensity of the chain fission reaction also increases).
   In water-cooled reactors, the so-called cavity effect is closely related to the temperature coefficient of reactivity: the influence of the amount of water and steam (steam bubbles form "cavities" in the cooling or moderation system) in the active circuit on the reactivity. When the temperature rises, part of the water turns into steam - a "cavity" is created with a positive or negative effect on reactivity. It is quantified by the cavity coefficient (void coefficient), which is a number indicating how much (in what proportion) the energy output of the reactor will decrease or increase as the volume of water and steam in the reactor core changes.
   In water-moderated reactors, the cavity coefficient and the temperature coefficient of reactivity are negative: as the temperature increases, the density of water decreases and thus the proton density, which reduces the moderation effect and fission reaction, overheating of the core converts part of the water into steam, leading to a radical reduction and thus to attenuate the fission reaction. These reactors are "undermoderated". Graphite-moderated reactors are "overmoderated" and have a positive reactivity temperature coefficient and cavity coefficient: as the temperature increases and the amount of steam in the reactor core increases, the amount of water-absorbed neutrons decreases, so the number of slow neutrons capable of further fissioning uranium increases (the main neutron moderator is not water but graphite, the amount of which in the reactor core is independent of temperature; water somewhat absorbs neutrons). From a control and safety point of view, reactors with a negative temperature reactivity are more advantageous, while reactors with a positive temperature reactivity are more difficult to regulate cooling and energy output, with a higher risk of unstability, faults and even the possibility of accidents.

Various constructions and functioning of nuclear reactors
The first nuclear reactor for the production of electricity was launched in 1954 in Obninsk in the USSR. Since then, the design of the reactors has undergone a number of changes and technical improvements. There are currently a number of types of nuclear reactors in operation in different countries, and some new technical solutions are being developed. We will briefly mention here only a few of the most important types of nuclear reactors. Types of nuclear reactors can be classified according to several basic aspects :

Division of nuclear reactors according to the purpose of use
According to the purpose of use, nuclear reactors can be divided into three groups :
- Research and experimental reactors are usually smaller instruments used for experiments in various fields of physics, engineering (such as materials engineering, metallurgy), biology, medicine. The intense flux of neutron radiation can be used for neutron activation analysis (§3.4, section "Neutron activation analysis"), for neutron radiotherapy (§3.6, section "Neutron capture therapy") and some other applications (see also the section "Irradiation in nuclear reactors" below). This includes also school reactors for teaching and prototype reactors for verification of new concepts and design solutions.
- Transmutation reactors for the production of radionuclides (see §1.4, section "Production of artificial radionuclides"), including some transurans, especially plutonium-239 (which can unfortunately be misused for military purposes...).
- Power reactors, used to produce heat and electricity, are the most important and numerous group of nuclear reactors. They are mostly large and expensive constructions, but there are also several smaller mobile reactors working on board submarines and large icebreakers.
Below we will focus mainly on power reactors.

Development generations of nuclear reactors
In terms of gradual technological development, nuclear reactors are divided into 4 or 5 generations. Generation I reactors were built in the 1950s and 1960s. The experience with these "prototype" reactors was followed by the second generation of reactors (so far the most frequently used), mostly light water pressure or boiling, or heavy water, graphite, water moderated - or carbon dioxide cooled. This is followed by Generation III reactors with a number of technical improvements, especially in terms of safety, reliability and economy of operation, with a higher degree of fuel burn-up and a smaller volume of radioactive waste. Generation IV reactors although they build on previous generations, they are based on completely new technologies and operating principles; they are mostly still in the stage of experiments and projects. These reactors should allow the use of all potential nuclear fuel - not only conventional fissile uranium-235, but also uranium-238 and thorium-232. It also uses fast neutrons (see "Fast FBR Propagation Reactors" below) and nuclear transmutation technologies, which would make it possible to "burn" even previously unusable fuel (235U in low concentrations, mentioned 238U and 232Th), as well as the resulting transurans. This would lead not only to an increase in the efficiency of the use of natural resources and energy recovery, but also to a reduction in the volume, activity and hazard of nuclear waste. The most advanced technology of this kind, which could perhaps already be included in Generation V, is the accelerator-controlled transmutation technology ADTT, described below.
   In the following, we will briefly describe some significant designs of nuclear reactors (partly "across generations") :

Graphite-moderated water-cooled reactors
The first types of reactors were single-circuit, the moderator was graphite and the coolant was water, the steam of which is led directly to the turbine. Such designs were, for example, RBMK ("high power, channel") reactors used, inter alia, at the Chernobyl nuclear power plant. In the graphite block, cooling channels (tubes) pass vertically, in which uranium-enriched fuel cells are located. There are also channels for inserting and removing control rods. Water flows through the cooling channels from the bottom up, which is heated by the released energy, removes heat from the reactor and in the upper part it changes into steam, led to the turbine el. generator. The cooled steam and condensed water are then returned to the bottom of the reactor.
Graphite termination of boron control rods
In some graphite-moderated reactors (RBMK), absorption-control rods were provided at their ends with a graphite part
(boron at the top, water gap in the middle, graphite at the bottom) for more homogeneous neutron flux and smoother positive or negative control during ejection and inserting the rods. The graphite part caused "displacement" of water from the channel as the rod moved. This was supposed to lead to a wider range of neutron flux regulation, as the insertion of the graphite part (slightly moderating) slightly increased the reactivity compared to "empty" channels with water (which easily absorbs neutrons). It should also have slightly increased the use of lower concentrations 235U in fuel cells. In practice, however, this "trick" did not apply too much, the effect is not significant and, according to some opinions, it could cause instability in the control of anomalous situations (though not proven, is briefly mentioned below in the passage of "nuclear reactor accident at Chernobyl").
   Reactors of this type they had, in addition to a simpler design, three advantages :
1. Since the graphite moderator absorbs neutrons only slightly, less uranium enrichment in the fuel cells was sufficient (around 2%).
2. Easy power control and the possibility of shutting down only part of the reactor.
3. The division of the fuel cells into independent channels allowed the gradual replacement of the fuel cells during operation, without a complete shutdown of the reactor. The fuel could be exchanged gradually by individual channels, while the rest of the reactor worked normally
(it was also easier to obtain the resulting radionuclides, including plutonium 239, from the exchanged spent rods).
   However, these reactors have also been shown to have disadvantages
(which ultimately predominate) :
a) The single-circuit design can lead to radioactive contamination of the turbine and an overall greater risk of radioactivity leakage.
b) Positive temperature coefficient reactivity: as the temperature increases and the amount of steam in the reactor channels increases, the amount of water-absorbed neutrons decreases, so that the number of slow neutrons capable of further fissioning uranium increases. The main moderator of neutrons is graphite, the amount of which in the core of the reactor is fixed. Elimination of this phenomenon places increased demands on control technology.
c) High demands on the tightness of a large number of channels.
   A positive temperature coefficient of power leads to the risk that in the event of a leak or boiling of water, the fission reaction continues at an increased rate (moderating effects of graphite persist) and if the absorption rod control is not applied, the core may overheat until the reactor crashes. These circumstances, combined with serious operator errors, became fatal for the RMBK-1000 reactor of unit 4 of the Chernobyl nuclear power plant
(described in the passage "Chernobyl nuclear reactor accident"). Otherwise, a number of reactors of this type, with proper operation, worked for several decades, reliably and safely...

Water moderated reactors
PWR - pressure water moderated

Reactors type PWR ( Presurized Water cooled and moderated Reactor), also known as the WWER (Water- Water Energy Reaktor) are now the most common type of reactors. The moderator and coolant are ordinary water, so it is also referred to as "light water". Reactor cooling is two-circuit: in the primary circuit, water flows under high pressure at a temperature of about 300 °C, in the steam generator it heats the water of the secondary circuit and only the steam generated here drives the turbine el. generator. These reactors are characterized by high operational safety and accident resistance. The use of water as a coolant and moderator leads to a negative temperature coefficient of reactivity : 1. As the temperature increases, the density of water decreases and thus the proton density, which reduces the moderating effect and the intensity of the fission reaction. 2. Overheating of the core and conversion of water into steam would lead to a radical reduction (or disappearance) of the moderating effect and thus to a attenuation of the fission reaction.
 The two-circuit solution also virtually eliminates the possibility of tritium contamination. The primary circuit is not in direct contact with the turbine, but water or steam from the reactor transfers heat indirectly to the non-radioactive water that drives the turbines. The reactors used in our country
(Jaslovské Bohunice, Dukovany, Temelín) are of the WWER type.
Boiling Water Reactor

The second most common type of reactor is BWR (Boiling Water Reactor). The water, which serves as both a coolant and a moderator, is heated to boiling directly in the pressure vessel of the core and this steam directly drives the turbine - the BWR reactors are single-circuit.

Gas-Cooled Graphite Moderated Reactors
GCR - Gas- Cooled Graphite Moderated Reactor

In a GCR (Gas Cooled
& Graphite Moderated Reactor) reactor, the core consists of graphite moderator blocks through which a large number of fuel rod channels pass (can be replaced during operation). The refrigerant driven by the core is carbon dioxide gas, which after heating is fed to a steam generator, where it heats the water of the secondary circuit and the generated steam drives the turbine.
HTGR - high temperature gas cooled graphite moderated reactor ("pebble" reactor)
The HTGR (High Temperature Gas Cooled Reactor) reactor differs from other types of reactors in the arrangement of the fuel and the core. The fuel is highly enriched uranium in the form of uranium dioxide, whose small spheres (0.5 mm) are dispersed in large numbers in spheres of graphite about 7 cm in diameter - some pebbles, or in hexagonal blocks. Fuel balls or blocks are loosely "strewed" or stacked in the active zone, the spent ones are gradually removed from the bottom and freshly filled from above. The refrigerant driven by the core is helium gas, which after heating is led to the steam generator, where it heats the water of the secondary circuit and the generated steam drives the turbine. The advantages of reactors of this type are smaller dimensions, relative simplicity and less economic demands - they resemble a bit of "permanent heating stoves", into which coke is poured from above and ash and slag are removed from below. They can therefore be a promising solution..?..

Heavy water moderated reactors
As mentioned above, deuterium in the form of heavy water (D
2O) has very good moderating properties, which allows the use of natural or only weakly enriched uranium as fissile material; it is mostly used in the form of oxide (UO2). Several types of "heavy water" reactors have been developed in which heavy water is moderator, but the individual variants differ in refrigerant and heat transfer method :
(Presurized Heavy Water Moderated and Cooled Reactor) - a pressure reactor moderated and cooled by heavy water uses natural uranium as fuel, the refrigerant and moderator is heavy water, which transfers its heat from the primary cooling circuit to ordinary water in a steam generator, from where the steam drives the turbine;
(Heavy Water Moderated Boling Light Water Cooled Reactor) - heavy water moderated and light water cooled boiling reactor;
(Boiling Heavy Water Cooled and Moderated Reactor) - boiling reactor moderated and cooled by heavy water ;
(Heavy Water Moderated Gas Cooled Reactor) - a heavy water moderated and gas cooled reactor .
   The technical details of the construction of various types of nuclear reactors are already outside the scope of our physically focused treatise...

Molten salt-based nuclear reactors ,
also called "salt reactors" and are abbreviated as
MSR (Molten Salt Reactor), are still in the experimental and design stage. This is an interesting and promising solution for Generation IV reactors using molten fluoride salts as solvents for nuclear fuel, as well as for cooling and heat dissipation. Fuel in the form of uranium fluoride UF4, plutonium fluoride PuF3, or thorium fluoride ThF4, can be dissolved in salts (fluorides) of lithium LiF *), beryllium BeF2, or sodium fluoride NaF. Thus, nuclear fuel is not fixed in the solid structure of fuel cells, but circulates dissolved in a liquid state.
*) It is not possible to use natural lithium, where 6Li strongly absorbs neutrons, but the almost pure (or highly enriched) isotope 7Li, in order to avoid the loss of thermal neutrons, which are the main "engine" of nuclear fission.
   The reactor can work both in the classical variant with neutron moderation (using graphite) for uranium combustion or thorium transmutation, and without moderation as a fast reactor for plutonium combustion. The primary circuit may also contain a chemical-isotope separation unit for the continuous removal of fission products or for the isolation of fuel in a breeding reactor. The most advanced reactors of this type would be the
ADTT transmutation reactors described below.
   Molten fluoride or chloride salts can also be used for cooling and heat dissipation for further energy use. The use of molten salts as a coolant has the advantage of a high volume heat capacity, which makes it possible to remove heat from the reactor core very efficiently. Reactors of this type operate at a high temperature (around 1000 °C), so the heat generated can be used not only for the production of electricity, but also for the efficient production of hydrogen as an important technological and energetic gas.

Compact self-regulating reactors
In the basic description of the principles of nuclear reactors, it was mentioned that an effective control mechanism of the fission reaction rate can be to change the moderator concentration in the reactor core
(see section " 3. Reactor control by controlled moderation" above). By a suitable technical construction and material design of the moderating substance, a negative reactivity temperature coefficient can be achieved, which can be used for the autoregulatory operation of the reactor on the basis of the operating temperature. Based on this principle, compact self-regulating reactors small dimensions are very interesting at the project stage, which do not contain any mechanically moving parts inside the core, are maintenance-free for the life of the fuel and are also safe against accidents thanks to the negative reactivity temperature coefficient.
Hydrogen-moderated small nuclear reactor

At advanced stage of development is the project of a small nuclear reactor, whose fuel is uranium (enriched to about 5% 235U) in the form of uranium hydride UH3, placed in the shape of granules in a gaseous hydrogen atmosphere. The hydrogen contained in UH3 hydride serves as a neutron moderator. Autoregulation is achieved by a thermally induced balance between chemical formation and decomposition of the UH3 moderator in a gaseous hydrogen atmosphere: UH3 « (800 °C) « U + 3H. As the temperature rises (to about 800 °C), UH3 decomposes and the reaction slows down due to the lack of moderator; on the contrary, as the temperature decreases, hydrogen binds to uranium in a hydrogen atmosphere, the concentration of the moderator UH3 increases and the fission reaction accelerates. The assembled reactor is started by introducing hydrogen gas into the core, by discharging the hydrogen the reaction can be stopped at any time. Also, each time the core overheats, the reaction stops. Molten potassium is planned as a refrigerant.

Fast breeder reactors and technology ADTT
Some other new and promising types of nuclear reactors (fast breeder reactors
FBR and technologies designed reactors ADTT ) mentioned below.

Irradiation in nuclear reactors
In addition to energy use, the nuclear reactor can also be used as a powerful source of neutrons for irradiation of various materials in which nuclear reactions (n,
g), (n, p), (n, d), (n, a) etc., arises artificial radioactivity. For this purpose, irradiation chambers or channels are located in the active zone of the reactors, where the irradiated material is inserted. Many radionuclides, including some transurans (especially plutonium), can also be separated from the spent nuclear reactor fuel. The production of radionuclides is discussed in §1.4. "Radionuclides", part "Production of artificial radionuclides", in §3.4 is described Neutron activation analysis.

Natural nuclear reactors ?
As experience shows, many physical phenomena that we study in laboratory conditions also occur in nature. The successful management of the fission reaction in reactors raises the question whether the chain fission reaction cannot occur even in nature?
   The basic condition for the chain fission reaction is that
235U (the only naturally occurring isotope that is potentially able to sustain the chain fission reaction) be present in a sufficient concentration in an appropriate volume greater than the average path length of the fission neutrons. Today's concentration of 235U is too low (approx. 0.72%) and far from sufficient for a chain reaction even in the richest uranium deposits. However, 235U decays about 6 times faster than 238U, so that in the distant past the proportion of 235U may have been significantly higher. As early as 1956, the Japanese nuclear physicist P.Kurota pointed out the possibility of a chain fission reaction in natural uranium deposits.
   About 2 billion years ago,
235U was about 3% (similar to enriched uranium used as fuel in today's nuclear reactors), which under favorable conditions is already sufficient to trigger a chain fission reaction. This "favorable condition" *) is the presence of a neutron moderator - a substance that slows down the neutrons emitted during fission to better cause the fission of other nuclei. Under natural conditions, such a moderating substance could be underground water seeping through pores in a uranium deposit.
*) On the contrary, an unfavorable circumstance could be the presence of larger amounts of boron, lithium, cadmium and other elements that effectively absorb neutrons and thus stop the fission reaction. However, these substances are not commonly found in larger quantities in uranium deposits.
   In 1972, during the analysis of uranium ore samples from the Oklo opencast mine in Gabon (in western Equatorial Africa), it was found that the ore from some parts of this deposit is depleted of uranium
235U. Further analyzes showed an increased occurrence of some lighter elements, especially xenon, which often arise during the decay of the heavy core 235U in two parts. These circumstances suggest that in the distant past there was a spontaneous ignition of the chain fission reaction, in which part of the 235U was consumed ("burned out"), split into lighter elements. As there are no signs of rock melting or explosion, it was a "controlled" natural reactor: as the temperature rose due to the energy released by the fission, some of the water evaporated and the loss of this moderator stopped the reaction. After cooling and soaking in the water again, the fission reaction could start again. In this way, the nuclear fission reaction could be ignited cyclically for many thousands of years.
Note: Such "moderation-controlled" nuclear reactors can also be used in current technical practice, as described above in the section "Compact self-regulatory reactors".
   Such places increased concentrations of uranium could be in the crust more so in the distant past, some uranium deposits could act as a natural analogue of nuclear reactors !
Now, however, after such a long time, all traces of the activity of these natural nuclear reactors are almost wiped out: fission radioactive products have long since disintegrated, other daughter elements have been washed away by groundwater, and the integrity of deposits has been violated during geological processes. Some ancient natural reactors could perhaps might reveal an increased incidence of xenon in the gas escaping from underground ..?..   
   In even earlier times - during the formation of planets and the entire solar system after the explosion of the parent supernova - there were probably often places with an increased concentration of 235U or other fissile materials. At that time, there were probably a number of massive flares of chain fission reactions, often of large scale and explosive nature.
   Otherwise, more than 12 billion years ago, supernova explosions was often occurred in the universe (and continue to do so today), that eject clouds of hot matter enriched with heavy elements, including uranium and transuranics (see, for example, "Cosmic Alchemy"). Shock waves in such clouds can form densities with the conditions for triggering a chain fission reaction, but compared to the massive flow of energy from a supernova explosion, the energy released during the chain fission reaction is of no greater astrophysical significance.

Other fissile materials. Transmutation. Breeder reactors.
So far, we have shown the fission of heavy atomic nuclei and their use in a nuclear reactor on the most common example of uranium
235U, which is the only fissile material available in nature (artificial 233U also appears to have similar properties). However, there are other heavy nuclei capable of fission reactions under the influence of neutrons. The most common isotope of uranium 238U (representing 99.3% of natural uranium) can only be cleaved by fast neutrons with a kinetic energy higher than 1.2 MeV and is not suitable for direct use in a chain fission reaction. A similar situation is with thorium 232Th. However, there are ways in which uranium 238 and thorium 232 to rework for fission and obtaining nuclear energy :
Transmutation fuel chains ,
which allow by nuclear reactions with neutrons to convert (transmute) the nuclides of uranium-238 and thorium-232 into elements, capable of chain cleavage reaction
(plutonium-239 or uranium-233). We will first introduce the method of "breeder" reactors, which is already being used now, the second way of the future (accelerator-controlled transmutation technology) will be mentioned below.
Fast breeding reactors with uranium-plutonium fuel cycle

Irradiation of uranium nuclei
238U with neutrons leads to the reaction :
      238 U 92 (n, g) 239 U 92 ® (b - ; 25min ) ® 239 Np 93 ® (b - ; 2,3 days ) ® 239 Pu 94 ,
which forms an important transuranic element plutonium
239Pu *), which, like 235U, cleaves by fast and slow neutrons and undergoes a nuclear chain reaction even at a much smaller critical mass (about 10 kg) than uranium; it can therefore be used in a nuclear reactor.
*) Plutonium 239 is a very dangerous radionuclide: it is
a-radioactive with a half-life of 2.44.104 years, easily contaminates, has high radiotoxicity (and chemical toxicity) and with a larger amount there is a high risk of radiation accident. For its low critical level is abused, inter alia as a primer to thermonuclear nuclear weapons....
  This way using
238U is used in reactors with a fast (non-slow) neutrons *) having no moderator, but contains more fissile material (239Pu, 235U) in the form of more enriched uranium 238 to about 20-50% (effective cross section of plutonium and uranium for the fission reaction with fast neutrons is lower than for slow neutrons). A higher concentration of fissile material leads to a more intense release of heat in the core per unit volume. Thus, a fast reactor must have more efficient heat dissipation using a medium capable of operating at a higher temperature, about 500 °C. Therefore, water (which would, after all, slow down neutrons) is not used for cooling in the primary circuit, but, for example, molten sodium metal, which has a much better thermal conductivity and a much higher boiling point (almost 900 °C) than water.
*) When using slow neutrons, the cleavage of 239Pu nuclei occurs in only about 65% of cases. In other cases, the plutonium nucleus 239Pu absorbs the neutron to form the isotope 240Pu, which does not have fission properties. However, if the plutonium-239 nucleus is affected fast neutron (instead of slow), in the vast majority of cases it will not be absorbed, but the 239Pu nucleus will split, producing 2-3 more neutrons for the chain fission reaction and for the production of more Pu-239 (from uranium-238) than the reactor consumes.
  The cleavage of 239Pu by fast neutrons produces an average of 3.02 new neutrons /1 fission. Less than two neutrons are consumed on average for further fission, and the remainder, a little more than one neutron on average, is captured by 238U nuclei, producing 239U, which is converted to plutonium 239Pu by the two beta conversions mentioned above. Thus, plutonium is constantly formed from uranium 238U here; to increase the yield of plutonium, the active zone of the enriched fissile material is surrounded by an additional layer of 238U (unenriched). Reactors of this type are sometimes called Fast Breeder Reactors (FBR) because they use fast neutrons to "multiplies" the fissile material plutonium in them, which is produced slightly more than is consumed for fission.
  Through plutonium, it is possible in principle to recover more than 90% of uranium-238 (and thus natural uranium) and thus multiply the available natural sources of fissile material for nuclear energy.
Breeder reactors with thorium-uranium fuel cycle
In a similar way, the possibility of using thorium
232 Th is considered, which would change by neutron capture to 233Th and this would b -decay gradually (over protactinium 233 Pa) to transmute uranium 233U :
      232 Th 90 (n, g ) 233 Th 90 ® (b - ; 12min ) ® 233 Pa 91 ® (b - ; 27 days ) ® 233 U 92 .
Uranium-233 is as good a fissile material, capable of chain fission reaction, as
235U or plutonium-239. "Excess" neutrons during fission 233U then transmutes thorium-232 to uranium-233, so that the 233U fissile material "multiplies" here at the expense of thorium *). This process can take place with both fast and slow neutrons (unlike the above-mentioned uranium-plutonium reactors operating only with fast neutrons).
*) The problem here is the somewhat long half-life of the intermediate protactinium-233 to fissile uranium
233U - 27 days. During this time, 233Pa can be converted to protactinium-234 by further neutron capture due to the intense neutron flux, which is converted to uranium-234 by b- radioactivity (with a half-life of about 7 hours); it cannot be used as fissile fuel. It would therefore be advantageous to continuously withdraw protactinium-233 from the reactor, leaving it in a suitable container (outside the reactor) decay into uranium-233 and back into the reactor insert to the thus formed "finished" 233U. It may be possible to implement in reactors with fuel dissolved in molten fluoride salts with a continuous chemical isotope separation.
   Thorium-uranium reactors could be promising given that thorium reserves in the Earth's rocks are about 4 times larger than uranium. A certain advantage of this reaction is that it generates radioactive waste with a lower specific activity
(standardized on the energy yield of the reaction) than in the uranium-plutonium cycle *).
*) Especially heavy long-lived radionuclides such as neptunium, americium, curium are formed here only in negligible amounts, because the nucleon number of 232Th is 6 units lower than 238U.

In every activity - in industry, transport, agriculture, health, science and technology, laboratory work, as well as in everyday life, sometimes something fails, goes wrong, "breaks" - an accident occurs.

Nuclear reactor accidents
A serious malfunction of a nuclear reactor, associated with its irreversible damage, is referred to as an accident. Such an event can in principle occur either by a technical failure or by a human factor, or a combination of both
(incorrect procedure of workers in solving a technical failure). Possibly also due to natural events (Fukushima).
  From the point of view of operation, such a reactor accident can occur in two phases :
× Accident in the phase of an ongoing chain fission reaction it can be caused either by an uncontrolled running of the chain reaction (failure of the neutron flux control) or by a failure of the cooling and drainage of the thermal power of the reaction. This is usually a very severe accident, associated often with the melting of the inner part and the destruction of the reactor.
× An accident in the shut down phase of a reactor may be caused by insufficient cooling of the residual heat output ("Nuclear reactor cooling problem" mentioned above), as well as some manipulations during fuel cell replacement.
  In principle, a nuclear reactor can not explode nuclear like an "atomic bomb"
(the physical conditions mentioned above in the section "Uncontrolled chain reaction - nuclear explosion" are not met here). However, the increased temperature may cause a rise of pressure, which can lead to pressure explosion. In the enormous increase in temperature can cause decomposition of water into hydrogen and oxygen and subsequent chemical explosion. If the temperature of the fuel cell exceeds a value of about 600-1000 °C, their hermetic shell (zirconium alloy) is thermally damaged and the radionuclides contained, especially fission products inside, may leak into the surrounding environment, so in the event of a more serious accident of a nuclear reactor, radioactivity *) may also leak into the surrounding space and the environment. The technical accident of the reactor can thus be accompanied by a radiation accident (in the terminology of radiation hygiene - §5.6, part "Radiation accidents") and radioactive contamination. The accident at the Chernobyl nuclear reactor and the recent accident at the Fukushima nuclear power plant are briefly described below. Some other aspects are discussed in the section "Safety and risks of nuclear energy").
*) In the event of a nuclear reactor accident with a leak of radioactivity, there is mainly a leakage of fission products. When overheated, substances with a low boiling point are preferably emitted into the air and evaporate easily; it is mainly radioiodine 131I and cesium 137Cs. Fortunately, heavy radionuclides, such as uranium or high-boiling plutonium, are released very little. However, if the tightness of the fuel cells is broken, all radionuclides can leak into the water (primary, nuclides formed by nuclear reactions and fission products, to the extent dependent on their amount and solubility).
  We will briefly mention the two most serious cases of nuclear reactor accidents
(focusing mainly on proven physical and technical aspects, without speculation about the subjectively debatable social background) :
Chernobyl nuclear reactor accident
Serious operator errors, partly in combination with the positive temperature coefficient of graphite-moderated reactors, have become fatal for the RMBK-1000 reactor of Unit 4 of the Chernobyl nuclear power plant. On April 26, 1986, technicians conducted a "safety" experiment with a partial shutdown of the reactor to verify what power for the water pumps of the primary reactor unit could still be obtained from the inertial deceleration of the unit turbines (bridging about 1 min. - in case of power failure) after shutdown. Due to broken coordination (interruption of the test for several hours - economic requirement for increased electricity supply to "meet the plan" - caused this very non-standard operation to be completed by another group of workers, little familiar with the test procedure) reactor power dropped to too low and operators then failed to "revive" the reaction; in fact, a larger amount of 135Xe has accumulated in the fuel cells, which absorbs neutrons very efficiently - the so - called "xenon poisoning" mentioned above in the passage "Neutron absorption by fission products, neutron" poison "-" reactor " poisoning". In this situation, the only sensible solution is to shut down the reactor, wait a few hours and then start it in the standard way.
   The technicians did not recognize it, their profession was mostly electrical engineers who did not know the complex details of the dynamics of the nuclear reactor. Above all, however, they were under pressure from an ambitious and despotic boss, who eagerly tried to complete the test
(for which he would have a functional promotion). In an effort reactor at all costs fast "start" committed a fatal error : off emergency protection of the reactor and pulled out from the core of almost all control rods above the permissible limits (with graphite end) - so high, the control rod in a functioning reactor with nuclear fuel must never extend !
   As a result, the fission reaction eventually started, but it was unstable way, with disconnected control and emergency protection! Another mistake was to disconnect the turbine and some circulation pumps of the primary circuit, straightforward in the spirit of the ongoing test
(which in this situation was already wrong and pointless, he had to stop - but the authoritarian boss insisted on it, had a personal career interest...).
   The flow of coolant through the reactor began to decrease, the temperature rose, and excessive steam generation and accumulation occurred in the core. In this unacceptable state, a positive temperature coefficient
("cavity effect") of the graphite-moderated reactor manifested itself - an increase in steam led to an increase in the fission reaction. And most importantly, due to the increase in neutrons, almost all 135Xe transformed very quickly to stable 136Xe, which no longer absorbs neutrons. As a result, the only neutron absorber that was in the core at that time disappeared, as the absorber rods were ejected! This led to a sharp uncontrolled increase in the chain fission reaction. Emergency insertion of the boron absorption rods failed, the reactor was enormously overheated and the channels were deformed *), the control rods jammed at about one third of the height. The chain fission reaction started uncontrollably at many times the nominal power, which resulted in overheating and reactor failure.
*) According to some opinions, the graphite ends (tips) of the control rods (mentioned above in the passage "Controlled chain reaction", paragraph 2. Neutron absorption - "Graphite-boron combination?") also contributed to the accident . However, this was of only marginal importance in terms of the cause, the perpetrators of the accident only excused themselves. During the emergency insertion of control rods, a slight short-term increase in reactivity was reflected only in a certain part. The real cause of the accident was the late insertion of the control rods (which were previously unacceptably high ejected) into the already overheated reactor with thermally deformed channels. If the emergency insertion of the control rods were started only a few minutes earlier, no accident would occur and the reactor could in principle be restarted in a regular manner after about 1 day (although after such a serious emergency it would certainly be appropriate to perform a thorough technical revision reactor! - which, moreover, so in the next few days were planning) ...
   Steam pressure caused expolosive tearing the lid of the reactor, the reactor entered air, graphite moderator blocks began to burn. There was also an explosion of hydrogen and oxygen, caused by the decomposition of water in contact with the hot materials of the reactor. The inner part of the reactor core has melted, the reactor was destroyed. The fire of the reactor unit lasted a whole week, dark smoke rising from the building, containing a large amount of radioactive isotopes. Atmospheric currents - the wind that was westward at the time, carried a radioactive cloud up to several hundred kilometers above Europe. With rainfall, there was a radioactive contamination of the natural environment - water, soil, plants.
   The main contaminants were radioiodine 131 I and cesium 137 Cs. Iodine 131I gradually disintegrated over several weeks with a half-life of 8 days, 137Cs (half-life 30 years) has been measurable for many years. With further rains, which are no longer radioactive, contaminating radionuclides gradually entered deeper soil layers and biosphere contamination was minimal.
  E.g. at our nuclear medicine workplace in Ostrava-Poruba, where it rained during storms on May 1, we observed an almost twofold increase in the value of the natural radiation background on radiometric instruments in the following days. In rainwater samples, we measured the activity of about 2-5 kBq/liter, especially radioiodine I131, on well scintillation spectrometers. I also took samples of rainwater in Konice in the Drahan Highlands and in Holešov in the Kromeríž region, where I had a trip in those days. In Konica there was also increased radioactivity (about half as less as in Ostrava), in Holešov, where it did not rain in those days, no increased radioactivity was measured in the samples above the usual natural background. Communities nuclear medicine professionals produced recommendations that in areas with increased contamination should be administered, especially for children, a small amount of iodine (non-radioactive) to displace the accumulation of radioiodine in the thyroid ..?..
When destruction of the nuclear reactor at Chernobyl was extensive contamination of the environment with radioactive fission products and exposure of 232 people with high doses of radiation (units up to tens of Sv), associated with deterministic effects and acute damage to health; in 31 cases there were even lethal effects. Of these, 2 workers were killed directly when the reactor exploded, but even if this did not happen, they would receive a lethal dose of radiation! Many hundreds of other people received radiation doses of tens to hundreds of mSv, for which an increased incidence of stochastic effects can be expected (by at least 1%, although this has not been directly confirmed ...).
   The burnt-out nuclear reactor building was removed and a large concrete cell was built around the remains of the reactor - "sarcophagus"- to prevent further contamination of the natural environment. It acts as a kind of temporary "intermediate storage" of nuclear waste. It is planned that after several decades (2030-40?) the reactor core will be mined and after appropriate modifications or reprocessing placed on permanent storage of nuclear waste. It will be a difficult task due to the high radioactivity and a large volume of nuclear waste and contaminated materials. Such a central repository is planned to build at the nearby campus of Chernobyl. Among experts there were even proposals to re-build a nuclear power plant Chernobyl (of course, with new technology), politicians and the public are against ...
  The Chernobyl accident became certain negative milestone  in nuclear energy and radiation protection; it was a big mistake that happened! Unfortunately, it is not emphasized that it was caused by the human factor - the accident was actually caused by one person who, in his despotic ambition, arbitrarily violated basic safety standards and threw the reactor into a completely unacceptable mode. Such an "barbaric" treatment would not be tolerated by any existing reactor, in any case it would result in a serious failure or even an accident. Thus, no technical error of the reactor (which, if properly operated, can function reliably for several decades) *) or of the political system (as ideologically argued by the supporters of the "Cold War"), and certainly not the risk of nuclear energy as such (as it is still misinformed by opponents of the "atom") !
*) Perhaps the only relevant design error of the RMBK-1000 reactor was the user possibility of inadmissible ejection of the absorption rods; it was assumed that the reactor would be operated by professionally erudite and responsible workers who would not do such "nonsense"... If this were mechanically blocked (and complex mechanical work would have to be done in service mode), the mania of the chief engineer would not pass and no accident would occur. Many reactors of this type are still operating reliably, some of which have operations planned for 2030 and beyond ...
  This tragic event has led to an unjustified attenuation of nuclear energy, radiophobia and large-scale tightening of safety regulations and standards of radiation protection not only in nuclear energy, but in the whole area of applications of ionizing radiation (this resulted in excessive bureaucratization of radiation protection - cf. the section "Bureaucratic requirements for radiation protection" in §5.8). On the other hand, it has become a lesson to prevent similar events.
During the modernization of the existing RBMK reactors, some technical modifications and revisions of their operating modes were performed. For example, the insertion speed of the control rods was increased, their construction was modified (proportions between the boron part and the graphite ends; these are just unimportant details). Most importantly, however, a technical barrier was implemented against arbitrary inadmissible pulling out of control rods, which was the main cause of the accident.
An accident as large as in Chernobyl will probably never happen again !
The accident at the Fukushima nuclear power plant
The last accident at the Fukushima nuclear power plant had completely different causes (and fortunately a much smaller extent of aftermath) than the Chernobyl accident. This large power plant is located on the northeast coast of the Japanese island of Honshu, was built in 1966-79 and is equipped with six boiling reactors (BWR; BWR-3,4,5) with a total electrical output of 4700 MWe. The cause of the accident was a huge natural disaster - a devastating earthquake (9 magnitude) with a subsequent tsunami that occurred on March 11, 2011. At that time, there were four reactors in operation, the other two were regularly maintained.
  At the first signs of earthquakes (recorded by sensors) are all running reactors immediately automatically shut down, the water pump, powered by backup diesel generators, regular ensure cooling of the residual heat in the active zones
(diesel generators were used because the earthquake was interrupted power supply - "black -out"). So far, everything would be fine.
   However, about an hour after the earthquake, a tsunami, more than 10 meters high, flooded the coast ! Nobody expected such a high wave in the construction of a flood barrier on the coast. Pumps and diesel generators located in the lower parts of the reactor buildings were flooded with water and stopped working. This interrupted the cooling of the residual heat, the temperature rose in the core, the water boiled, the fuel rods became hot and hydrogen and oxygen were formed in contact with water and steam. Hydrogen and oxygen exploded, damaging the reactor structure. Some radioactive fission products began to be released from the superheated fuel rods. The reactor buildings also housed tanks with spent fuel cells
(not only from Fukushima, but also from other nuclear power plants), from which radioactive substances also began to be released. Further overheating was temporarily prevented by cooling with seawater. After a few weeks, the situation partially stabilized, but four reactors were severely damaged or destroyed. A relatively large amount of radioactive substances escaped into the seawater, which, however, soon dispersed in the large dilution space and diluted to below-limit specific activity.
  No one was to blame for the Fukushima accident ! To the address of "nitpickers", who claim the opposite and only criticize and "look for lice", one can aptly respond with the proverb " After the battle, everyone is a general". After all, since the world's mass media it has been very unfair, as disproportionate
(and often distorted)*) paid attention to the radiation aspects of this accident, which was in fact just a small episode in the terrible tragedy that struck Japan and killed thousands of people! When the Fukushima disaster no one perish, and no one was irradiated with high radiation dose at which it was threatened deterministic radiation effects. According to the Japanese Atomic Energy Agency, only 6 workers exceeded the effective dose of 250mSv and several dozen others received doses higher than 100mSv, which may increase the risk of cancer by only about 1% (from spontaneous 20% to 21%). It is estimated that several thousand people near Fukushima could receive doses in the range of 10-30 mSv (as if they had undergone one X-ray CT scan - irrelevant!). The relevant Japanese institutions dealt very responsibly with the radiation protection of the population. The effects of the Fukushima nuclear accident are only local and do not exceed the severity of other major non-nuclear industrial accidents. The main health risks and injuries were caused not by radiation, but by stress from evacuation and concerns arising from overestimation of risks - radiophobia; of these causes several hundred people died, the evacuation was overvalued ...
*)  The disinformation about Fukushimské crash paradoxically contributed very much in Japan, where this event has been misused to fight among influential individuals, political and economic groups, enforcement of their particular interests. The subjective, biased and even false reports of the commissions were pushed to the official publication, claiming, among other things, that the accident was not caused by a tsunami after the earthquake, but by humans: "It was a serious man-made disaster be prevented ", in stark contrast to the facts. And to promote the cessation of nuclear energy in Japan ... It is debatable whether the severity and impact of accidents could be mitigated by more efficient responses and organizational expertise circles ..?...
   It for adverse events is a sensible approach constructively and take them positive lessons to of the future. The Fukushima accident revealed, among other things, one important lesson: for inherent safety, cooling of the residual heat of the reactors should be provided from water tanks located above the reactor so that the cooling water flows by gravity - "self heawy" - and is not tied to pumps that may fail, eg when flooded.

   Some general aspects of radiation accidents are discussed in §5.6, section "
Radiation accidents and incidents".

Safety and risks of nuclear energy
Nuclear safety is ensured by a set of technical means and measures to prevent the process of obtaining nuclear energy from escaping control and to prevent the emergence of radioactive substances from entering the environment. The safety of nuclear facilities is based primarily on the well-thought-out design of all links in the nuclear chain, with multiple barriers against unwanted leakage of radioactive substances and multiple secured regulatory and safety systems. An important element is also the passive safety of reactors, given the self-regulatory properties, which in the case of an anomalous situation will stop or dampen the fission reaction without human intervention. Inherently safe nuclear reactors are designed in such a way that in the event of any failure, the reactor is shut down by the action of physical laws only, regardless of the operator's activity
(lat. in = in, haereo = imprison ; inhaerent = inseparable, intrinsically connected, innate, essential ). Part of the safety of a nuclear reactor is also to ensure the cooling of the reactor core, not only during operation, but also the cooling of residual heat after shutdown *). The safest reactor is one that does not have enough fuel to generate an excess of neutrons, so that it cannot occur in an uncontrolled chain fission reaction under any circumstances; however, such a reactor must have an independent external neutron source to operate (see below)ADTT). And of course the thermonuclear reactor (below the section "Fusion of atomic nuclei"), where no chain reaction takes place.
*) The recent accident at the Fukushima spring power plant teaches that cooling of the residual heat of the reactors should be provided from water tanks located above the reactor so that the cooling water flows by gravity and is not tied to pumps (which may fail, eg when flooded).

  Opinions differ widely on the safety or "danger" of nuclear energy. While experts generally agree that nuclear energy is relatively very safe, there is no such agreement in the lay public. Serious voices of experts are shouted in the mass media by very agile groups of opponents of nuclear energy. The sad event that significantly "encouraged" these activists was the human factor caused by the tragic accident at the Chernobyl nuclear power plant
(described above in the section "Chernobyl nuclear reactor accident"). For political or lobbying reasons, some mass media inflated this accident to catastrophic proportions and misused it to fight nuclear energy as such. Recently, the accident caused by the natural disaster at the Fikushima nuclear power plant (passage "Accident at the Fukushima nuclear power plant"), which was only an insignificant episode in the tragic context of a natural disaster ...
   The objective problem of nuclear energy is
nuclear waste (see below) - spent fuel cells containing significant amounts of radionuclides, some of which have a very long half-life. So far, these wastes are stored in specially adapted repositories, but technologies are being developed for their efficient disposal or further processing (see ADTT below).
  Ordinary environmental activists undoubtedly have good intentions and are convinced that they are fighting for a better environment. However, it is mostly lay people who, without real knowledge of things, "cry on the wrong grave": they do not realize that the "threads" that actually control them secretly come from the opposite camp - from economic lobbies, which for their particular interests and profits are able to devastate the environment uncontrollably.
It is not generally known, for example, that thermal power plants, in addition to enormous contamination with sulfur or nitrogen compounds and other harmful substances, contaminate the environment with radioactivity, much more than nuclear power plants! Nuclear energy, especially the implementation of promising new technologies - in future nuclear fusion - is the only reasonable alternative for the present inefficient and environmentally harmful use of fossil fuels.
   However, what can be fully agreed with "green" ecologists is that the best energy is "saved energy" - the development of modern technological processes that have less energy intensity... Some social aspects of obtaining and using energy are discussed at the end of this chapter in the passage "

Nuclear waste
The usual "charge" of fuel for a (light water) nuclear reactor with a capacity of 1000 MW is about 100 tons of uranium enriched to about 3%. One ton of such fuel contains 967 kg of uranium-238 and 33 kg of uranium-235. After three years of reactor operation, about 25 kg of uranium-235 and 24 kg of uranium-238 will "burn" (transmute) one ton of this fuel. This produces 35 kg of fission products (a number of different nuclides), about 9 kg of plutonium isotopes, 4.5 kg of uranium-236 isotope, 0.5 kg of neptunium-237 isotope, 120 g of americium-243 and a smaller amount of other transurans. From the point of view of a conventional reactor, all these radionuclides contained in spent nuclear fuel are nuclear waste.
   Thus, one of the main problems of current nuclear energy is spent nuclear fuel, which contains high activities of a number of radioisotopes *), often with a considerably long half - life. Their escape into the biosphere is a potential risk for a long time. In addition to relatively short-lived radionuclides (such as
131I with T1/2 8 days), there is a large amount of eg 137Cs (T1/2 30 years), 90Sr (T1/2 28.8 years), 241Am (T1/2 458 years), 239Pu (T1/2 2.104 years), 240Pu (T1/2 6.103 years) and a number of other long-lived radionuclides. Spent nuclear fuel from the reactor produces heat for several years and has shown radioecologically increased radioactivity for hundreds and thousands of years.
*) In §1.2 "Radioactivity" it was derived that the activity of a given number of nuclei is inversely proportional to the half-life of T1/2 . New (fresh, unused) fuel cells have a relatively low activity due to the long half-life a decay of uranium (450 million years). However, the fission of uranium produces radionuclides with significantly shorter half-lives (of the order of days or years), so that freshly burned fuel cells are highly radioactive !
   With these hazardous radioactive waste can be managed in essentially three ways
(after a short cooling period and temporary storage in intermediate storage facilities, as mentioned above) :

Thus, in addition to chemical treatment and separation of nuclear waste, it offers a very promising possibility to transmutate the respective radioisotopes into stable nuclei by means of a series of repeated neutron absorption *), followed by b-decay or fission. Unfortunately, however, this neutron absorption in a classical nuclear reactor proceeds with little efficiency because the effective cross section of slow neutron capture is very low for most isotopes and, in addition, most neutrons are consumed to sustain the chain reaction. Classical nuclear reactors "struggle" with a neutron balance, neutrons can not "wasting". For efective transmutation, additional higher energy neutrons must be used, which can be achieved with the aid of an accelerator, as outlined below.
*) Possibilities of nuclear transmutations are also considered with the use of accelerated protons or other charged particles, but neutron transmutation is probably more feasible and efficient.

Nuclear reactor with an external neutron source. Accelerator-controlled transmutation technology - ADTT
As follows from the above analysis of the possibilities and current technical solutions for obtaining energy by fission of heavy atomic nuclei, there are three permanent problems of this technology :
¨ Nuclear waste with high activity and long half-lives.
¨ Low utilization (burning) of fissile material or primary fuel.
¨ Reactor safety - a supercritical amount of fuel (reactivity supply) is required for operation, so there is a possibility of an accident.
   Recently, attempts have been made that could simultaneously solve all these problems and result in the construction of a completely new type of nuclear reactor, which is in terms of fissile material subcritical and necessary neutron balance for fission is provided by an external source of neutrons: a fission reactor combined with a powerful accelerator. This program is called ADTT (Accelerator Driven Transmutation Technologies *).
*) Sometimes these systems are also referred to as ADS (Accelerator Driven Systems) - "accelerator-controlled systems", or more specifically ATW (Accelerator Transmutation of Waste) - "accelerator-performed transmutation of waste".
  Compared to existing technologies, the ADTT system would have three main advantages :

In such a reactor with a lower concentration of fissile elements, a separate chain fission reaction is not maintained - the reactor is subcritical, but the supply of missing neutrons is provided by an external source - a powerful proton accelerator that fires nuclei of heavy elements (lead, tungsten, ...) in a target in reactor active zone and the necessary neutrons are ejected from them by the fragmentation reaction - Fig.1.3.5.

Simplified schematic diagram of a reactor for accelerator-controlled transmutation technology.

Each proton with an energy of about 1 GeV will eject about 20-50 neutrons of different energies from the heavy nucleus, which pass through the basic moderator (eg a layer of heavy water D2O to increase the probability of fission) into the reactor's own core. Here, the fissile material as well as the waste isotopes that we want to transmute, would be dissolved in a suitable environment (molten fluoride salts are proposed). In the outer part of the reactor, the action of neutrons could lead to transmutation of thorium-232 by a series of reactions: n + 232Th ® 233Th + g, 233Th ® 233Pa + e-+n, 233Pa®233U+e-+n. Thorium reserves in the earth's crust minerals are about 4 times larger than uranium, which could cover human energy needs for a long time. The resulting uranium-233 would be led to the central part, where the absorption of neutrons would fission it to release the relevant nuclear energy. In addition to the thorium-uranium fuel cycle, a more common uranium-plutonium fuel cycle can also take place here.
   Since the reactor operates continuously in the subcritical mode, it is operationally safe, there can be no uncontrolled chain fission reaction - the reaction rate is determined by the flow of protons from the accelerator and when it is turned off, the reaction stops. Series: fission
® transmutation ® b-decays, taking place in the ADTT-reactor would function both as a source of nuclear energy and as an efficient neutron "incinerator" for radioactive waste, where long-lived radionuclides would be gradually transmuted to short-lived or stable. For neutron transmutation, radionuclides with a high effective cross section sn of neutron capture are suitable; of long-term radionuclides in fission products it is mainly :
99 Tc (T 1/2 = 2.1.10 5 years) + n ( s n = 20b) ® 100 Tc (T 1/2 = 16sec.) ® 100 Ru (stable),
129 I (T 1/2 = 15.7.10 6 years) + n ( s n = 18b) ® 130 I (T 1/2 = 12h) ® 130 Xe (stable).
Less suitable is zirconium
93Zr (T1/2 = 1,5.106 years) + n (sn = 2,7b) ® 94Zr (stable), which has an effective neutron reaction cross section with only sn=2.7 barn; similarly in 107Pd, 126Sn, 79Se (which, after all, are formed only in small amounts).
   An efficient chemical-isotope separation unit would have to be included in the circuit of the transmutation reactor, which would continuously separate the long-lived isotopes and (possibly together with
233U) return them back to the reactor core. This continuous "on-line" separation and reprocessing is only possible when using nuclear fuel in liquid form (melted in fluoride salts, as mentioned above in the "Salt Reactors" section). Short-lived and stable isotopes could then be stored in ordinary storage; their activity would fall to the level of the natural radioactive background in a few decades.

Transmutation technology :
Successful mastery of transmutation technology would function as a rich source of nuclear energy and at the same time as a neutron "incinerator" for hazardous radioactive waste.

Electricity would then be produced downstream of the heat exchanger in the secondary circuit by conventional steam turbines. With a technically advanced solution, the accelerator (proton energy approx. 1GeV, flux of tens to hundreds of mA) would consume approx. 20% of the energy produced, the rest could be supplied to the network. After overcoming the technical problems (there are many of them and they are very difficult!), it would be possible in the future to satisfactorily close the nuclear fuel cycle in fission reactors as well. However, unless thermonuclear fusion, discussed below, becomes a more promising way in this direction (section "Fusion of atomic nuclei. Thermonuclear reactions"); that would definitely be a more favorable option! After all, in addition to accelerator-controlled technology, thermonuclear-controlled transmutation technology is also being considered, as discussed below in the "Thermonuclear Fusion" chapter, "Hybrid Fusion-Fission Nuclear Power" section.

T r a n s u r a n s
At this place, in connection with the heavy fissile materials discussed above, it is a good opportunity to discuss briefly the specific issue of the heaviest atomic nuclei. As transuranium elements are designated elements that follow uranium in Mendeleyev's periodic table and are "heavier" than uranium. They are not commonly found in nature because they are radioactive with a half-life shorter than that of natural (primary) radionuclides *). However, they are formed artificially during some processes in nuclear reactors and during the bombardment of heavy nuclei with accelerated ions.
*) Transuranic nuclei undoubtedly formed during the explosion of supernovae similar to other heavy elements (such as uranium) - see eg "Cosmic alchemy", but due to its relatively short half-lives, has completely disintegrated over the past billion years and has not been preserved on Earth or in the solar system.
   The names of the first two transurans - neptunium and plutonium - are derived from the planets Neptune and Pluto, whose orbits lie beyond planet Uranus. Another TRU were named after countries and cities - eg. americium , californium , moscovium. Many of the TRU was named after the prominent researchers in the field of physics and chemistry - eg. einsteinium, mendelejevium, curium, fermium, ruthefordium, bohrium, copernicum, ... Or according to researchers directly involved in the discovery of new transurans - seaborgium, flerovium, or laboratories involved in the preparation of new transurans - berkelium, lawrencium, dubnium, darmstadtium.
Lighter transurans
Lighter transurans, such as neptunium, plutonium, americium, curium, are commonly formed from uranium by neutron fusion as "by-products" in nuclear reactors. Because they have relatively long half-lives, we can chemically extract them from spent nuclear fuel.
   In the section on fissile materials, it was mentioned above how neptunium
237Np and the important transuranic element plutonium 239Pu are formed in a nuclear reactor during irradiation of uranium-238 with neutrons. Further irradiation of plutonium with neutrons in the reactor among other things, reactions occur 239Pu94(n,g)240Pu94(n,g)241Pu94 ®(b-,13 years)® 241Am95 , during which the following transuranic element americium -241 is formed (is a-radioactive with a half-life of 458 years). Further irradiation of plutonium and americium targets with neutrons in the reactor can also produce some other transuranic isotopes, such as berkelium Bk or californium Cf. In addition to plutonium and americium, from a transuranic radionuclides is used californium, especially 252Cf98 , which, in addition to a-radioactivity, exhibits spontaneous fission with a half-life of 2.65 years, emitting fission neutrons - such a radionuclide can serve as an intense laboratory source of neutrons.
Heavy transurans
Heavier transuranic nuclei (Z> 100) can no longer be obtained by neutron fusion in a nuclear reactor. They can only be created with the help of accelerators: existing heavy nuclei are bombarded by other accelerated nuclei so that during the nuclear reaction they "fold" or "merge" - fuse, to form a new superheavy transuranic nucleus. In the simplest cases
, we bombard uranium or lighter transuranic nuclei with a-particles, ie helium nuclei (with an energy of about 40 MeV). The classic case is the reaction 239Pu + 4a ® 242Cm + 1n, which in the 1940s G.Seaborg formed from plutonium-239 the curium 242. In the same way, from americium-241 were formed berkelium Bk97 and from curium made the californium 252Cf98 .
   For the preparation of the heaviest transuraniums, irradiation with particles a (helium nuclei) is no longer sufficient, but it is necessary to bombard with heavier accelerated nuclei. We bombarded heavy target nuclei of lead, uranium or lighter transuranium, with multiply charged ions (eg carbon C6+, oxygen, neon, boron) accelerated in cyclotrons to energies exceeding the value of the Coulomb potential wall for the given interaction (energies around 120-400 MeV and higher are used). The first such successful reaction was carried out in 1958 in Berkeley, when carbon nuclei were fired at the curium target 244Cm + 12C ® 254No102 + 2n, managed to prove the formation of nobelium nuclei with a proton number Z = 102. Soon after, the same laboratory succeeded in obtaining a lawrencium with Z=103 by bombarding a target from californium with accelerated boron nuclei.
   The formation of the heaviest transuranics (Z> 100, N> 250) is technologically and experimentally highly demanding, mainly for two reasons :

Compound nuclei, formed during fusion reactions of accelerated nuclei with heavy target nuclei, are usually formed in an energetically excited state. If this excitation is high, the resulting nucleus tends to split spontaneously into two lighter fragments (+neutrons) very quickly - we will not detect the transuranic nucleus. In contrast, at low excitation, the complex nucleus of excess energy is emitted by the emission of only a small number of particles such as neutrons, protons or a-particle; the result may be the desired transuranic core. The successful synthesis of heavy TRU's therefore greatly depends on the proper "tuning" the energy bombarding nuclei only slightly higher than what is needed to overcome the repulsive electric Coulomb barrier, so that it occur the so-called "soft fusion", leading to low excitation compound nucleus.

Fig.1.3.6. Preparation, separation and analysis of heavy transuraniums.
Above: One of the older simple arrangements for the production, separation and detection of intermediate-lived transurans. Expression analysis is mediated by a fast belt conveyor, on the surface of which a target layer is applied (modification of this arrangement was used at the JINR in Dubna in the preparation of transuranium with Z = 102 and 104) . Bottom: An electromagnetic velocity filter separator is now preferably used to identify a small number of short-lived heavy transuraniums against a large background of other nuclei and processes (analogous filters are used, for example, in mass spectrometers). The high-energy ion beam from the accelerator hits a heavy metal target (lead, bismuth or transuran), where a number of different nuclear reactions take place. The products of these reactions are ejected from the target and move at high speed through the evacuated space. They pass through a system of deflection electrodes and electromagnets generating such perpendicular combinations of electric and magnetic fields, that the electric and magnetic forces cancel each other out at a certain velocity of the passing ions. These ions pass through a velocity filter ("useful particles"), while particles of other velocities are diverted by the magnetic field and leave (into the absorber). Thus the device using a suitably configured system electromagnetic field separates the required radionuclide from other reaction products as well as from primary particles. Only the nuclei of selected velocities, corresponding to the kinematics of the desired production process, fall into the detection system, where their energy, position, energy of decay products and radiation g from the excited levels are measured. The studied nuclei fly into a semiconductor detector, where they are braked ("implanted" into its material) and the radiation emitted during their subsequent radioactive transformation (alpha or spontaneous fission) is registered there. This selection method can significantly reduce the number of alternative undesirable detected processes, ie significantly reduce the background and thus increase the chance of observing rare cases of production of the desired transuranic nuclei.

The heavier the transuranic nucleus, the shorter the half-life is usually observed *). However, some experts predict that for even heavier nuclei, the half-life will temporarily increase again - that there could be some "island of stability" (but relative stability) in the superheavy nuclei. However, so far it is only a hypothesis based only on the extrapolation of the magic numbers 2, 8, 20, 28, 50, 82 and 126, corresponding to the filled proton or neutron shells in the nucleus, which results in configurations with increased stability. The core 126 of protons and neutrons 184 might perhaps form the center of the hypothetical island increased stability..?.. The short range strong nuclear interaction, however causes, that the super-heawy cores will certainly highly instable due to alpha radioactivity and spontaneous fission; therefore, no significant "island of stability" can be expected..?..
*) The half-life also depends significantly on the number of neutrons in the nucleus, ie on the isotope of transuran. If an isotope with a longer half-life can be prepared, this can facilitate the analysis of physical and chemical properties.
    Using the methods outlined above, a number of heavy transurans were created: mendelevium 255-257Md101, nobelium 251-257No102, lawrencium 256,259Lw103, ruthefordium 260Rf104, dubnium Db105, seaborgium Sg106, bohrium Bh107, hassium Hs108, meitnerium Mt109, darmstadtium Dt110, and higher.
   Elements with a proton number greater than 110 have not been named until recently and were given provisional names and marks derived from the Latin name of the number of their protons: unununium Uuu111, ununbium Uub112, ununtrium Uut113, ununquartium Uuq114 (also called ununquadium), ununpentium Uup115, ununhexium Uuh116, ununseptium Uus117, ... In the last published transuran with the designation ununoctium Uuo118, krypton ions accelerated to 450 MeV in a reaction of 86Kr36 + 208Pb82 ® 293Uuo118 + 1n were fired at the Berkeley laboratory by bombarding lead nuclei, only 3 cores detected; half-life < 1ms, the experiment was not entirely conclusive. A hypothetical element with a proton number of, for example, 126 would have the provisional name unbihexium and the brand Ubh126.
   Definitive names and designations of new elements are assigned by the commission IUPAC
International Union of Pure and Applied Chemistry, an organization dealing with, among other things, chemical nomenclature and terminology), based on the proposals of their discoverers, only after the definitive demonstration of a new element. Of the super-heavy transurans, the elements Roentgenium Rg111, Copernicium Cn112, Flerovium FI114 and Livermorium Lv116 have recently been officially named in this way. The synthesis of elements with proton numbers 113, 115, 117 and 118 has recently been recognized as proven by this commission, so their names are now also established - see table.
Note: The question may arise, why is the discovery and recognition of new superheavy elements so "skipping"? In general, the rule is that the heavier the nucleus, the more difficult it is to synthesize and discover. However, there are some exceptions to this rule, stemming from experimental techniques and from the nuclear-physical properties of the structure of heavy nuclei and their nuclear reactions.

 Three laboratories are mainly involved in the research of the heaviest transuraniums: Lawrence's Laboratory in Berkeley, JINR in Dubna and GSI in Darmstadt (leading experts and pioneers in the preparation of heavy transuranium were G.T.Seaborg and G.N.Flerov in particular). Although these elements have no practical significance, the search for the heaviest elements at the very limit of stability can be of considerable theoretical importance for understanding the laws of atomic nucleus structure, the properties of nuclear forces, and for verifying and refining the atomic nucleus shell model.

Brief overview of transuranics :
The name of transuran Half-life T1/2 of the most important isotopes Production Discovery
Neptunium Np 93 237 Np: 2.14.10 6 years, ... 238 U + 2n ® 237 U ( b - ) ® 237 Np 1940
Plutonium Pu 94 239 Pu: 2.44.10 4 years, ... 238 U + n ® 239 Pu Berkeley, 1941
Americium Am 95 241 Am: 458 years, ... 239 Pu + n + n ® 241 Am Berkeley, 1944
Curium Cm 96 246 Cm: 15.6.10 6 y., 248 Cm: 348000 y., ... 239 Pu + 242 Cm Berkeley, 1944
Berkelium Bk 97 247 Bk: 1380 y., 247 Bk: 300 y., ... 241 Am + 243 Bk Berkeley, 1949
Californium Cf 98 251 Cf: 898 y., 249 Cf: 351 y., ... 242 Cm + 245 Cf Berkeley, 1950
Einsteinium Es 99 252 Es: 472 d., 254 Es: 276 d., ... 238 U + n + ... + n ( b - ) Berkeley, 1952
Fermium Fm 100 257 Fm: 100.5 d., 253 Fm: 3 d., ... 238 U + 16 O ® 245 Fm Berkeley, 1952
Mendelejevium Md 101 258 Md: 51.5 d., 260 Md: 32 d., ... 253 Es + 258 Md Berkeley, 1955
Nobelium No 102 259 No: 58 min., 253 No: 1.6 min., ... 244 Cm + 12 C ® 244 No Berkeley, 1958
Lawrencium Lr 103 266 Lr: 11 hrs., 262 Lr: 3.6 hrs., ... 245 Cf + 10 B ® 257 No Berkeley, 1961
Rudhefordium Rf 104 263 Rf: 10 min., 265 Rf: 1.5 min., ... 242 Pu + 22 Ne ® 260 Rf
249 Cf + 12 C ® 258 Rf
SUJV Dubna, 1964
Berkeley, 1969
Dubnium Db 105 268 Db: 29 hrs., 270 Db: 23 hrs., ... 243 Am + 22 Ne ® 260 Db
249 Cf + 14 N ® 260 Db
SUJV Dubna, 1967
Berkeley, 1970
Seaborgium Sg 106 271 Sg: 2 min., 267 Sg: 1.4 min., ... 249 Cf + 18 O ® 263 Sg Berkeley + Dubna, 1974
Bohrium Bh 107 267 Bh: 17 s., 272 Bh: 10 s., ... 209 Bi + 54 Cr ® 262 Bh
249 Bk + 22 Ne ® 266 Bh
SUJV Dubna, 1976
Hassium Hs 108 269 Hs: 27 s., 270 Hs: 3.6 s., ... 208 Pb + 58 Fe ® 265 Hs GSI, 1984
Meitnerium Mt 109 278 Mt: 8 s., 276 Hs: 0.2 s., ... 209 Bi + 58 Fe ® 266 Mt GSI, 1982
Darmstadtium Ds 110 281 Ds: 10 s., 279 Ds: 0.2 s., ... 208 Pb + 62 Ni ® 269 Dt GSI, 1994
Roentgenium Rg 111 282 Rg: 2 min., 281 Rg: 17 s., ... 209 Bi + 64 Ni ® 272 Rg GSI, 1994
Copernicium Cn 112 285 Cn: 29 sec., 283 Cn: 4 sec., ... 208 Pb + 70 Zn ® 277 Cn GSI, 1996
Nihonium Nh 113 (formerly Ununtrium Uut)
286 Nh: 20 sec., 285 Nh: 5 sec. 287.8 Uup ( a ) ® 283.4 Nh SUJV April, 2003
Flerovium FI 114
(formerly Ununquadium Uuq)
289 FI: 2.6sec., 288 FI: 0.8 sec., ... 244 Pu + 48 Ca ® 291 FI SUJV Dubna, 1998
Moscovium Mc 115 (formerly Ununpentium Uup)
285 Mc: 0.22 sec., 288 Mc: 0.088 sec., ... 241 Am + 48 Ca ® 187.8 Mc Dubna + Berkeley, 2003
Livermorium Lv 116
(formerly Ununsextium Uus)
293 Lv: 0.06 sec., 290 Lw: 0.02 sec., ... 248 Cm + 48 Ca ® 292 Lv Berkeley + Dubna, 1999
Tennesine Ts 117 (formerly Ununseptium Uus)
294 Ts: 0.05 sec., 293 Ts: 0.02 sec., ...   Dubna 2010
Oganesson Og 118 (formerly Ununoctium Uuo)
294 Og: 0.7 msec. 208 Pb + 86 Kr ® 293 Og
249 Cf + 48 Ca ® 294 Og
Dubna, Berkeley 1999,2006
Note : For reasons of space in the column "Production", the production reaction are write only very simplified and do not include the particles emitted during the reaction (usually neutrons, electrons, or a particles).
The physical properties of transurans used in practice are described in more detail in the conclusion of §1.4 "Radionuclides", passage "Transurans".

All TRU disintegrate by a -radioactivity, the heavier ones also by spontaneous fission. Alpha-decays, event. combined with b- decays, followed by several in a row, until this decay chain hits one of the 4 nuclides: thorium 232Th, uranium 238U, uranium 235U or neptunium 237Np. Further decay then continues with one of the 4 standard decay series shown in Fig.1.4.1 in §1.4 "Radionuclides".
E.g. 241Am ® a + 237Np ® 7 a + 4 b + 209Bi - neptunium decay series; 239Pu ® a + 235U ® 7 a + 4 b + 207Pb - 235U - actinium decay series; 252Cf ® a + 248Cm ® a + 244Pu ® a + 240U ® b + 240Np ® b + 240Pu ® a + 236U ® a + 232Th ® 6 a + 4 b + 208Pb- thorium decay series; analogously other transurans.

Chemical properties of transurans
From the point of view of classical chemistry, it can be expected that the chemical properties of transurans should correspond to their position in the Mendeleev periodic table, determined by proton number Z.
For lighter transuraniums with Z from 93 to 103, it was verified that their basic chemical properties actually correspond to their position in the relevant columns of the periodic table. However, ruthefordium (104) and dubnium (105) showed differences in chemical behavior (Rf in solution reacts similarly to plutonium or samarium and Db exhibits protactinium-like behavior; whereas according to the periodic table they should behave like the elements hafnium and tantalum, located just above them). Seaborgium (106) and bohrium (107) behave as tungsten and rhenium according to chemical experiments, in concordance with the periodic table.
   We can prepare superheavy transurans only in very small trace amounts, sometimes only a few nuclei. They are often very unstable and break down into lighter elements in a fraction of a second. It is therefore very difficult to investigate their chemical properties. The usual method of analytical chemistry cannot be used here: to put a substance in a test tube and observe how it reacts with other chemicals, usually in a "wet" way in solution. The methods of current expression chemical analysis make it possible to investigate the properties of isotopes with a lifetime longer than about 1 second. For the newly discovered most heaies elements, however, it may be an express analytical "chemistry of one atom".!..
   In short-term heavy transurans we are able to observe fragments of their nuclear decay, which carry information about the physical properties of these nuclei. Investigating the chemical properties of atoms of these elements nuclear physicists and chemists try to do with complicated experiments. The surface of the target, maintained at very low temperature, is covered with a coating of selected chemicals. Depending on the coating to which the affinity of the resulting atoms of the investigated transuran is observed, their chemical behavior is judged. Spectrometrically can measure the properties of the performed chemical reaction
(here so far achieved not convincing results...).
Different chemical properties of heavy transurans ? 
It is expected that the principle of similar behavior of elements in the same column of the periodic table may be disrupted for very heavy atoms due to relativistic effects. With a high number of protons, the electric charge of the nucleus is high, which also leads to a high velocity of electrons on the internal orbitals. In heavy transuranics, the inner electrons reach orbital velocities that are already approaching the speed of light (they become "relativistic"), so the effects of the special theory of relativity are beginning to apply here. The inertial mass of the electrons increases, which (together with the relativistic contraction of the lengths) causes a decrease in the size (shrinkage) of the internal orbitals *).
*) At Z> 170, electron collapse could even occur from the K-shell to the nucleus (there it combines with protons - cf. §1.2, passage "Electron capture (EC)"), so these superheavy nuclei (if they can exist at all?) probably can't form atoms...
   Reducing the radius of the inner orbitals results in an increase in the electrical "shielding" of the positive charge of the nucleus by these electrons, so that more distant electrons (no longer relativistic) are attracted to the nucleus by less force. External orbitals, especially valence ones, are less bound to heavy atoms than would correspond to a conventional non-relativistic quantum model of an atom. And also the energy distance between the external levels is smaller. There is less electrical cohesion between the nucleus and the shell of less ionizing energy for the electrons in the outer valence shell. The relativistic quantum mechanical effects thus cause changes in the structure of the atomic shell, whereby the atoms of very heavy elements may behave chemically differently than we would assume based on their proton number and location in Mendeleev's periodic table.
   E.g. the last known transuran oganesson
(Z = 118) is included in the noble gas column; therefore, it also received the traditional suffix "on", it was assumed that it would be another even heavier radioactive gas after radon. However, due to the above differences, it is expected that it will actually have a higher reactivity, it will not be an inert gas, but will also have metallic properties and form oxides and halides ...
   If other even heavier transurans are discovered, their proton numbers will only be formal, as their chemical properties will be different, not corresponding to the position in the relevant column of the table..! .. From the point of view of chemistry, however, this is irrelevant, because these superheavy nuclei decay so fast, that their volatile atoms are not enough to form any compounds...

Fusion of atomic nuclei. Thermonuclear reactions.
The second way
(as opposed to the fission discussed above) to obtain energy in nuclear reactions, is the synthesis - connection, merging, fusion - of light element nuclei into heavier elements. A large amount of binding energy is released, because medium-heavy nuclei have a much higher binding energy of nucleons than light nuclei, see a very steep increase in the binding energy curve in Fig.1.3.3 (this picture is presented here again for clarity) in the area of light nuclei :

Fig.1.3.3. Dependence of the mean binding energy E
b/one nucleon on the nucleon number N of the nucleus. In the initial part of the graph, the scale on the horizontal axis is slightly stretched to better see the differences in binding energy for the lightest nuclei. The right part schematically shows both ways of releasing the binding energy: the splitting of the heavy nucleus and the merging of the two light nuclei.

The most energy efficient and at the same time the easiest to implement (with the lowest activation energy) are fusions of light nuclei 1H, 2H, 3H, 3He, 6Li, in which a helium nucleus 4He is usually formed, which has a particularly high binding energy between light nuclei, see the ascending part of the graph in Fig.1.3.3. There are several reactions to the synthesis of the lightest nuclei :

2 H 1 + 2 H 1 ® 3 He 2 (0.8MeV) + 1 n 0 (2.5MeV) Þ total yield 3.13 MeV
2 H 1 + 2 H 1 ® 3 H 1 (1.0MeV) + 1 H 1 (3.0MeV) Þ total yield 4.03 MeV
2 H 1 + 3 H 1 ® 4 He 2 (3,5MeV) + 1 n 0 (14.1MeV) Þ total yield 17.6 MeV
1 H 1 + 3 H 1 ® 4 He 2 (19.9MeV) Þ total yield 19.9 MeV
2 H 1 + 6 Li 3 ® 4 He 2 (11.2MeV) + 4 He 2 (11.2MeV) Þ total yield 22.4 MeV

For energy use, the most promising reaction so far is between deuterium (D º 2H1) and tritium (T º 3H1) :
2H1 + 3H1 ® 4He2 + 1n0 + 17.6 MeV ,
which takes place most easily of all (at the lowest energy ~ temperature) and releases a considerable amount of energy; the released energy is carried away in the form of their kinetic energy by neutrons (14.1 MeV) and helium nuclei (3.5 MeV).
   Compared to nuclear fission, the nuclear fusion has great principal advantages :

If we can effectively manage the process of thermonuclear fusion and be able to use it energetically, humanity will forever get rid of its dependence on fossil fuels and gain access to a practically unlimited source of clean (low-emission, carbon-free) energy.
   The only downside is that
we are not able to do that yet make..!.. - at least not in a way that can be used for energy production.
Thermonuclear reactions in stars <-- versus --> in terrestrial conditions: 10 times higher temperature than in the stars ! 
We try to imitate the production of energy in the stars to some extent
(it is analyzed in detail in §4.1 "Gravity and evolution of stars", part "Evolution of stars" - "Thermonuclear reactions inside stars" monograph "Gravity, black holes and space-time physics"). In the interior of stars, during their formation (from a protostar), the first thermonuclear reactions can take place at temperatures of about 1 million degrees. The main thermonuclear reactions of the synthesis of hydrogen nuclei to helium then have been going on for many millions and billions of years at temperatures around 10 million degrees. This is due to the fact that the massive gravity compresses huge masses of thermonuclear "fuel", hydrogen, to high densities and during this adiabatic compression it heats them to temperatures around 106 degrees, at which these densities fusions of hydrogen nuclei with low volume intensity (cca 300 W/m3), but sufficient overall intensity can already take place to cover the vast radiant energy of stars.
   However, in our terrestrial conditions, we do not have the massive gravity or accumulation of huge amounts of thermonuclear fuel, so we must "overcome" the conditions in the stars - reach ten times the temperature than inside the stars
(see also the discussion "Thermonuclear fusion inside the stars" below), so that in our small volumes of sparse plasma, sufficiently intense thermonuclear fusions took place for energy use. That's why it's so difficult! Below we will show the ways in which we try to realize this difficult task in terrestrial laboratories ...

Thermonuclear reactions
How to realize core merging? In order for the two nuclei to merge, they must approach each other at a distance of
»10-13 cm, where attractive nuclear forces begin to act. In doing so, they must overcome the Coulomb electric repulsive forces acting between consistently positively charged nuclei, which they can realize only by their accelerating to large kinetic energies - by supplying high activation energy. For experimental purposes, this can be achieved with an accelerator (eg bombarding a tritium target with accelerated deuterons), but the amount of nuclei thus combined will be negligible and most of the supplied kinetic energy of the accelerated beam will be converted into a heat which heats the target (due to electrical Coulomb collisions, which are much more likely than nuclear collisions); the input energy will always be significantly higher (by many orders of magnitude!) than the output energy (obtained). To carry out nuclear fusion and obtain nuclear energy on a macroscopic scale, there is only one way to achieve the required activation energy: to carry out the reaction at a very high temperature - hence the name thermonuclear reaction. Heating the fuel to a sufficiently high temperature will cause the kinetic energy of the thermal motion of the atoms of the reacting fuel to increase to such an extent that it is sufficient to overcome the electrostatic repulsive barrier between the fuel nuclei and the synthesis of the nuclei can take place due to the attractive strong nuclear interaction (so far, hypothetical alternatives are briefly discussed below in the section "Alternatives to Nuclear Fusion").
 Temperature for realization of thermonuclear fusion
In order for a nuclear reaction to occur, the nuclei must approach each other at a distance rs » 10-13 cm, where attractive strong nuclear interactions begin to act. This requires a relatively high kinetic energy EC which overcomes electrostatic repulsion barrier (Coulomb potential "hump") between two nuclei with charge Z1.e and Z2.e : EC = Z1.Z2.e2/rs . Between two hydrogen nuclei with the proton number Z1=Z2=1 there will be a barrier height EC » 1MeV. A temperature higher than 1010 degrees would be required to thermally reach such a value of the mean kinetic energy of the nuclei. Achieving such a high temperature in the macroscopic volume of plasma in laboratory terrestrial conditions is not realistic. However, there are two favorable circumstances that significantly reduce the minimum temperature required for the effective formation of fusion reactions :
Tunnel effect , thanks to which there is always a certain non-zero probability that the Coulomb barrier will be overcome by a particle whose energy is lower than EC (this probability of overcoming for a particle with energy E is approximately PE ~ exp[(EC/E)] ); see §1.1, section "Quantum nature of the microworld", passage "Quantum tunneling").
Maxwell statistical distribution *) at the thermal motion of the particles shows that there is always a certain number of particles moving at substantially higher speeds than the mean kinetic energy <ET> = 3/2 .kT.
*) Maxwell-Boltzmann statistical distribution of thermal motion of particles
Particles of idealized "gas" in this case, hydrogen ions of mass m , is constantly moving, and colides, each of which has a different instantaneous speed v , direction of movement and different kinetic energy E = m.v2/2, which are randomly and erratically changing due to collisions. The distribution of velocities and energies of random motion of ideal gas particles is described by the so-called Maxwell-Boltzmann distribution function P , determining the probability of the number of particles in the state with velocity v : P(v) = 4p.(m/2pkT)3/2.v2.exp(-mv2/2kT), or equivalent with energy E : P(E) = 2p.(1/2pkT)3/2.v2.exp(-E/kT), where T is the thermodynamic temperature and k is the Boltzmann constant (expressing the relationship between temperature and energy of gas particles: it is the amount of kinetic energy of one particle, which corresponds to a change in gas temperature by 1 °K; it has the value k = 1.38.10-23 JK-1). The graph of this distribution function is a wide "bell-shaped" (but asymmetrical) curve, the shape of which depends on the temperature: the higher the temperature, the wider the shape of the curve and its maximum is shifted towards higher energies and velocities. The maximum of the curve determines the most probable velocity vp = Ö (2kT/m), but from a physical point of view the more important is the mean square velocity of particles vk = Ö (3kT/m), which corresponds to the mean kinetic energy of particles at temperature T: <E T > = 3/2.kT. When converted to nuclear power units [eV], the mean energy of 1eV particles corresponds to a temperature of 11600 °K, so that a temperature of 1keV represents 11.6 million degrees. With temperature T , not only does the mean value of velocity or energy <E T > increase, but also the relative proportion of particles with high velocity and energy E >> <E T > increases.
   Due to these two circumstances (and under the conditions of a high effective cross-section of the respective reactions), even in sparse plasma, thermonuclear reactions between the lightest nuclei can take place relatively efficiently from temperatures of »1.5.108 degrees.
Analogy of chemical combustion and thermonuclear fusion
  Nuclear fusion is a "nuclear analogy" of chemical fusion of atoms, such as conventional combustion (fusion with oxygen). The fire is ignited only when the external supply (activation) energy reaches the necessary ignition temperature, the kinetic energy of atoms overcome the barriers of the electrical repulsive forces and the atoms closer together so they may be sharing valence electrons and form electro-chemical linkage (as discussed in §1.1, section "Interaction of atoms"). This releases the bond energy; if it is higher than the supplied energy, the reaction is exothermic and can already maintain the required temperature on its own - burning continues. The frequency of individual reactions is so high that the energy released is sufficient to cover the energy losses in the system.
  Similarly, to ignite nuclear fusion, it is necessary to first supply the activation energy - to reach a high temperature, in this case almost a million times higher than with chemical combustion. On the other hand, the energy released during nuclear fusion is more than a million times higher than during chemical fusion. If at least part of this released energy is kept in the reaction space, the required high temperature can be maintained and the "fusion combustion" can continue. Due to the high energy efficiency, nuclear fusion suffices with incomparably less "fuel" than fire and produces only a small amount of "flue gas".
  The composition and pressure of the atmosphere here on Earth create suitable conditions for chemical combustion, which can lead to the risk of fire or explosion. However, for nuclear fusion, there are natural conditions only in the center of the stars
(see below "Thermonuclear reactions in stars", or "Thermonuclear reactions inside stars"). Under terrestrial conditions, nuclear fusion "combustion" is very difficult to perform, in high-temperature plasma - either isolated by a magnetic field or briefly created by intense irradiation. This difficulty, on the other hand, ensures that controlled nuclear fusion is a safe process. If the fusion reaction comes into contact with the substance under terrestrial conditions, it cools immediately and stops (a special exception is the uncontrolled explosive thermonuclear fusion mentioned below, which, however, can only be induced in terrestrial conditions by an explosive fission nuclear reaction; an explosion on a macroscopic scale cannot occur with the energetically use of fusion).
  The reacting deuterium and tritium (thermonuclear "fuel") must therefore be heated to a temperature of min. »108 degrees. At such a temperature, each substance is in a state of fully ionized plasma - all atoms are decomposed into free electrons and bare nuclei; these nuclei can then collided sharply and merge with each other.
Plasma - 4th state of matter
At high temperatures, in an electric discharge or by the action of ionizing radiation, electrons are ejected from the gas atoms and the atoms themselves become positive ions. Such a partially or fully ionized gas is called plasma
(Greek plasma = formable, malleable material; the electric discharge copies the shape of the tube and its shape is easily influenced by electric and magnetic fields). Plasma is sometimes referred to as the 4th state of matter (1st solid, 2nd liquid, 3rd gas, 4th plasma). In order to distinguish this ionized substance from other situations with electrically charged particles, we require two additional properties in the physical definition of plasma :
- Electrical neutrality on a macroscopic scale (on average the same number of electrons and positive ions) - we do not consider charged particle beams to be plasma;
- Collective behavior caused by a long-range interaction of sufficiently close charged particles - it is not a very dilute or weakly ionized gas by plasma.
  Thus, the general physical definition of plasma is: "Plasma is a set of particles with free charge carriers that is globally neutral and exhibits collective behavior". This definition also includes exotic forms of the substance, such as quark-gluon plasma
(§1.5, passage "Quark-gluon plasma -"5th state of matter" ").
  Plasma has significant electrical properties: it is electrically conductive, it reacts to a magnetic field, it can generate electric and magnetic fields on its own, complex electro- and magneto-dynamic processes take place in it. It is these phenomena that are very important for achieving the conditions of the thermonuclear fusion described below in tokamaks.
  In ordinary terrestrial nature, plasma occurs relatively rarely in atmospheric discharges, lightning. From a global perspective, however, plasma is a very important form of matter - most of the observed substance in the universe is in the plasma state.
  Plasma is characterized mainly by two quantities :
- Plasma density n , which is the number of ions in a unit of volume [m-3].
- Plasma temperature T, measured either in the temperature scale [°C], [°K], or equivalent in units of kinetic energy [eV], [keV] of particle motion. The mean energy of 1eV particles corresponds to a temperature of 11600 °K, so that the temperature of 1 keV is 11.6 million degrees.
  Electrons and ions in neutral plasma act on each other by electric Coulomb forces. As the electrons move relative to the ions, the Coulomb force will pull them back, acting as a "return force". In the field of electric forces, electrons and ions can perform longitudinal harmonics - plasma oscillations, the frequency of which (circular frequency
w = 2p f) depends on the plasma density n, on the charge and on the mass of the particles. Electron plasma frequency wpe = (n.e2/me.eo)1/2 is significantly higher than the ion plasma frequency wpi = (n.e2/mi.eo)1/2, because the mass of ions mi is at least 1750 times greater lower than the mass of electrons me.
  The situation where the plasma is in a magnetic field is important for carrying out a controlled thermonuclear fusion. When charged particles move, a Lorentz force acts on them here perpendicular to the direction of movement, as a result of which the particles they rotate around magnetic field lines - they perform so-called gyrooscillations or cyclotron oscillations with the Larmor frequency given by the charge of the particle q, its mass m and the intensity of the magnetic field B:
wc = q.B/m. The electron cyclotron frequency wce = e.B/me is again significantly higher than the ionic cyclotron frequency wci = e.B/mi .
  In addition to these "pure" oscillations and frequencies, "mixed" so-called hybrid oscillations are also considered in plasma physics, which are the result of the interaction between the oscillations of ions and electrons. The lower hybrid frequency
wLH = [(wci.wce)-1 + wpi-2]-1/2 is a combination of the cyclotron ionic frequency wci and electron wce (their geometric diameter) and the ion plasma frequency wpi (at stronger magnetic fields, the contribution wpi is negligibly small). Upper hybrid frequency wUH = (wpe2 + wce2]1/2 is a quadratic combination of electron plasma wpe and cyclotron wce frequency.
Language note: The word "plasma" has two main meanings: 1. Physical - ionized gas; 2. Biological - a component of blood (blood plasma), in cells the protoplasm or cytoplasm.

Explosive thermonuclear reactions
Similar to fission nuclear reactions, fusion thermonuclear reactions can take place in an uncontrolled (explosive) or controlled (steady) manner. Unlike the fission of heavy nuclei discussed above, thermonuclear fusion does not result in a chain reaction because the heat and pressure produced are not sufficient to trigger further fusion
(except perhaps the thermonuclear chain reaction in a nova explosion where strong gravity interacts - see "The role of gravity in and evolution of stars", section"Thermonuclear reactions"). The conditions for a nuclear fusion must be ensured from the outside: high temperature and pressure + maintenance of high-temperature plasma in the reaction volume for a sufficiently long time - either inertially by explosion or by a strong magnetic field (see below), or gravity in the stars.
Fusion thermonuclear weapons 
Uncontrolled explosive thermonuclear reaction is the essence of the misuse of nuclear fusion in thermonuclear weapons, also called the "hydrogen bombs"
(there is a fusion reaction of hydrogen isotopes - deuterium and tritium). We cannot carry out a "pure" thermonuclear explosion in terrestrial conditions (perhaps with the exception of the "thermonuclear microexplosion" of a small D-T capsule using powerful laser irradiation - see "Inertial Fusion" below). The energy of a fission nuclear charge must be used to compress and heat the thermonuclear fuel to the fusion temperature.
  The fission charge and the fusion material are placed right next to each other inside the solid envelope
(pictured right). A mixture of tritium and deuterium (most often formed from a compound of lithium and deuterium LiD) with a nuclear detonator (explosive fission reaction 235U or 239Pu - actually by the explosion of a smaller "atomic bomb" - was described above in the section "Atomic nuclear fission", passage "Uncontrolled chain reaction - nuclear explosion") compresses rapidly and heats to a temperature of about 100 million degrees, which causes an explosive thermonuclear reaction for releasing many times more energy than a fission "atomic bomb".

Basic principles of construction with the activities of fissile and thermonuclear nuclear weapons
Left: Fission nuclear bomb (two different constructions)                            Right: Thermonuclear bomb

The first experimental thermonuclear explosions used a mixture of liquid deuterium and tritium, which is not usable for military purposes. In military thermonuclear warheads, a compound (hydride - deuteride) of the lighter isotope lithium with deuterium 6Li 2H is used as an explosive "charge" and plutonium as a detonator. When the detonator explodes by chain fission of plutonium, a large amount of neutrons is formed, which in lithium deuteride react 6Li (n, a )3H converts lithium to tritium. At the same time, the energy released by the nuclear fission of the igniter compresses and heats the resulting reaction mixture to the temperature required for the subsequent D+T fusion. The first thermonuclear bomb was developed in 1951 by E.Teller and S.Ulam with collaborators in nuclear laboratories in Los Alamos.
  The design of thermonuclear warheads was later improved to a three-layer system. In addition to
6Li 2H and plutonium, they also contain a mixture of gaseous deuterium and tritium surrounded by plutonium and beryllium in the upper layer. In the center of the fission stage is a small amount of deuterium-tritium gas, which during the explosion produces neutrons by fusion reaction, inducing more efficient fission of uranium or plutonium ("boosting") in this first degree. The thermonuclear stage then includes a housing made of uranium-238 ("depleted uranium") and a fissile 239Pu rod. This is because thermonuclear fusion produces a huge amount of high-energy neutrons, which are able to fission 238U (which is not otherwise a fission material for slow neutrons), which further increases the energy yield of the explosion; however, it also causes large radioactive contamination with fission products ...
  A special variant of a thermonuclear weapon is the so-called neutron bomb *) , which uses penetrating neutron radiation, created by the explosion of a small thermonuclear charge.
*) Neutron weapon: The miniature explosive thermonuclear reaction was designed for military abuse in the so-called neutron bomb. LiD (a solid-state lithium-deuterium compound) is most commonly used as a thermonuclear explosive, and 239-plutonium is a fissile detonator. The addition of beryllium leads to the intensive production of neutrons by reactions (
a, n). It was designed as a tactical radiation weapon against "living force", with a suppressed destructive effect.
  Fortunately, destructive thermonuclear weapons have never been used in military operations. However, incomparably more powerful thermonuclear explosions (compared to which our nuclear weapons are just "baby capsules") occur in universe. It's in the so-called nova and supernova explosion - see §4.1 "The role of gravity in the formation and evolution of stars", section "Thermonuclear reactions", passage "Late stages of stellar evolution", in the book "Gravity, black holes and space-time physics".

Controlled thermonuclear reaction
Peaceful use of thermonuclear energy is possible only if controlled thermonuclear fusion will be realized - to construct a thermonuclear reactor. In order for such a thermonuclear reaction to take place, two basic conditions need to be ensured :

Conditions for Sustaining Nuclear Fusion and Positive Energy Yield - Lawson's Criterion
For energy recovery, we need to achieve an energy gain - that the thermonuclear reaction produce more energy than it needs to generate and heat plasma and compensate for energy losses by radiation and plasma leakage. Or, that the fusion power P
f exceeds the required energy input P: Pf/P ³ 1. For the successful course and use of thermonuclear fusion, certain very demanding criteria must be met for plasma density, temperature and holding time of sufficient temperature to ignite the fusion and for the duration of the reaction, the existence of hot plasma was not dependent on external heating; this is a basic prerequisite for a fusion reactor with a positive energy yield.
   Consider the unit volume (eg 1cm
3) of a high-temperature plasma in an active thermonuclear zone of temperature T , containing the number n1 and n2 of both light nuclei (mostly deuterium and tritium, ie n1 = nd , n2 = nt) prepared in volume unit for fusion. Under equilibrium, the ion density is equal to the electron density. Total energy density W the kinetic energies of electrons and ions are W = 3n.kB.T, where kB is the Boltzman constant and n is the total particle density. For the density of the particles are in relation n1.n2 = 1/4 .n2 for a mixture of deuterium and tritium and n1.n2 = 1/2 .n2 for pure deuterium plasma.
  In principle, the following important phenomena will take place in this test unit volume :
J Fusion reaction with volume rate (density, reactivity) f = n1.n2.<v. s>, at which nuclear fusion energy with (density of) power Pf = n1.n2 . <v.s>. ef is released, where v is the average collision rate of light nuclei, s (T) is the nuclear effective cross section of the fusion reaction at temperature T and ef is the energy released in one fusion reaction; <> denotes the averaging over the Maxwell velocity distribution at temperature T.
L Energy losses of Pdam in the plasma cloud due to two mechanisms :
1. Photon radiation by electrical interactions of electrons - bremsstrahlung
(§1.6, part "Interaction of charged particles") or cyclotron radiation (in the presence of a magnetic field). In the inner parts of the plasma cloud, this photon radiation is re-absorbed. The photon radiation of a hot plasma cloud (its power) is given by the approximate relation Prad = 1.4.10-34.n e2 .T1/2 [W/cm3], where ne is the number of electrons in a unit volume (electron density of the plasma ).
2. Leakage of particles from the active zone - transfer of kinetic energy of plasma particles (especially electrons) to the environment, heat conduction, with power density P
cond (when analyzing the inner regions of the plasma cloud, it is usually neglected, but in the peripheral parts it is crucial). In the most commonly used Deuterium+Tritium fusion reaction, considerable energy is also carried away by fast neutrons, which no an electric charge and are not held back by a magnetic field. However, these neutrons can subsequently be used to obtain thermal energy and to produce tritium in reaction with lithium.
  Energy losses cause the plasma temperature to drop rapidly if energy is not replenished and the fusion reaction to stop. The holding time
tE [s] of the plasma energy (at a temperature higher than the critical fusion temperature) depends on the energy losses Pdam from the plasma cloud. If these losses are not compensated, tE ~ W/Pdam .

Fig.1.3.7. Dependence of some important quantities for thermonuclear fusion D-T and D-D on energy E
~ plasma temperature T.
Left: Interaction effective cross section
s of thermonuclear reactions depending on the kinetic energy of nuclei. Middle: Dependence of the mean value of the parameter <v. s > fusion reactivity (reaction rate) on plasma temperature. Right: Temperature dependence of the minimum value of the product of the plasma electron density ne and the holding time tE according to the Lawson criterion; value of n.tE the plasma must lie above the plotted curve of the given reaction in order for the fusion self-heating to exceed the energy loss.

To maintain the fusion reaction, part of the energy obtained Pf must be used to heat the plasma and compensate for energy losses by radiation and conduction to satisfy condition h.(Pf + Prad + Pcond) l Prad + Pcond , where h is the efficiency conversion of all three forms of energy to plasma heating. Thermal energy in plasma can be supplemented by two mechanisms :
a) Fusion self-heating directly from the products of fusion - 100% -absorbed absorbed kinetic energy E
q of released charged particles, especially alpha - helium nuclei (neutrons escape from the core and do not contribute to plasma self-heating): f.Eq. For the deuterium-tritium reaction, Eq = 3.5 MeV, for D-D fusion, Eq = 1MeV. Self-sustaining fusion reaction occurs when fusion heat exceed the loss of energy in the plasma F.eq ³ Pdam, which for D-T fusion makes: 1/4 .n2 <v. s > .E q ³ 3n.kB,T/tE; this can be rewritten in the form of an inequality for the product plasma density and holding time of its supercritical temperature: n .tE ³ (12/Eq). (kB T)/<v. s > º L (L is the Lawson factor). This is one of the three variants of the so-called Lawson's criterion *) of the sustainability of thermonuclear fusion. It is graphically shown in Fig.1.3.7 on the right. Size T/<v.s> is a function of temperature and for the D-T reaction it has a minimum at a temperature of about 25 keV (300 million degrees), which gives the numerical Lawson criterion n.tE ³ »1.5.1020 s/m3.
*) A detailed analysis of the kinetics and energy balance of thermonuclear fusion in 1955-57 was mainly dealt with by J.D.Lawson, who derived important requirements for the formation and maintenance of thermonuclear fusion, now called Lawson's criterion (similar results were reached independently by Soviet experts P.L.Kapica, L.A.Arcimovic and col.). It requires that the energy obtained by the fusion be greater than the energy expended in creating and maintaining the fusion, by means of the minimum product of the density of the thermonuclear fuel and the time for which the density and temperature are maintained at the value required for the fusion to proceed.
b) Electric heating supplied by recirculation of part of the electricity produced in the reactor (described below in the section "Tokamaks"). With the total efficiency h of the conversion of individual forms of energy into plasma heating, the Lawson criterion has the final form: n.tE l 3kB.T/a.{[h/(1-h)].<v.s>.ef - T1/2}, where the coefficient a=1/4 for a mixture of deuterium tritium, a=1/2 for pure deuterium, at the same concentration of nuclei n.
  For a more complex analysis of the fusion reaction, it is preferred that the Lawson product is explicitly temperature of plasma T is also included. Thus, the "triple" product L (Lawson's) of plasma density n (number of ions/m3), its temperature T (measured either in temperature degrees Kelvin or Celsius, or in kinetic energy of particles [keV]) and time tE [s ] maintaining its supercritical energy :
          L = n. t E .T ³ (12 / E q ). (k B T 2 ) / <v. s > = c crit ,
which must be higher than a certain critical value c
crit - generalized Lawson's criterion. For the D-T reaction, the minimum of the triple product is around 14 keV, which gives the numerical Lawson criterion n.T.tE l »3.1021 keV.s/m3.
  All these conditions are only approximate and idealized. For the D-T reaction, the value of ccrit ~5.1021 s.keV.m-3, assuming that the released thermonuclear energy (vs. loss energy of radiation and escaping particles) is returned to the plasma with an efficiency of about 33%. At ion temperatures T » 2.108 °C, for D-T reaction, the product of plasma density and retention time must be n.TE ³ 0.5.1020 m-3 s .
  For example, at a plasma temperature significantly lower than about 10
8 °K, the frequency of fusion reactions would be too low at the densities used, at higher temperatures (>200 million degrees) the energy losses from the plasma increase significantly.
  Lawson's criteria place drastic limitations on the ability to achieve energetically positive thermonuclear fusion - in terms of our capabilities, these are extreme requirements. Above all, it is difficult to reach very high temperatures of hundreds of millions of degrees, 5-6 orders of magnitude above the ignition temperature of chemical fuels. No material can withstand these temperatures, so high-temperature fusion fuel needs to be thermally insulated  complex physical methods described below. Furthermore, it is necessary to achieve a sufficiently long time maintenance of the supercritical plasma temperature against energy losses and plasma scattering. Unfortunately, we do not have the powerful gravitational forces that control fusion in stars
(see "Thermonuclear reactions in stars" below) . And our technical capabilities are not yet sufficient for the energy use of thermonuclear fusion..!.. Lawson's criteria have not yet been met for existing thermonuclear plants, even though the JET instrument is approaching them. They should be met by the forthcoming ITER tokamak (see below).
   Thus, in order to carry out a "successful" thermonuclear fusion, it is necessary, in addition to a sufficient temperature T, in principle to achieve a sufficiently high product of the plasma density and the holding time n.TE > ccrit . According to this criterion, it is not necessary to achieve high values for both parameters n and TE, it is sufficient to focus on the achievement of a sufficient value for one of them :
- Achieving high values of density of plasma is oriented technique inertial confinement of plasma using concentrated energy pulses of the laser, by which the plasma is pressed to n »1029 cm3 - for a short time. The holding time is very short tE » 10-9 s, it would work in pulse mode.
- To prolong the holding time by the method of magnetic retention and to close the movement of plasma particles in a tokamak or stellarator. The plasma density used here is relatively low n » 5.1017 cm-3, but the retention time tE tries to reach the order of a few seconds.
Both of these methods will be discussed in more detail below :

Possibilities of technical implementation of controlled thermonuclear fusion
Attempts to carry out a controlled thermonuclear reaction proceed in two fundamentally different ways according to the method of maintaining the required temperature and density of the reaction plasma cloud
(some alternative methods will be discussed below) :

¨ Inertial fusion - inertial retention of plasma ,
  in which rapid local heating of a small volume of nuclear fuel results in the formation of very hot and dense plasma and thermonuclear fusion on a small scale, before this fuel can be explode to the environment by thermal motion. The plasma is not held by any external force field, but simply by its own mechanical inertia. For a short time (approx. 1 ns) they are maintained by the "inertial resistance" of the mass to acceleration, by its inertia the plasma remains compressed in its original place for a certain sufficient time. The principle of this method
(whose not very apt name arose from the use of inertia and the law of action and reaction) is shown in Fig.1.3.8 left. A small capsule of nuclear fuel, containing several milligrams of D+T, is irradiated from several directions simultaneously by high-power pulses of radiation from lasers or particle beams (Phase A). The absorption of this radiation leads to a sudden heating of the surface layer of the capsule (so-called ablator), which evaporates rapidly and expands into space. Due to the law of action and reaction, this rapid expansion of the evaporated ablation layer results in rapid compression, implosion, of the inner part of the capsule D+T - the effect of a "spherical rocket engine" - Phase B. The inside of the capsule should be briefly compressed to a central density of about 200g/cm3, with a simultaneous sharp rise in temperature (adiabatic effect). If the temperature in the middle exceeds the ignition temperature, the fuel will "ignite" thermonuclearly and the wave of thermonuclear "burning" will rapidly spread to other parts of the fuel. In a strongly compressed and adiabatically heated plasma inside the capsule, thermonuclear fusion of D and T can occur - a kind of "thermonuclear micro-explosion" (Phase C), in which up to about 30% of the amount of D+T mixture can fuse to 4He and flying-out neutrons no. Helium nuclei and neutrons fly out with high kinetic energy, for a total of 17.6 MeV/1 fusion.
   It is very important to ensure instantaneous perfectly isotropic homogeneous irradiation, so that the capsule is compressed as symmetrically as possible. This is not easy to achieve with several independent lasers, so a single default laser is used, whose light is split into multiple beams, amplified and directed at the target. Neodymium lasers are mainly used in the current experiments for primary high-performance irradiation of inertial fusion fuel with a large number of beams (often more than 100). It shines at a wavelength of 1.054 mm (infrared region), in the final phase the conversion to the 3rd harmonic 0.351 mm (ultraviolet region) is usually performed. A short power pulse is obtained by powering from a charged capacitor batery. The priming laser beam is divided into a plurality of beams (channels) which are passed through laser amplifiers consisting of a series of glass plates with neodymium admixture. These plates are irradiated with xenon lamps that excite neodymium. As the laser beam passes, stimulated deexcitation occurs, amplifying the laser beam. The laser beams thus amplified are then guided from many different directions into a reaction chamber, in the center of which they converge into a capsule with nuclear fuel.
   Recently, attempts to make an additional "rapid ignition" (Fast Ignition) thermonuclear fusion: compressed implosion plasma stage (Stage B obr.1.3.8 left) is subsequently irradiated with radiation from a short burst of high power laser beam to a diameter of concentrated
»1 mm, where the intensity is approx. 1017 W/cm2. The absorbed energy strongly increases the temperature in the center, which can lead to a more efficient ignition of the thermonuclear fusion. This can save energy for the primary irradiation of the capsule.
On the ablator material specific requirements are placed, especially high ablation rate and good absorption of radiation from lasers, low reflectivity and high opacity. Plastic materials
(possibly doped with germanium), beryllium (possibly with an admixture of copper), high-density carbon (prepared by the method of production of artificial diamonds) are tested.
   The method of direct energy supply to the nuclear fuel target according to Fig.1.3.8 on the left is referred to as "directly driven inertial fusion". In order to achieve the required pressure and temperature in the center, high demands are placed on the homogeneity, symmetry and isotropy of energy absorption from the external rays. Therefore, experiments are being made with so-called "indirectly driven inertial fusion", where the capsule with the fuel is placed inside a suitable package (made of a material with a high atomic number, eg gold) - in a hollow tube *), the inner walls of which are irradiated with laser beams through openings at the end; sources converted to soft X-radiation in thermal equilibrium, acting isotropically a capsule with fuel.
*) This reaction vessel is sometimes called "hohlraum" (from german cavity). This method is probably only a makeshift laboratory solution that will probably not be applied when other attempts energy utilization inertial thermonuclear fusion ...
   A thermonuclear reactor based on this principle of inertial fusion ICF (Inertial Confinement Fusion) would operate in a fast pulse mode, where the focus of the laser beams would be in small capsules of nuclear fuel (D+T) were thrown in quick succession, and synchronous triggering of lasers would induce thermonuclear fusion in each capsule. Furthermore, it would be necessary to solve the removal of the released energy from the reaction space (cooling technique); the main part of the energy carried by neutrons would be drawn by cooling the envelope (blanket) of the reaction chamber, made of neutron absorbing material (beryllium or lithium - similar to tokamaks, see below).
   Currently, the two largest experimental devices for laser inertial fusion are operating :
- NIF (National Ignition Facility) at Lawrence Livemore National Laboratory in California, USA, completed in 2010. It consists of 192 laser channels.
- LMJ (Laser MegaJoule ) in Le Barp near Bordeaux in France, completed in 2006, has 256 laser beams.
Both of these devices achieve a cumulative energy of laser beams of 1800 kJ with a pulse length of 5-15 ns and a peak power of 360 TW.
   We are still very far from the creation of a thermonuclear power plant, that would be able in inertial fusion microreactions to release energy covering its entire necessary energy input and produce additional energy. Inertial fusion will probably never be used in terrestrial energetics. Much further in this direction is the method of magnetic plasma containment using tokamaks, described below. However, the future use of inertial thermonuclear fusion of deuterium and helium-3 *) to propulsion of interstellar rockets is being considered - cf. below "Nuclear Propulsion of Space Rockets"..?..
*) Unstable tritium with a half-life of 12 years does not occur in space. However, helium-3 is found on some planets from where it could in principle be extracted, along with deuterium.

Fig.1.3.8. Two basic methods of controlled thermonuclear fusion.
Left : Simplified principle of inertial fusion and the course of thermonuclear micro-explosion.
Right : Simplified tokamak schematic diagram.

¨ Magnetic holding and closing of high-temperature plasma ,
   which is performed in so-called tokamaks (Fig.1.3.8 on the right). The tokamak *) consists of a toroidal working chamber placed in a strong magnetic field inside a coil wound around the chamber in a toroidal arrangement. The lines of force of this toroidal magnetic field run along the long circumference of the toroid. This whole toroidal system is further "threaded" on the ferromagnetic core of the "transformer", the primary winding of which, wound on the core in the axis of the toroidal system, is supplied with alternating current. Single "secondary circuit thread"
(as if connected in "short circuit") of this transformer forms a ring of high temperature plasma inside the working toroidal chamber. Plasma has good electrical conductivity, so a strong electrical current it induces in it (for larger devices even several million amperes). This electric current both causes induction heating of the plasma to a very high temperature (approximately 10 million degrees), and also creates a magnetic field in the so-called poloidal direction with lines of force directed along the shorter circumference of the tube. The entire tube is further surrounded by external coils of the poloidal field, which shape the plasma and contribute to the equilibrium of forces in the plasma. By combining the stronger toroidal and weaker poloidal components of the magnetic field, "helical" slowly twisting lines of force of the resulting magnetic field are created, within which plasma particles can move along closed paths. This result in the magnetic closure of charged plasma particles into the center of the toroidal working tube.
*) The word "tokamak" originated as an abbreviation of the name "toroidalnaja kamera s magnitnimi katuškami" - toroidal chamber with magnetic coils. The device was developed as early as 1951 by a team led by A.O.Lavrentev, A.D.Sacharov, I.E.Tamm and L.I.Arcimovic in Kurchatov's nuclear laboratories in the USSR.
   These two mutually perpendicular magnetic fields - toroidal and poloidal - form a kind of "magnetic vessel" inside the toroidal plasma chamber or a "trap" in which Lorentz forces acting on moving electrically charged plasma particles (D and T cores) hold the resulting plasma in the toroid axis and do not allow immediate escape of the particles by thermal motion to the chamber walls *). The plasma seems to "levitate" in the tube space, and during the working cycle, the hot plasma is kept at a sufficient distance from the walls of the tube
(the temperature of the chamber walls should not exceed 1000 °C) **). If this time of magnetic retention of the plasma, heated to a sufficiently high temperature, is sufficiently long relative to its density, conditions for the nuclear fusion of D and T nuclei can occur in the tokamak chamber (in accordance with the above Lawson criterion).
*) The compression of a discharge in the plasma by magnetic forces into a thin strand is referred to as a "pinch-effect" ( pinch - pressing, clamping, constriction ). It is commonly observed in spark discharge, lightning, solar protuberances.
**) In some tokamaks, a poloidal limiter is used - an annular aperture defining the cross-section of the plasma to reduce the thermal load on the tube wall.
Equilibrium of plasma and magnetic field in a tokamak tube 
The basic mechanism of magnetic plasma retention is magnetohydrodynamic phenomena in an ionized substance, in which the pressure gradient is given by the Lorentz force, determined by the product of the (vector) electric current density and the magnetic induction. At equilibrium, the pressure gradient in the plasma is then perpendicular to the lines of force of the magnetic field and also perpendicular to the direction in which the electric current flows. Constant pressure surfaces, determined by the directions of the electric current and the magnetic field, are created in the plasma. Under simplified conditions, the equilibrium arrangement of the magnetic field and plasma can be described by electrodynamics of a continuum with free charge carriers (such a description was made in 1958-66 by H.Grad, H Rubin and V.D.Šafranov in radial coordinates with toroidal symmetry). In fact, plasma drifts and magnetic field expansion occur in the toroidal tube, leading to an additional vertical toroidal electric current (described in 1962 by D.Pfirsch and A.Schlüter). In practice, the situation is much more complicated, the turbulence of heat transfer and particle in plasma is applied. ....
A separate variant of tokamak are so-called stellarators (Stellar generator - "star generator", developed by group of L.Spitzer in the USA), which do not have a central primary winding and in which all components of the magnetic field are generated by intricately configured external coils. Stellarators probably not be used as energy thermonuclear reactors in future, but they are of considerable experimental importance. They make it possible to model in more detail the different shapes and courses of magnetic fields and their influence on the behavior of high-temperature plasma in terms of thermonuclear reactions.
Sferomak, Dynamak 
Other methods using special magnetohydrodynamic phenomena are also tested due to currents generated inside the plasma itself
(these are phenomena similar to the coronary loops of the Sun or relativistic jets from accretion disks). It is tested in experimental facilities called Spheromak. ......... The combination of electric currents inside the plasma and their magnetic fields results in closed magnetic field lines that can maintain the shape of the plasma ring without the need for or with the minimization of strong external electromagnets. This would allow the construction of simpler and less expensive fusion devices than tokamaks. This method is being developed in the laboratories of the University of Washington, and the experimental instrument has been given the working name Dynamak .... .
Tokamak duty cycle 
Tokamak operates in cyclic pulse mode. At the beginning of the cycle, "fuel", D+T gas with a density of about 1015-18 particles/cm3, is filled into the evacuated toroidal chamber. Then an electrical voltage is applied to the primary winding of the "transformer" from a very powerful ("hard") source. With an induced current of many thousands to millions of amperes, the plasma is heated rapidly to about 107 degrees, while being maintained in the toroid axis by the magnetic field.
Induction heating - ohmic
If an electrical voltage U
prim is applied to the primary winding of a tokamak, an electric current Iprim begins to flow, which changes with time according to the exponential dependence Iprim(t) = (Uprim/Rprim).(1 - e-t.Rprim/Lprim), where Rprim is the total active resistance of the primary circuit (sum of the resistance of the turns of the primary winding and the internal resistance of the source) and Lprim is proper primary winding inductance. This rapidly increasing current through the primary winding generates a rapidly increasing magnetic field B(t) in the direction of the toroid. According to Faraday's law of electromagnetic induction, an electromotive force will be induced inside the tube along the toroid Utor = -dF/dt = -S.dB/dt, where F(t) = B.S = Lprim.Iprim is the magnetic flux through the surface S of the toroid. In the gas charge of the toroid, due to electric forces, free electrons *) begin to accelerate, which ionize the gas with shocks (avalanche process). A electrical discharge will be gerated and a current Iplasm = Utor/Rplasm will flow trough the plasma, where Rplasm is an electrical (ohmic) resistance of the plasma. The ionized gas plasma in a toroidal-tube starts quickly heated by the Joule heat of power P = Rplasm .Iplasm2. It is an ohmic or resistance heating with induced current.
*) There is a small amount of electrons and ions in each gas due to natural radiation. When using a mixture of D + T, a large amount of electrons and ions is formed due to the radioactivity of tritium. In experiments with a neutral gas (eg pure H), it is appropriate to initiate the initial weak ionization by electron injection.
   With a sufficiently powerful supply of the primary winding, the plasma in the toroidal tube is inductively heated to a temperature of approx. 10
7 degrees within a few milliseconds. With increasing temperature T increases the degree of ionization and decreases the electrical resistance of plasma (Rplasm ~ T-3/2) - inductive heating is no longer effective. At this point, for the next required temperature increase, additional heating - non-inductive - must start from external sources :
Additional hybrid heating of plasma - non-inductive
Additional non-inductive plasma heating can be performed in two basic ways :

Electromagnetic waves of high frequencies - microwaves, which are absorbed in plasma, vibrates charged particles and its energy is converted into thermal motion of electrons and ions in the plasma. Frequencies from about 20 MHz to many GHz are used. The absorption of electromagnetic waves are most effective, when their frequency resonates with some natural oscillations in the plasma. One such oscillation is the so-called cyclotron rotation particles (ions and electrons) along magnetic field lines with (Larmor) frequency given by the charge of the particle, its mass and the intensity of the magnetic field. In a typical tokamak with magnetic field of about 4-8 T, deuterium ions have a cyclotron frequency in the range of about 20-60MHz. Plasma heating using microwaves with a frequency of ion rotation in a magnetic field is called ICRH (Ion Cyclotron Resonance Heating). Electrons, which are about 4,000 times lighter than deuterium ions, have much higher cyclotron frequencies - of the order of 100 GHz. The method of heating plasma using microwaves with this high frequency of electron rotation in a magnetic field is called ECRH (Electron Cyclotron Resonance Heating). Particulalarly effective is heating with microwaves of about 70-200 GHz excited in gyrotrons (their principle is described in §1.5, passage "High frequency generators"). The so-called hybrid frequencies arising from the combination (geometric average) of electronic and ionic cyclotron frequencies are also used. Their values lie between the ionic and electron cyclotron frequencies; the use of microwaves of the so-called lower hybrid frequency for non-inductive excitation of toroidal current in plasma is mentioned below. Such radio frequency waves could provide both additional heating of the plasma and the generation of an electric current in the plasma to generate a poloidal magnetic field.
¨ By injecting neutral accelerated particles - atoms which transfer their kinetic energy by collisions with plasma particles and thus increase the temperature. The particles must be neutral so that the strong magnetic field in the tube "lets" them into the interior of the plasma. Generating intense neutral beams of fast atoms is not easy. We cannot accelerate neutral particles, so it is necessary to first accelerate charged ions (hydrogen, deuterium, or tritium) in a high voltage field to an energy of about 100keV - 1MeV and then neutralize these accelerated ions by passing through a gaseous medium. From the point of view of neutralization, it seems more advantageous to accelerate the negative ions, which are more easily neutralized when passing through a gaseous medium (by strip- interaction by electron detachment). The use of accelerated heavy ions also seems promising (eg cesium ions were tested).
   After reaching the ignition thermonuclear temperature (min. 108 °C), part of the energy released by the plasma fusion reactions it further heats the plasma - "self-heating" occurs and thermonuclear fusion can continue "alone". The fusion reaction is able to maintain the required temperature if the power released by the fusion covers self-heating and energy losses. When this "burning plasma" is reached, the external heating can be reduced or switched off.
If the primary winding of the tokamak "transformer" is connected to a DC voltage source, the magnetic flux in the core soon saturates, the electromagnetic induction disappears and the plasma current ceases - the poloidal field disappears and the plasma begins to escape from the center of the tube towards the walls. This problem can be solved in two ways :
1. By quickly reversing the polarity of the power supply of the primary winding, which restores the induction in the opposite direction.
2. By applying high-frequency electromagnetic waves of a frequency of several GHz (approx. 2-5 GHz) in the tangential direction to the plasma. With proper synchronization, the electrons will be accelerated - "dragged" - at the wavefront (similar to the linear accelerator - LINAC), creating an electric current in the toroidal direction, generating the required poloidal magnetic field. This method of non-inductively exciting the plasma current by microwave radiation is sometimes referred to as LHCD (Lower Hybrid Current Drive); the name is related to the use of the so-called lower hybrid frequency lying between the above-mentioned ionic and electron cyclotron frequencies (ICRH, ECRH - is their geometric average). At this frequency, a component of the electric field parallel to the magnetic field will accelerate the electrons moving along the field lines.
   In addition, the so-called bootstrap curent can be applied : Due to the variable plasma density, a current in the toroidal direction is automatically generated, which can contribute to the formation of a poloidal field. It is an internal process that takes place spontaneously without external excitation.
   After completion of a given cycle of fusion reaction, the particles remaining after reaction (helium, remaining D and T, impurities formed by the action of plasma to the tube walls) are pumped out by means of a divertor, located around the circumference at the bottom of the tube. The device is then ready for the next cycle. In the case of continuous operation, it would be necessary to ensure the continuous removal of the reaction products.
Divertor - "plasma cleaner" - consists of collecting plates that capture helium atoms, unburned hydrogen and impurities released from the walls of the tube (or penetrating leaks into the vacuum tube). The basic toroidal magnetic field is modified so that the magnetic field lines at the outer edge of the plasma ring direct the plasma particles into the region of the divertor. The ions are captured here on the collecting plates and recombined into neutral atoms. The gas generated in this way is sucked out of the divertor area by powerful pumps and discharged (it is a kind of "exhaust gas" from the reactor). The effluent atoms of the unburned hydrogen fuel are separated from the helium "ash" and impurities and can be reused for fusion. The divertor is highly thermally stressed and must be intensively cooled. In large tokamaks with a suitably shaped magnetic field, thermal and radiation stress can be reduced due to the relatively long path of the "waste" plasma particles from the edge of the plasma ring to the divertor region; the plasma simply cools to such an extent that electrons and ions recombine into neutral atoms before they reach the surface of the collecting plates.
   Part of the fusion of the released energy heats the walls of the tube and the divertor (drained by coolant), most are carried away by high-energy neutrons, which are not captured by the magnetic field or the tube wall, but by the reactor envelope - blanket - water-cooled material containing beryllium. Instead of beryllium, the use of lithium 6,7Li seems promising here, which would not only be a neutron absorber, but by neutron absorption, lithium would be converted to tritium *) (as discussed above), which would make it possible to obtain and burn the most difficult to obtain fuel component (and in addition radioactive) - tritium T º 3H1 in a closed circuit (Fig.1.3.8 right).
*) A sufficient amount of tritium here can be obtained by a cascade of two reactions:
1. The neutron hits the lithium 7nucleus, creating a tritium ion and a neutron (endothermic reaction);
This secondary neutron strikes the nucleus of the lithium isotope 6 and produces a second tritium ion.
All this tritium needs to be collected with high efficiency and introduced into the plasma in the reaction tube. A suitable material for a tokamak blanket could be a eutectic LiPb lithium-lead alloy.

   From the point of view of energy utilization, the energy yield Q is important, which is the ratio of energy obtained from fusion to energy that needs to be supplied to excite magnetic fields and create high temperature plasma :
         Q = [thermonuclear power] / [external power to create and maintain plasma] .
   In previous smaller experimental tokamaks, if they achieved fusion at all, the energy yield was very low, Q <0.01. Newer large devices already achieve a yield of about 0.6 (JET). For practical use in energy, it is necessary to significantly exceed the profitability limit - Q >> 1; the planned ITER should have a Q » 10.

Design development of tokamaks
The construction arrangement of tokamaks has undergone a number of technical modifications and improvements since their inception. E.g. the cross-section of the plasma toroidal tube is no longer circular or elliptical, but a cross-section of a shape similar to the letter "
D", with a straight part adjacent to the central electromagnet, has proved to be more advantageous; this shape better copies the actual configuration of the constant magnetic flux surfaces in the poloidal cross-section of the tube, which is established as a result of magnetohydrodynamic processes. In the lower part of the chamber, the collector plates of the divertor are arranged around the perimeter for the capture and removal of reaction products and unwanted impurities. The former manual control of tokamaks has been replaced by fully electronic regulation all phases of the cycle, using computer control and simulations.
   We are also working on the possibility of replacing the current pulse mode with a continuous mode: deuterium and tritium *) would be fed into the reaction tube, where the high-temperature plasma would be maintained permanently, the helium ions formed would be separated out. However, superconducting electromagnets are a prerequisite for continuous operation, as conventional copper coils make it possible to maintain the fusion reaction for only a few seconds without overheating. The possibilities of using reactions other than D+T are also being considered, which, however, would usually require an even higher plasma temperature
(discussed below).
*) Refueling hydrogen inside the hot plasma ring in a continuous mode encounters technical difficulties. During normal filling of atoms, due to the high temperatures in the tube, the atoms are rapidly ionized and a strong magnetic field prevents them for the necessary penetrating into the center of the tube. Hydrogen fuel must therefore be injected at a high speed of a few km/s, either in the form of gas, or small capsules of frozen hydrogen (which can reach the central region of the hot plasma before it evaporates).
   High technical demands are placed on the wall material of the working toroidal tube :
¨ High mechanical strength ;
¨ High thermal resistance (>1000 °C), including resistance to rapid temperature changes, good thermal conductivity and cooling capability ;
¨ High radiation resistance, especially to intense neutron flux (energy 14 MeV), as well as low effective cross section for nuclear reactions causing activation (formation of radioactive elements in the material) ;
¨ Gases should not be released from the inner wall material, which could break the vacuum inside the tube, contaminate the plasma and violate the conditions for proper fusion.
   Special composite materials based on tungsten, carbon, beryllium are used, with a special coating of the inner wall, which comes into direct contact with hot plasma. Alloys of tungsten, tantalum, vanadium and chromium with special quaternary crystallization, which show high temperature and radiation resistance, are also tested. The inner wall can be covered with graphite, or coated with beryllium.
   The largest tokamak to date is the JET device (Joint European Torus), built in collaboration with several european countries in Abingdon (
Oxfordshire), UK, with a main toroidal tube radius of 2.96 m. It is capable of producing a thermonuclear power of 4 MW for 4 seconds, with efficiency Q»0.62.
Large Tokamak ITER 
Currently, a project of a new and improved considerably larger tokamak ITER (International Thermonuclear Experimental Reactor *) is gradualy realized, in partnership with the European Union and several economically strongest countries in the world
(being built in the south of France), which will have more than twice the diameter of the toriod chamber (6.2 m). More than 20 powerful microwave generators - gyrotrons (described in §1.5, passage "High frequency generators") will be placed around the perimeter of the working toroidal chamber, providing additional non-inductive heating of deuterium-tritium plasma.
*) One of the Latin meanings of the word iter is the path - we believe that it will be the right path for the technological mastery of thermonuclear energy..!..

All electromagnets will be here superconducting (physical principles of superconducting magnets are briefly discussed in §1.5, section "Electromagnets in accelerators", section "Superconducting electromagnets"), which will significantly reduce the consumption of electrical energy to excite the magnetic fields. This thermonuclear reactor will therefore already have a positive energy yield - will be able to release more energy than the energy supplied (Q » 10). There will also be examined by the above production technology of tritium from lithium (fusion reaction with neutrons, as described above) in a closed cycle.

Difficulties and perspectives of thermonuclear fusion
In the 60.-70. years when many successes were achieved in improving the tokamaks, there was general optimism. Most nuclear physicists were convinced that thermonuclear fusion would be successfully mastered and technically exploited by the end of the 20th century.
I remember as a student of the Faculty of Mathematics and Physics in the 1970s that our professors and we students were then convinced that after 2000, "obsolete fission nuclear reactors" will be shut down and energy in power plants will be obtained in thermonuclear fusion reactors...
   However, further experiments, in an effort to maintain a sufficiently hot and dense plasma for thermonuclear fusion for a longer period of time, began to encounter serious difficulties. One of the main problems is plasma instability - its oscillations and turbulence, leading to too high heat diffusion in the plasma and thus to large energy losses, shortening the retention time of thermal energy inside the plasma.

Simply put, plasma "has no desire to submit to us": the hotter the plasma we create and the harder we compress it, the more it "hinders" our efforts to keep it; finds a way to "burst" to the sides ...
   The time of holding the thermal energy inside the plasma can be increased in basically two ways : 

Greenwald's plasma density limit in tokamak
In tokamak experiments, it is observed that the plasma becomes uncontrolled - it expands beyond the magnetic fields that keep it in the tokamak tube - when its density rises above a certain limit. Based on a series of experiments on several tokamaks, M. Greenwald in 1988 set an upper limit of plasma density n
Gw , above which it can no longer be magnetically held in a tokamak tube: nGw [1020m-3] = Ip /p.a2 , where Ip is the plasma current [MA], a is the smaller tube radius [m].
   This Greenwald limit represents an unfavorable circumstance caused by a number of factors - radiation losses, discontinuities in the peripheral parts of the plasma, differences between power input and radiation transport processes, released impurities
(such as carbon and tungsten) into the tokamak plasma from divertors and limiters, higher thermal conductivity of dense plasmas (heat losses may exceed energy input - thermal quenching may occur).
   Overall, the Greenwald plasma density limit is due to the same effects that affect the energy balance in the plasma environment in the toroidal tube - mentioned above. Additional hybrid plasma heating in newer tokamaks may increase the Gw density limit. Some recent experiments further show that plasma can maintain a stable higher density, if is increasing the performance of the fusion reaction. This could increase the achievable power of large tokamaks..?..
Increase performance and retention time. L-mode and H-mode of the tokamak
In an effort to increase the power P in the tokamaks, the retention time
tE (roughly as tE ~ P-1/2) began to decrease due to greater turbulence. However, in experiments with medium-sized tokamaks, it was observed that increasing the power at a certain value significantly suppressed the turbulence in the plasma. This is a beneficial phenomenon which increases the efficiency of magnetic confinement, and retention time tE. This mode has been called H-mode (high confinment mode) and the normal mode (preceding this mode) is called L-mode (low confinment mode). ...
   In addition to the spontaneous onset of H-mode, other methods of increased plasma retention in the tokamak are being tested. Increased power and hold time can also be achieved by fine-tuning the current and electrical profile of the pulse (in feedback), which creates internal transport barriers to plasma fluctuations. Also, specific hybrid heating scenarios have a stabilizing effect on plasma by reducing transport processes leading to losses and turbulence.

Serious technical problems that can stand in the way of energy use of thermonuclear fusion are associated with thermal and radiation stress of the walls of the toroidal tokamak tube (especially very strong neutron flux) and the surrounding blanket, their cooling and heat transfer to the electric generator - unfortunately it won't work without steam yet *)....
*) The theoretical exception could be special neutron-free fusion reactions, where the fusion energy is carried away by charged particles, which could be - at least in principle - used for direct conversion to electrical energy, without the need to convert via heat - is briefly discussed below in the passage "
Neutron-free fusion".
   The custom ignition of a thermonuclear reaction may be the easier part of the whole problem of fusion energy utilization ! We do not yet have materials capable of withstanding high temperatures and intense bombardment by high-energy nuclear particles (subatomic stress). New materials with significantly improved thermal, mechanical and radiation properties will need to bedeveloped, and a new technical solution for the liquid blanket is being considered, where the solid materials of the blank enclosing the fusion chamber would be replaced by liquid materials (lithium-containing), which would circulate and thus transfer heat well, effectively cool the chamber and the necessary tritium could be separated from them.
  The magnetic field in a tokamak must be generated in superconducting electromagnets
(the physical principles of superconducting magnets are briefly discussed in §1.5, section "Electromagnets in accelerators", section "Superconducting electromagnets"), so that the energy for its generation does not exceed the energy obtained during fusion. Appropriate cryogenic systems, operating at temperatures close to absolute zero, are located in close proximity to plasma heated to hundreds of millions of degrees! In addition, neutrons adversely affect the superconducting materials of the coils. How to insulate heat-radiation these lowest and highest temperatures what can we imagine?
   A major problem with D-T fusion may be the recovery of tritium
3H, which, unlike deuterium, is very rare in nature (we cannot yet create the conditions for the fusion of deuterium itself or the other reactions mentioned below). We have presented nuclear reactions that allow a thermonuclear reactor itself to "produce" the necessary tritium - D-T (-Li) cycle. Inside the envelope (blanket) of the reaction tube or vessel, there will be channels with lithium, which will capture neutrons and form helium and the necessary tritium, drained channels and after separation injected back into the reaction space (Fig.1.3.8 right). In each fusion reaction, one tritium nucleus is consumed and one neutron is formed. Each neutron flying out of the reaction tube must produce at least one tritium nucleus - otherwise the system will soon run into a tritium deficit (it will consume more tritium than it will produce) and D+T fusion will no longer be maintained. This can only be achieved through a series of two reactions: In the first reaction, the neutron hits a 7Li nucleus to form both a tritium and a flying neutron (this is a slightly endothermic reaction). The released secondary neutron during its flight in the blanket then hits the 6Li nucleus and produces a second tritium nucleus (+ helium; it is an exothermic reaction). All the tritium formed in this way must be collected with almost 100% efficiency and reintroduced into the reaction. Together with the fact that not all neutrons will participate in the required reactions (some of them always escape or be swallowed differently) , this is a difficult problem to solve ...
   Experiments on previous tokamaks, especially on JET, have already contributed to solving many problems. Much is expected from the forthcoming ITER project , which perhaps could be completed around 2040 in southern France and the experimental stage could take min. 20 years. It should be followed by the DEMO tokamak and then the energy thermonuclear reactors. Therefore, if there is no happy turnaround (finding new advantageous technical solutions), the beginning of the energy use of thermonuclear fusion can be expected in the best case only in the second half of the 21st century.
   The second basic pathway studied, inertial fusion, is still at an even earlier stage of development than tokamaks. Instead of the necessary fast sequence of fusions, experiments are currently being carried out with individual laboriously and expensively prepared D+T fuel capsules. Until the routine production of a large number of cheap fuel capsules is mastered, inertial fusion cannot compete with tokamaks
Alternative options for nuclear fusion
Electrical acceleration and plasma retention - fusors
In addition to heating nuclear fuel to a very high temperature, light nuclei can be accelerated to effect their fusion using an electric field. A certain advantage of this method is that, in addition to accelerating the nuclei, it directs their movement, so that instead of accidental movement during thermal collisions, there is a targeted collision of the nuclei "against each other". When directing the chaotic movement of fuel particles, we do not have to reach such high energies ~ temperatures as with tokamaks, smaller and simpler devices will suffice. A device that uses an electric field to accelerate and collisions ions under conditions suitable for nuclear fusion is called a fusor. The first prototype fusor was designed in 1964-67 by P.T.Fransworth and R.L.Hirsh. The fusor is basically a large vacuum tube with two spherical concentric electrodes made of wire mesh, the cathode is inside the anode. Fill the flask with a dilute fuel mixture (D+T). The voltage between the outer and inner electrodes causes ionization and then accelerates and at the same time directs the movement of the fuel ions towards the center. Accelerated ions fly through the cathode wire mesh on all sides and collide at the center, which can cause nuclear fusion in a non-thermal manner. There are the inertial electrostatic plasma retention (IEC
- inertial electrostatic confinement).
   The internal electrode (cathode) causes certain problems with fusors, on the wires of which a large part of the ions terminate, and due to bombardment by these fast particles, the electrode material degrades rapidly. An improved variant of fusors is called polywell
(the name originated as an abbreviation of the Greek polyhedron = polyhedron and English well = well, pit - here a potential pit). It does not have an internal metal electrode, instead a strong magnetic field is applied by means of superconducting coils arranged in a polyhedron, most often 6 coils arranged as cube walls. Electron nozzles are located in the axes of the coils, high voltage is applied between the coils and the nozzles. Electrons fly out of the electron nozzles towards the center, where they are captured by the magnetic field. The resulting cloud of electrons with a negative charge in the center forms a kind of "virtual cathode" that attracts positive ions. These cores accelerate in the electric field between the coils and the virtual cathode and collide in the middle, with the possibility of mutual fusion.
   So far, it has not been possible to design the fusor device so that it supplies more energy than it consumes by nuclear fusion, or it has at least partially approached this goal. However, the fusors were used as suitable laboratories neutron sources
(cf. §1.5, section "Neutron generators").
Muon catalysis of nuclear fusion
A certain physical way to reduce the repulsive electrical force of nuclei and thus allow fusion at lower temperatures
(with the exaggeration of "cold fusion"), perhaps the use of muons m- (§1.5, section "Elementary particles and their properties"). Negative muons are no different from electrons except for mass and instability, so they can replace them in the electron shells of atoms. This creates so-called mesoatoms (muons were formerly called mi-mesons). The hydrogen mesoatom represents a bound system (p+ m-) in which an electron in a hydrogen atom (deuterium, tritium) is replaced by a muon; on the outside it is electrically neutral. The muon is 207-x heavier than an electron, so it orbits in a much closer orbit around the deuterium nucleus - the better it shields the electrostatic repulsion from another hydrogen nucleus. The size of such mesoatoms will be much smaller than that of atoms (1000 times smaller than a hydrogen atom) and the nuclei may be closer to each other, which would lead (in co-production with the tunneling phenomenon) to an increased probability of merging two of their nuclei even at lower temperatures. After fusion, the muon is released and can enter another mesoatom and catalyze further reactions.
   If muons were stable particles, or at least with a lifespan of the order of milliseconds, muon catalysis would perhaps be a promising option for low-temperature nuclear fusion. However, the muon decays in a few microseconds (
half-life 2.2.10-6 s), so in its short life it may be sufficient to catalyze only a few fusion reactions (roughly 5). In addition, some of the muons may be trapped on the helium nuclei formed during the synthesis and thus be lost from the catalytic circulation. Muons have to be produced in a relatively complicated and energy consumed way in an accelerator. In this situation, the energy required to produce muons would be many times higher than the energy extracted during fusion. The possibility of energy utilization of muon catalysis of nuclear fusion is not yet feasible in practice !
(no) Possibility of cold nuclear fusion?
Occasionally there is speculation about the possibility of "cold" fusion at or near normal room temperatures. In 1989, chemists M.Fleichsman and S.Pons
(University of Utah) described an experiment with heavy water electrolysis using palladium electrodes, which allegedly involved nuclear fusion of deuterium. The fusion reaction should perhaps have been catalyzed in the palladium crystal lattice. They inferred the fusion reaction from a not very convincing calorimetric measurement; their electrochemical laboratory did not have the appropriate detection technique to measure gamma and neutron radiation, which would be a key indicator of fusion. No one else has succeeded in repeating this experiment positively, so practically all experts are absolutely skeptical about it...
   Nuclear physics convincingly shows that cold nuclear fusion is not possible, as it is prevented by large electrical repulsive forces between positively charged nuclei. No chemical or electrochemical methods in any substance can achieve a sufficient proximity of the nuclei to a distance of the order of 10
-13 cm to apply a strong interaction, which only can lead to fusion.
*) Hypothetical possibility of cold fusion in space ?
When speculating about the extremely long-term development of the open universe (§5.6 "
The future of the universe. The arrow of time. Dark matter. Dark energy.", the passage "Open universe" in the monograph "Gravity, black holes and space-time physics"), in the time horizon >>10100 years , the quantum tunneling effect could hypothetically be applied, which with a small probability would help to overcome the strong electrical repulsive barrier between atomic nuclei. In rare cases, spontaneous cold fusion of lighter nuclei into heavier nuclei would occur. This exotic process will forever remain only hypothetical, it will never be possible to verify it experimentally ...
   Instead of "cold fusion", however, according to some opinions, it could hypothetically be possible to realize other reactions, which on a smaller scale could somewhat resemble cold fusion in external manifestations: low-energy nuclear reactions (LENR) taking place primarily with the help of the weak interaction. A certain possibility is to produce neutrons (using very strong alternating electromagnetic fields to achieve the fusion of an electron with a proton to form a neutron), which would be absorbed by suitable atomic nuclei. These nuclei would become beta-radioactive and the energy of the emitted particles could be harnessed..?..
There is a bit of a similar information situation around cold fusion as with perpetuum mobile (or in UFO ). From time to time, sensational news flashes about the success of fraudsters or amateur researchers - "do-it-yourselfers". It usually "fizzle out" soon, but soon others appear. Experts do not usually deal with this, on the refutation of errors or fraud is written only marginally in professional magazines, they do not reach the lay public. Many people are thus convinced of the possibilities and real perspective of cold fusion (or similarly about the functioning of perpetuum mobile or UFO contacts with aliens)...
Hybrid fusion-fission nuclear energy ?
Let's imagine briefly (details are not yet known and are now irrelevant), a bit "futurologically", the situation after the successful management of thermonuclear fusion and its use in nuclear energy. Fission reactors in nuclear power plants will be gradually shut down and replaced fusion thermonuclear. Will the fission reactors be completely abandoned? It is possible that fission nuclear reactions will find their "floor" alongside fusion reactions, or rather the two modalities will coexist or even cooperate. For chain cleavage reaction even in thermonuclear fusion D+T play a major role neutrons. And it is precisely for thoughtful "management" of neutrons that it could be useful to combine the advantages and possibilities of both of these methods of obtaining nuclear energy - to design hybrid fusion + fission nuclear reactors.
   The envelope of a tokamak (or inertial fusion reactor) would contain uranium-238 or thorium-232 in addition to lithium; by interaction of neutrons it would thus produce both tritium for a thermonuclear reactor, as well as plutonium-239 or uranium-233, which would be burned by chain reaction in satellite fission reactors with slow neutrons. This would create an interconnected fusion and fission complex with an optimized neutron balance and a balanced fuel cycle. From the long-term perspective of ecologically "clean" nuclear energy without highly radioactive nuclear waste, however, this solution is probably not entirely optimal... An exception could be complex hybrid systems of thermonuclear-controlled transmutation reactors, ideologically similar to the
ADTT accelerator-controlled reactor technology described above. The "heart" of the system would be a thermonuclear reactor (such as the tokamak of Fig. 1.3.8 on the right), which would not only produce energy, but would also supply neutrons to control the operation of a subcritically operating fission reactor. This reactor would contain both fissile materials (235U, 239Pu, 233U) and 238U or 232Th for transmutation to 239Pu or 233U fissile materials. Neutron-controlled fission would produce energy and at the same time neutron "burned" ("liquidated") hazardous radioactive waste - by converting long-lived radionuclides to stable or short-lived nuclides (as discussed above in the "ADTT" section). However, mastery of these technologies can be expected only in the distant future (the problem is, among other things, the neutron deficit)...
 Other fusion reactions
The possibilities of using reactions other than D+T are also being considered, which, however, would require higher temperatures than we can create so far. These are mainly reactions of combustion of deuterium itself (D-D fuel cycle) :
          D + D ® 3 He + n + 3.3 MeV ,      D + D ® 3 H + 1 H + 4 MeV .
Deuterium in water is a practically inexhaustible supply. In addition, fuel cycles by the reaction of hydrogen and deuterium with lithium, helium-3 or boron-11 could be considered :
          H + 6 Li ® 4He + 3 He + 4 MeV ,      D + 3 He ® 4 He + 1 H + 18.3 MeV ,      H + 11 B ® 3 4He + 8.7 MeV .
Neutron-free fusion reactions - direct conversion to electrical energy ?
In the fusion reactions discussed so far, which are suitable for the energy use of thermonuclear fusion, in particular deuterium-tritium fusion, most of the energy is carried away by neutrons. We cannot use this kinetic energy other than through heat - the old inefficient way of a steam generator, turbine and alternator. In addition, the massive neutron flux causes unwanted radiation and induced radioactivity of the materials. However, there are special fusion reactions (some of which have already been mentioned in several places in this chapter), in which neutrons are almost not formed - the so-called neutron-free fusion reactions. Several such reactions have been investigated, which have a sufficiently high effective cross section :
............ table ......
   In addition to the deuterium-lithium reaction (discussed above in ....), special attention was paid to devoted to proton-boron fusion ..... However, the kinetic energy of the nuclei of about 600 keV is required for its efficient course, which corresponds to a temperature of about 6.6 billion degrees. This is not achievable in a tokamak, but inertial laser fusion pathways are being sought using several carefully synchronized lasers with very short high-energy pulses .......
   Neutron-free fusion produces energy in the form of electrically charged particles
( not neutrons as in most fusion reactions) , mostly positively charged helium 4He++ nuclei and photons. This in principle allows direct electrical conversion of the fusion energy released, without the need for a thermal-steam cycle, which must be used for neutrons. These direct conversions of fusion energy to electric voltage can be based on three basic mechanisms :
- Electrostatic direct conversion uses the kinetic energy of charged particle motion (against electric potential) to create a high positive electric voltage at the collecting electrodes (the opposite effect of electrostatic particle acceleration). This electric potential would generate an electric current in the electrical circuit connected to the electrodes - electrical power.
- Inductive based on changes in magnetic fields during the passage of charged particles. The electromotive force is then electromagnetically induced in the coils.
- Photoelectric energy conversion of electromagnetic radiation (in the field of X, optical and infrared), arising during the acceleration and deceleration of charged particles - braking or cyclotron radiation.
   So  far, these mechanisms have only been tested in small laboratory experiments with artificially accelerated particles and negligible electrical powers...
   Neutron-free fusion reactions would therefore have the advantage of substantially easier conversion of energy into electricity and also in lower induced radioactivity of materials. Some of these alternative fusion reactions are likely to include the distant future of nuclear energy ..?..

The "Holy Grail" of energetics !
Despite all the above problems
(and some others that are likely to arise during development), there is a real hope for the successful implementation of energy-efficient nuclear fusion in the foreseeable future. Then the following optimistic statement will apply :

Thermonuclear fusion: the final solution to the energy problem of humanity
Successful management of controlled nuclear fusion opens up a long-term perspective of obtaining large amounts of nuclear energy without accidents and without hazardous radioactive waste

It would be inherently secure "clean" energy, without carbon emissions, on a large scale, that could satisfy the entire planet. And at the same time save the Earth from a climate catastrophe...
Thermonuclear reactions in stars
What we have tried hardly and so far little successfully in our laboratories, has been happening on a colossal scale for billions of years in nature - in universe. We can see a huge thermonuclear reactor in the sky every day! And on clear nights, we can see thousands of such thermonuclear reactors in the sky and with the naked eye. According to the findings of contemporary astrophysics, each star, including our Sun, is a huge thermonuclear reactor held together by its own gravity - the gravitational pull to shrink the star is balanced by pressure from heating and radiation during thermonuclear reactions inside the star (discussed in detail in §4.1 "Gravity and evolution of stars", part "
Thermonuclear reactions inside the stars" monograph "Gravity, black holes and space-time physics"). At high temperature and high pressure, thermonuclear fusion proceeds very efficiently. Gravity is also a force that maintains equilibrium operation of thermonuclear reactions for a long time (several million to several billion years!): when the reaction begins to slow and the pressure reduced, gravity slightly compresses the core of star, pressure and temperature will increase and reaction starts more quickly; when the reaction starts too accelerate, pressure increase and against gravity the star's core somewhat expanse, whereby the pressure and the temperature is lowered and decreasing the intensity of the nuclear fusion.
   In stars, within the interior of which there is a huge accumulation of densely compressed plasma, thermonuclear reactions between hydrogen nuclei take place sufficiently efficiently *) at temperatures of about 15 million degrees. However, in our terrestrial conditions of a small volume of sparse plasma, ten times higher temperatures are required for the efficient course of fusion reactions ! - that's why it's so difficult ...
*) For stellar conditions, "efficient enough" means a fusion energy output of around 300 W/m3. With a huge volume of hot plasma inside the star, even a small value of power is enough to cover the energy output of the star and ensure thermodynamic balance.
   The perfect control ability of gravity for thermonuclear reactions of stars fails only in the final stages of star evolution, when the basic "fuel" (hydrogen, helium and other lighter elements) is already consumed inside the star, the balance is disturbed, oscillations occur and in the case of material stars, nothing can prevent a "nuclear suicide" of a star: a catastrophic gravitational collapse into a neutron star or even a black hole, with a massive supernova explosion
- see the book "Gravity, Black Holes and Space- Time Physics", §4.2, section "Supernova Explosion. Neutron Star. Pulsars.". A supernova explosion can be considered the biggest "nuclear accident" in the universe!

Possibilities of obtaining energy from matter
At the end of this chapter on nuclear reactions and the possibilities of their energy use, we will roughly compare the efficiencies of individual methods of obtaining energy from matter. We can compare this efficiency with the ideal situation of the conversion of all matter m into energy according to the Einstein relation E = m.c
2, which we assign an efficiency of 100%. From this point of view, the basic methods of obtaining energy from matter will look something like this (numerical values are rounded; a more detailed analysis was given in the picture above - part "Nuclear energy") :

actually available ß      ®  sci-fi
chemical reactions (combustion) fission of heavy nuclei synthesis of light nuclei gravity (rotating black hole) annihilation of electrons and positrons
0.000 000 01% 0.1% 1% max 42% 100%

During chemical reactions (combustion), part of the electrical binding energy of the envelope electrons in atoms is released; this energy of valence electrons is relatively small, but is easily achieved by conventional means in nature. During nuclear reactions (fission of heavy nuclei and fusion of light nuclei), part of the binding energy of the strong interaction of nucleons in the nuclei is released. When gravity is used, part of the gravitational binding energy of matter can be released in the field of a very massive compact object (black holes); however, such objects are not available in near space. We also do not have antimatter available.
   So far, only the first two items in the table are practically used, nuclear fusion will hopefully be used relatively soon (in the order of several decades). There is no hope for the foreseeable future of the use of relativistic gravitational energy of matter collapsing into a black hole, which is a powerful source of energy in quasars
(see §4.8 "Astrophysical significance of black holes" in the book "Gravity, black holes and space-time physics"). The same probably applies to the last item - annihilation (see the relevant discussion in the passage "Antiparticles - antiatoms - antimatter - antworlds" in §1.5 "Elementary particles").

Nuclear propulsion of space rockets ?
The production of electricity is undoubtedly the main benefit of obtaining energy from atomic nuclei. Another area in which it is necessary to supply a large amount of energy in a concentrated manner is the propulsion of space rockets. Chemical rocket engines are now used, in which highly exothermic chemical reactions in the propellant release thermal energy in the form of hot gases (temperature approx. 2000 °C), which rapidly expand outwards in the nozzle, transfer momentum and, as a result of the law of action and reaction, force is created - thrust propelling the rocket forward. Most chemical rocket engines use liquid fuel, where hydrogen or hydrocarbons are burned with oxygen, so the propellant "exhaust" gas is water and carbon dioxide. The specific impulse - thrust - transfer of momentum - is given by the speed of the exhaust gas stream. Current rockets powered by chemical fuel are slow "clumsy snails"
(reaching a maximum speed of approx. 20 km/s), not allowing them to reach more distant space objects in a reasonable time. The use of nuclear energy to propel space rockets could improve this unfavorable situation.
A thermal nuclear rocked
The basic, straightforward variant of a nuclear rocket engine is a nuclear thermal rocket. Here, the chemical energy for heating the exhaust gases is replaced by the heat from the nuclear fission reaction. The working gas, usually hydrogen, is heated to a high temperature (approx. 2500
°C) in a nuclear reactor and fed into a nozzle where it expands and creates thrust. The basic layout is shown in Fig.1.3.11. From the tank with liquid hydrogen, hydrogen is injected by means of a turbine pump into the internal space between the fuel cells of the reactor (where it can also cooperate as a moderator), where by nuclear fission is heated to a high temperature, led into the nozzle and there it rapidly expands.

Fig. 1.3.11. The basic version of the rocket's nuclear drive - hydrogen heated to a high temperature in a nuclear fission reactor is fed into the nozzle.

The significantly more effective ratio between the weight of the consumed fuel and the created accelerating thrust of the rocket is caused by two circumstances here :
--> The source of thermal energy is a long-term operating nuclear reactor, without the consumption of chemical fuel and oxidizer.
--> The "exhaust" gas of a nuclear thermal engine is hydrogen gas with a molecular weight of 2, while for chemical fuels it is water (with a molecular weight of 18) and CO2 (with a molecular weight of 44). Light molecules have more kinetic energy per unit mass, so low molecular weight propellant gases are more effective for thrust than high molecular weight gases. Nuclear thermal engines with gaseous hydrogen propulsion can achieve 3-4 times greater specific thrust impulse (momentum change per unit mass of propellant) than chemical rockets.
   For launching from Earth, when it is necessary to overcome strong gravity, this nuclear drive is not usable, due to the higher weight. So far, the start is only possible with the use of chemical fuel. Nuclear heat engines are suitable for use only in orbit outside the Earth's gravity and further in outer space. Outside of the Earth's atmosphere and in more distant space, there is also no need to address the issue of radiation protection and radioactive contamination
(especially in the case of unmanned flights).
   In addition to the usual fissile material uranium
235U, other radionuclides were also experimentally proposed. Transuranic americium 242mAm is interesting, which has a very high effective cross-section of fission by slow neutrons (thousands of barns) and a low critical mass (approx. 0.1 uranium) --> low reactor weight. It can also maintain a nuclear fission reaction in the form of very thin metal strips less than a micrometer thick, from which high-energy fission products can escape and be used for efficient heating of the exhaust gas to high temperatures, or in principle also for direct rocket propulsion. For laboratory experiments, a small amount of 242mAm is obtained in a nuclear reactor by neutron capture in transuranium 241Am; however, it cannot yet be produced in sufficient quantities for the chain fission reaction.
   In the more distant future, the use of fusion thermonuclear reaction to propel space rockets into distant universe is also being considered. Rather than robust tokamaks, laser-triggered inertial fusion of deuterium and helium-3 could perhaps be used here ..?..
   All concepts of nuclear propulsion of space rockets are still only at the stage of ground laboratory experiments and projects, no such rocket has yet taken off ...

Energy - life - society - little reflection on energy consumption
The functioning of all life is conditioned by energy conversion through complex chemical reactions
(see eg §5.2, section "Cells - basic units of living organisms"). However, man is the only creature on our planet who, in addition to energy, the source of which is food, purposefully uses energy from other external sources. In earlier times, before the era of technical development, it was the use of thermal energy from a fire, in which mainly wood was burned, and to a lesser extent the energy of water and wind (water or windmills). Energy consumption was low and was drawn from sources constantly renewed by nature (perhaps with the exception of ill-considered deforestation); a small part of the energy of solar radiation, transformed by the photosynthesis of plants, is enough for this renewal. With the development of technology (roughly from the 19th century), our energy consumption gradually increased and had to be drawn mainly from fossil fuels - coal, oil, natural gas. These fuels, in which part of the energy from solar radiation, converted and preserved into a chemical form, has accumulated over a long period of time, can easily be converted into thermal energy by combustion and then relatively simply into mechanical and electrical energy. However, fossil fuels are no longer renewed (at least not in our time horizon), their supply is not unlimited and there is a risk of depletion. In addition, a large part of the energy remains unused, due to the imperfection of the technologies used and the fundamental limitations imposed by the laws of thermodynamics. Furthermore, the combustion of these fuels produces a number of undesirable and harmful by-products *). Finally, the question arises as to whether the combustion of non-renewable fossil materials is a sensible conduct, whether it would not be more appropriate to save these substances and use them as chemical raw materials.
*) From a global point of view, it is an increase in the content of carbon dioxide in the air and the related increase in the temperature of the earth's surface ("greenhouse effect"). Many toxic and harmful substances, acidic combustion products, sulfur and nitrogen oxides, heavy metal compounds, etc., also escape into the air when fossil fuels burn, which can have a number of negative consequences for nature and human health.
It is not generally known that a conventional fossil fuel power plant also pollutes the environment with the radioactivity (release of natural radionuclides uranium, radon, and other into the air), much more than a correctly functioning nuclear power plant! During coal combusion into the air released natural radionuclides, especially radon,
222Rn T1/2 = 3.8 days), polonium 210Po (T1/2 = 138 days) and lead 210Pb (T1/2= 22 years), which accumulate at greater depths underground due to the decay of the primary natural radionuclides uranium and thorium.
After all, similar phenomena occur during volcanic activity: the ejected clouds of volcanic smoke and dust contain a significant amount of radionuclides radon, poloniun-210, lead-210, from great underground depths. A large volcanic eruption can be considered, with a bit of exaggeration, a "natural radiation accident" in which the extent of radioactive contamination of the environment is comparable to a nuclear reactor accident (but the isotopic composition and half-lives of contaminants are completely different).
   At the same time, the high pace of drawing energy from external sources today determines all our economic activity and the development of human civilization. Even our current way of life, highly dependent on the use of technology. Energy consumption can be expected to increase further as the Earth's population demands ever higher living standards. The largest part of the world's energy, more than 80%, is drawn from fossil fuels, which, in addition to the risk of depletion, leads to significant pollution of the environment with harmful emissions. Only a small part (approx. 7%) of energy comes from naturally renewable sources - hydroelectric and wind, solar thermal or photovoltaic energy, biomass, etc. Nuclear power from fission reactors currently covers about 8% of global energy consumption.
   We encounter various, often conflicting views on the risks and hopes of these individual types of energy. With regard to the burning of fossil fuels, almost everyone already agrees that this is not a promising way of sustainable development. The importance of naturally renewable resources is sometimes overestimated. So far, we do not have a sufficiently efficient and affordable technology to directly convert sunlight into electricity in large quantities. The mentioned alternative sources, such as hydro and wind power plants, or solar thermal heating, may be a useful and welcome solution at the local level, but from a global perspective they are only auxiliary and peripheral sources.
   The biggest and most tumultuous differences of opinion appear in nuclear energy. Here it is necessary to realize that every human activity has its advantages and disadvantages or risks under certain circumstances. This also applies to nuclear energy. However, for an objective assessment, these advantages and risks need to be assessed in comparison with the advantages and disadvantages of other, non-nuclear, energy sources. In the lay public, this is often not reflected, under the pressure of emotional attitudes, not always sufficiently substantiated by information
(or even deliberate distortion of facts by some groups). The benefits and risks of energy from fission nuclear reactors, where the fuel is uranium *), have been discussed in detail above in the section "Nuclear reactors". Some new and perhaps promising technologies have also been shown there, enabling the processing of hitherto unusable materials (uranium 238, thorium) as well as the reprocessing of nuclear waste and reducing its danger (fast "breeding" reactors, transmutation technologies such as ADTT). Realization this technology could also make fission reactors a reasonable alternative to conventional fuels for many decades.
*) Even heavy natural elements, uranium and thorium, can in a sense be considered "fossil" fuels: more than 5 billion years ago, a small amount of energy was "stored" in the nuclei of these elements by endothermic reactions during the supernova explosion, from whose products our Solar System and Earth were formed. We are now drawing this energy with split the nuclei. The situation is different for light elements, hydrogen + deuterium (coming from the very beginning of the universe), where their fusion into helium releases "new" energy, similar to what stars do.
   However, a truly promising and long-term solution will be the controlled fusion of atomic nuclei, thermonuclear energy
(discussed in detail above in the section "Fusion of atomic nuclei. Thermonuclear reactions."). The fuel efficiency of nuclear fusion is about 100 million times higher than that of chemical reactions (such as combustion). There is enough fuel on Earth to obtain energy in this most efficient way available, so this source could provide an almost unlimited amount of energy even for the distant future. At the same time, this method is not associated with virtually no risk of accident, health hazard or significant generation of unwanted radioactive waste. We are currently throwing hope for the beginning of its use to the second half of the 21st century.
Rational use of energy 
Let's think about the view from the opposite side, saving energy - "the cheapest energy is saved energy". The energy savings resulting multiple paths. From a technical point of view, it is the introduction of modern and efficient technologies. Examples include microelectronic devices with low power consumption, which replacing the earlier machines and apparatus with much higher wattage, or better insulation, optimization technogical processes, etc.
    For reduction in energy consumption would also significally could contribute, if we revise the current strong focus on the consumerist lifestyle and re-evaluated the scale of our life values. Do we really need to buy a new type of luxury car or large-format TV every 2 years, change furniture according to the latest advertisement, build stately villas for many millions, with large halls and many unused rooms, with pools on large lands? Squander millions for fleeting "pleasures" and a false sense of "prestige" and "superiority"? Organizations and companies, insurance companies and banks behave in a similar way, with their exhibition buildings with luxuriously equipped workrooms and offices. We often see a colossal waste of material and energy, an "devouring, greed" that nature cannot bear in the long run. The situation would change, if people came to recognition, that rather than the consumer "to have", greater joy and lasting satisfaction brings us the experience of beautiful unspoiled nature, of discovering new things in nature and the universe, of a work of art, of friendly coexistence with other good peoples. Than chassing after consumer "goods", for which we pay dearly with "our soul" !
   But what we should definitely not miss energy for are global projects of universal significance. What would really raise our level not only materially, but mainly cultural and educational - learning about the laws and phenomena in nature and universe, improving our health, harmonious development of society and improving life in poor areas
(but not just importing consumer goods!). And for what might even save humanity in the future - eg before the fall of an asteroid, a deadly flash of cosmic rays and other threats (see §1.6, passage "Biological significance of cosmic rays", or passage "Astrophysics and cosmology: - human hopelessness?" in §5.6 of the book "Gravity, black holes and physics of spacetime").

1.2. Radioactivity   1.4. Radionuclides

Back: Nuclear physics and physics of ionizing radiation
Nuclear and radiation physics Radiation detection and spectrometry Radiation applications
With cintigraphy Computer evaluation of scintigraphy Radiation protection
Gravity, black holes and space   -   time physics Anthropic principle or cosmic God
AstroNuclPhysics ® Nuclear Physics - Astrophysics - Cosmology - Philosophy

Vojtech Ullmann