Fission of uranium nuclei and chain reaction. Nuclear chain reaction

The theory of relativity says that mass is a special form of energy. It follows from this that it is possible to convert mass into energy and energy into mass. At the intraatomic level, such reactions take place. In particular, a certain amount of mass itself may well be converted into energy. This happens in several ways. First, a nucleus can decay into a number of smaller nuclei, a reaction called “decay.” Secondly, smaller nuclei can easily combine to form a larger one - this is a fusion reaction. Such reactions are very common in the Universe. Suffice it to say that the fusion reaction is a source of energy for stars. But the decay reaction is used by humanity because people have learned to control these complex processes. But what is a nuclear chain reaction? How to manage it?

What happens in the nucleus of an atom

Nuclear chain reaction - a process that occurs during a collision elementary particles or kernels with other kernels. Why "chain"? This is a set of sequential single nuclear reactions. As a result of this process, a change occurs in the quantum state and nucleonic composition of the original nucleus, and even new particles appear - reaction products. The nuclear chain reaction, the physics of which makes it possible to study the mechanisms of interaction of nuclei with nuclei and with particles, is the main method for obtaining new elements and isotopes. In order to understand the course of a chain reaction, you must first deal with single ones.

What is needed for a reaction

In order to carry out a process such as a nuclear chain reaction, it is necessary to bring particles (a nucleus and a nucleon, two nuclei) closer to the distance of the strong interaction radius (approximately one Fermi). If the distances are large, then the interaction of charged particles will be purely Coulomb. In a nuclear reaction, all laws are observed: conservation of energy, momentum, momentum, baryon charge. A nuclear chain reaction is denoted by the symbols a, b, c, d. The symbol a denotes the original nucleus, b the incoming particle, c the new emitted particle, and d denotes the resulting nucleus.

Reaction energy

A nuclear chain reaction can occur with both absorption and release of energy, which is equal to the difference in the masses of particles after the reaction and before it. The absorbed energy determines the minimum kinetic energy of the collision, the so-called threshold of a nuclear reaction, at which it can proceed freely. This threshold depends on the particles that participate in the interaction and their characteristics. On initial stage all particles are in a predetermined quantum state.

Carrying out the reaction

The main source of charged particles with which the nucleus is bombarded is which produces beams of protons, heavy ions and light nuclei. Slow neutrons are produced through the use of nuclear reactors. To capture incoming charged particles can be used different types nuclear reactions - both fusion and decay. Their probability depends on the parameters of the particles that collide. This probability is associated with such a characteristic as the reaction cross section - the value of the effective area, which characterizes the nucleus as a target for incident particles and which is a measure of the probability of the particle and the nucleus entering into interaction. If particles with a non-zero spin value take part in the reaction, then the cross section directly depends on their orientation. Since the spins of the incident particles are not completely chaotically oriented, but more or less ordered, all corpuscles will be polarized. The quantitative characteristic of the oriented beam spins is described by the polarization vector.

Reaction mechanism

What is a nuclear chain reaction? As already mentioned, this sequence is more simple reactions. The characteristics of the incident particle and its interaction with the nucleus depend on the mass, charge, kinetic energy. The interaction is determined by the degree of freedom of the nuclei, which are excited during the collision. Gaining control over all these mechanisms allows for a process such as a controlled nuclear chain reaction.

Direct reactions

If a charged particle that strikes a target nucleus only touches it, then the duration of the collision will be equal to that required to cover the radius of the nucleus. This nuclear reaction is called direct. General characteristics for all reactions of this type is the excitation of a small number of degrees of freedom. In such a process, after the first collision, the particle still has enough energy to overcome nuclear attraction. For example, interactions such as inelastic neutron scattering and charge exchange are classified as direct. The contribution of such processes to the characteristic called “total cross section” is quite negligible. However, the distribution of the products of a direct nuclear reaction makes it possible to determine the probability of escape from the beam direction angle, the selectivity of populated states, and determine their structure.

Pre-equilibrium emission

If the particle does not leave the region of nuclear interaction after the first collision, then it will be involved in a whole cascade of successive collisions. This is actually what is called a nuclear chain reaction. As a result of this situation, the kinetic energy of the particle is distributed among the constituent parts of the nucleus. The state of the nucleus itself will gradually become much more complicated. During this process, energy sufficient for the emission of this nucleon from the nucleus can be concentrated on a certain nucleon or an entire cluster (group of nucleons). Further relaxation will lead to the formation of statistical equilibrium and the formation of a compound nucleus.

Chain reactions

What is a nuclear chain reaction? This is her sequence components. That is, multiple sequential single nuclear reactions caused by charged particles appear as reaction products in previous steps. What is a nuclear chain reaction? For example, the fission of heavy nuclei, when multiple fission events are initiated by neutrons obtained from previous decays.

Features of a nuclear chain reaction

Among all chemical reactions Chain ones have become widespread. Particles with unused bonds act as free atoms or radicals. In a process such as a nuclear chain reaction, the mechanism for its occurrence is provided by neutrons, which do not have a Coulomb barrier and excite the nucleus upon absorption. If a necessary particle appears in the medium, it causes a chain of subsequent transformations that will continue until the chain breaks due to the loss of the carrier particle.

Why is the media lost?

There are only two reasons for the loss of a carrier particle in a continuous chain of reactions. The first is the absorption of a particle without the process of emitting a secondary one. The second is the departure of a particle beyond the volume limit of the substance that supports the chain process.

Two types of process

If in each period of a chain reaction an exclusively single carrier particle is born, then this process can be called unbranched. It cannot lead to the release of energy on a large scale. If many carrier particles appear, then this is called a branched reaction. What is a branching nuclear chain reaction? One of the secondary particles obtained in the previous act will continue the chain started earlier, but others will create new reactions that will also branch. Processes leading to a break will compete with this process. The resulting situation will give rise to specific critical and limiting phenomena. For example, if there are more breaks than purely new chains, then self-sustaining of the reaction will be impossible. Even if you excite it artificially by introducing it into a given environment required quantity particles, then the process will still decay over time (usually quite quickly). If the number of new chains exceeds the number of breaks, then the nuclear chain reaction will begin to spread throughout the substance.

Critical condition

The critical state separates the region of the state of a substance with a developed self-sustaining chain reaction, and the region where this reaction is impossible at all. This parameter is characterized by equality between the number of new circuits and the number of possible breaks. Like the presence of a free carrier particle, the critical state is the main item on such a list as “conditions for a nuclear chain reaction.” Achieving this state can be determined by a number of possible factors. of a heavy element is excited by just one neutron. As a result of a process called nuclear fission chain reaction, more neutrons are produced. Consequently, this process can produce a branched reaction, where neutrons act as carriers. In the case when the rate of neutron capture without fission or emission (loss rate) is compensated by the rate of multiplication of carrier particles, the chain reaction will proceed in a stationary mode. This equality characterizes the reproduction coefficient. In the above case it is equal to one. Thanks to the introduction between the rate of energy release and the multiplication factor, it is possible to control the course of a nuclear reaction. If this coefficient is greater than one, then the reaction will develop exponentially. Uncontrolled chain reactions are used in nuclear weapons.

Nuclear chain reaction in energy

Reactor reactivity is determined big amount processes that occur in its active zone. All these influences are determined by the so-called reactivity coefficient. Effect of temperature change graphite rods, coolants or uranium on the reactor reactivity and the intensity of a process such as a nuclear chain reaction are characterized by a temperature coefficient (for coolant, for uranium, for graphite). There are also dependent characteristics for power, barometric indicators, and steam indicators. To maintain a nuclear reaction in a reactor, it is necessary to transform some elements into others. To do this, it is necessary to take into account the conditions for the occurrence of a nuclear chain reaction - the presence of a substance that is capable of dividing and releasing from itself during decay a certain number of elementary particles, which, as a consequence, will cause the fission of other nuclei. Uranium-238, uranium-235, and plutonium-239 are often used as such substances. During a nuclear chain reaction, isotopes of these elements will decay and form two or more others chemical substances. During this process, so-called “gamma” rays are emitted, an intense release of energy occurs, and two or three neutrons are formed that are capable of continuing the reaction acts. There are slow and fast neutrons, because in order for the nucleus of an atom to decay, these particles must fly at a certain speed.

Nuclear chain reaction

Nuclear chain reaction- a sequence of single nuclear reactions, each of which is caused by a particle that appeared as a reaction product at the previous step of the sequence. An example of a nuclear chain reaction is a chain reaction of fission of nuclei of heavy elements, in which the main number of fission events is initiated by neutrons obtained during the fission of nuclei in the previous generation.

Energy release mechanism

The transformation of the substance is accompanied by the release free energy only if the substance has a reserve of energy. The latter means that microparticles of a substance are in a state with a rest energy greater than in another possible state to which a transition exists. A spontaneous transition is always prevented by an energy barrier, to overcome which the microparticle must receive a certain amount of energy from the outside - excitation energy. The exoenergetic reaction consists in the fact that in the transformation following excitation, more energy is released than is required to excite the process. There are two ways to overcome the energy barrier: either due to the kinetic energy of colliding particles, or due to the binding energy of the joining particle.

If we keep in mind the macroscopic scale of energy release, then all or initially at least some fraction of particles of the substance must have the kinetic energy necessary to excite reactions. This is achievable only by increasing the temperature of the medium to a value at which the energy of thermal motion approaches the energy threshold limiting the course of the process. In the case of molecular transformations, that is, chemical reactions, such an increase is usually hundreds of kelvins, but in the case of nuclear reactions it is at least 10 7 K due to the very high altitude Coulomb barriers of colliding nuclei. Thermal excitation Nuclear reactions have been carried out in practice only with the synthesis of the lightest nuclei, in which the Coulomb barriers are minimal (thermonuclear fusion).

Excitation by joining particles does not require large kinetic energy, and, therefore, does not depend on the temperature of the medium, since it occurs due to unused bonds inherent in the attractive forces of particles. But to excite reactions, the particles themselves are necessary. And if we again mean not a separate act of reaction, but the production of energy on a macroscopic scale, then this is possible only when a chain reaction occurs. The latter occurs when the particles that excite the reaction reappear as products of an exoenergetic reaction.

Chain reactions

Chain reactions are widespread among chemical reactions, where the role of particles with unused bonds is played by free atoms or radicals. The chain reaction mechanism during nuclear transformations can be provided by neutrons that do not have a Coulomb barrier and excite nuclei upon absorption. The appearance of the necessary particle in the environment causes a chain of reactions that follow one after another, which continues until the chain breaks due to the loss of the reaction carrier particle. There are two main reasons for losses: the absorption of a particle without the emission of a secondary one and the departure of the particle beyond the volume of the substance that supports the chain process. If in each act of reaction only one carrier particle appears, then the chain reaction is called unbranched. An unbranched chain reaction cannot lead to energy release on a large scale.

If in each act of reaction or in some links of the chain more than one particle appears, then a branched chain reaction occurs, because one of the secondary particles continues the started chain, while the others give rise to new chains that branch again. True, processes that lead to chain breaks compete with the branching process, and the resulting situation gives rise to limiting or critical phenomena specific to branched chain reactions. If the number of broken circuits is greater than the number of new circuits appearing, then self-sustaining chain reaction(SCR) turns out to be impossible. Even if it is excited artificially by introducing a certain amount of necessary particles into the medium, then, since the number of chains in this case can only decrease, the process that has begun quickly fades out. If the number of new chains formed exceeds the number of breaks, the chain reaction quickly spreads throughout the entire volume of the substance when at least one initial particle appears.

The region of states of matter with the development of a self-sustaining chain reaction is separated from the region where a chain reaction is generally impossible, critical condition. The critical state is characterized by equality between the number of new circuits and the number of breaks.

Achieving a critical state is determined by a number of factors. The fission of a heavy nucleus is excited by one neutron, and as a result of the fission act more than one neutron appears (for example, for 235 U the number of neutrons produced in one fission act is on average 2.5). Consequently, the fission process can give rise to a branched chain reaction, the carriers of which will be neutrons. If the rate of neutron losses (captures without fission, escapes from the reaction volume, etc.) compensates for the rate of neutron multiplication in such a way that the effective neutron multiplication factor is exactly equal to unity, then the chain reaction proceeds in a stationary mode. The introduction of negative feedback between the effective multiplication factor and the rate of energy release allows for a controlled chain reaction, which is used, for example, in nuclear power. If the multiplication factor is greater than one, the chain reaction develops exponentially; runaway fission chain reaction is used in nuclear weapons.

see also

• Chemical chain reaction

Literature

• Klimov A. N. Nuclear physics and nuclear reactors.- M. Atomizdat, .
• Levin V. E. Nuclear physics and nuclear reactors/ 4th ed. - M.: Atomizdat, .
• Petunin V. P. Thermal power engineering of nuclear installations.- M.: Atomizdat, .

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See what “Nuclear chain reaction” is in other dictionaries:

Chain nuclear reaction is a sequence of nuclear reactions excited by particles (for example, neutrons) born in each reaction event. Depending on the average number of reactions following one previous one is less than, equal to or... ... Nuclear energy terms

nuclear chain reaction- A sequence of nuclear reactions excited by particles (for example, neutrons) born in each reaction event. Depending on the average number of reactions following one previous reaction less than, equal to or greater than one... ...

nuclear chain reaction- grandininė branduolinė reakcija statusas T sritis fizika atitikmenys: engl. nuclear chain reaction vok. Kettenkernreaktion, f rus. nuclear chain reaction, f pranc. réaction en chaîne nucléaire, f; réaction nucléaire en chaîne, f … Fizikos terminų žodynas

The fission reaction of atomic nuclei of heavy elements under the influence of neutrons; in each act of the swarm, the number of neutrons increases, so that a self-sustaining fission process can occur. For example, during the fission of one nucleus of the uranium isotope 235U under the influence of ... Big Encyclopedic Polytechnic Dictionary

Nuclear chain reaction- the reaction of fission of atomic nuclei under the influence of neutrons, in each act of which at least one neutron is emitted, which ensures the maintenance of the reaction. Used as a source of energy in nuclear charges (explosive nuclear reactors) and nuclear reactors... ... Glossary of military terms

nuclear fission chain reaction with neutrons- - [A.S. Goldberg. English-Russian energy dictionary. 2006] Topics: energy in general EN divergent reaction... Technical Translator's Guide

Self-sustaining nuclear chain reaction- 7. Self-sustaining nuclear chain reaction SCR A nuclear chain reaction characterized by an effective multiplication factor greater than or equal to unity

In which the particles that cause them are also formed as products of these reactions. This reaction is the fission of uranium and some trans-uranium elements (for example, 23 9 Pu) under the influence of neutrons. It was first carried out by E. Fermi in 1942. After the discovery nuclear fission W. Zinn, L. Szilard and G. N. Flerov showed that during the fission of a uranium nucleus U more than one neutron is emitted: n + U → A + B + v. Here A And IN— fission fragments with mass numbers A from 90 to 150, v— number of secondary neutrons.

Neutron multiplication factor. For a chain reaction to occur, it is necessary that the average number of released neutrons in a given mass of uranium does not decrease with time, or that neutron multiplication factor k was greater than or equal to one.

The neutron multiplication factor is the ratio of the number of neutrons in a generation to the number of neutrons in the previous generation. Generational change is understood as nuclear fission, during which neutrons from the old generation are absorbed and new neutrons are born.

If k ≥ 1, then the number of neutrons increases over time or remains constant, and a chain reaction occurs. At k > 1 the number of neutrons decreases, and a chain reaction is impossible.

For a number of reasons, of all the nuclei found in nature, only isotope nuclei are suitable for carrying out a nuclear chain reaction. The multiplication factor is determined by: 1) the capture of slow neutrons by nuclei, subsequent fission and the capture of fast neutrons by nuclei and, also with subsequent fission; 2) capture of neutrons without fission by uranium nuclei; 3) capture of neutrons by fission products, moderator and structural elements of the installation; 4) the emission of neutrons from the fissile substance to the outside.

Only the first process is accompanied by an increase in the number of neutrons. For a stationary reaction k must be equal to 1. Already at k = 1.01 an explosion will occur almost instantly.

Plutonium formation. As a result of the capture of a neutron by a uranium isotope, a radioactive isotope with a half-life of 23 minutes is formed. During decay, the first transura-new element appears neptunium:

.

β-radioactive neptunium (with a half-life of about two days), emitting an electron, turns into the following transuranium element - plutonium:

Plutonium has a half-life of 24,000 years and is the most important property is the ability to fission under the influence of slow neutrons in the same way as an isotope. With the help of plutonium, a chain reaction can be carried out with the release of a huge amount of energy.

Chain reaction accompanied by the release of enormous energy; When each nucleus fissions, 200 MeV is released. The fission of 1 uranium nucleus releases the same energy as the combustion of 3 coal or 2.5 tons of oil.

Let's consider the mechanism of the fission chain reaction. When heavy nuclei fission under the influence of neutrons, new neutrons are produced. For example, with each fission of the uranium 92 U 235 nucleus, an average of 2.4 neutrons are produced. Some of these neutrons can again cause nuclear fission. This avalanche-like process is called chain reaction .
The fission chain reaction occurs in an environment in which the process of neutron multiplication occurs. This environment is called core . The most important physical quantity, which characterizes the intensity of neutron multiplication, is neutron multiplication factor in the medium k ∞ . The multiplication coefficient is equal to the ratio of the number of neutrons in one generation to their number in the previous generation. The index ∞ indicates that we are talking about an ideal environment of infinite dimensions. Similarly to the value k ∞ is determined neutron multiplication factor in a physical system k. The k factor is a characteristic of a specific installation.
In a fissile medium of finite dimensions, some neutrons will escape from the core to the outside. Therefore, the coefficient k also depends on the probability P for a neutron not to escape from the core. A-priory

The value of P depends on the composition of the active zone, its size, shape, and also on the extent to which the substance surrounding the active zone reflects neutrons.
The important concepts of critical mass and critical dimensions are associated with the possibility of neutrons leaving the core. Critical size is the size of the active zone at which k = 1. Critical mass is called the mass of the core of critical dimensions. It is obvious that when the mass is below the critical one, the chain reaction does not occur, even if > 1. On the contrary, a noticeable excess of the mass above the critical one leads to an uncontrolled reaction - an explosion.
If in the first generation there are N neutrons, then in the nth generation there will be Nk n. Therefore, at k = 1 the chain reaction proceeds stationary, at k< 1 реакция гаснет, а при k >1 the intensity of the reaction increases. When k = 1 the reaction mode is called critical , for k > 1 – supercritical and at k< 1 – subcritical .
The lifetime of one generation of neutrons strongly depends on the properties of the medium and is on the order of 10–4 to 10–8 s. Due to the shortness of this time, in order to carry out a controlled chain reaction, it is necessary to maintain the equality k = 1 with great accuracy, since, say, at k = 1.01 the system will explode almost instantly. Let's see what factors determine the coefficients k ∞ and k.
The first quantity that determines k ∞ (or k) is the average number of neutrons emitted in one fission event. The number depends on the type of fuel and the energy of the incident neutron. In table Table 1 shows the values ​​of the main isotopes of nuclear energy for both thermal and fast (E = 1 MeV) neutrons.

The energy spectrum of fission neutrons for the 235 U isotope is shown in Fig. 1. Spectra of this kind are similar for all fissile isotopes: there is a strong scatter in energies, with the bulk of neutrons having energies in the range of 1–3 MeV. The neutrons produced during fission slow down, diffuse over a certain distance and are absorbed either with or without fission. Depending on the properties of the medium, neutrons have time to slow down to different energies. In the presence of a good moderator, the majority of neutrons have time to slow down to thermal energies of the order of 0.025 eV. In this case the chain reaction is called slow, or, what is the same, thermal. In the absence of a special moderator, neutrons only have time to slow down to energies of 0.1–0.4 MeV, since all fissile isotopes are heavy and therefore slow down poorly. The corresponding chain reactions are called fast(we emphasize that the epithets “fast” and “slow” characterize the speed of neutrons, and not the speed of the reaction). Chain reactions in which neutrons are slowed down to energies ranging from tens to one keV are called intermediate .
When a neutron collides with a heavy nucleus, radiative capture of a neutron (n, γ) is always possible. This process will compete with division and thereby reduce the multiplication rate. It follows from this that the second physical quantity that affects the coefficients k ∞ , k is the probability of fission when a neutron is captured by the nucleus of a fissile isotope. This probability for monoenergetic neutrons is obviously equal to

where nf, nγ are the fission and radiation capture cross sections, respectively. To simultaneously take into account both the number of neutrons per fission event and the probability of radiative capture, a coefficient η is introduced, equal to the average number of secondary neutrons per neutron capture by a fissile nucleus.

the value of η depends on the type of fuel and on the neutron energy. The values ​​of η for the most important isotopes for thermal and fast neutrons are given in the same table. 1. The value of η is the most important characteristic of fuel nuclei. A chain reaction can only occur when η > 1. The higher the value of η, the higher the quality of the fuel.

Table 1. Values ​​of ν, η for fissile isotopes

The quality of nuclear fuel is determined by its availability and coefficient η. Only three isotopes are found in nature that can serve as nuclear fuel or raw materials for its production. These are the isotope of thorium 232 Th and the isotopes of uranium 238 U and 235 U. Of these, the first two do not give a chain reaction, but can be processed into isotopes on which the reaction occurs. The 235 U isotope itself gives a chain reaction. IN earth's crust thorium is several times more than uranium. Natural thorium practically consists of only one isotope, 232 Th. Natural uranium consists mainly of the 238 U isotope and only 0.7% of the 235 U isotope.
In practice, the question of the feasibility of a chain reaction on a natural mixture of uranium isotopes, in which there are 140 238 U nuclei per 235 U nucleus, is extremely important. Let us show that on a natural mixture a slow reaction is possible, but a fast one is not. To consider a chain reaction in a natural mixture, it is convenient to introduce a new quantity - the average neutron absorption cross section per one nucleus of the 235 U isotope. By definition

For thermal neutrons = 2.47, = 580 barn, = 112 barn, = 2.8 barn (note how small the last cross section is). Substituting these figures into (5), we obtain that for slow neutrons in a natural mixture

This means that 100 thermal neutrons, absorbed in the natural mixture, will create 132 new neutrons. It directly follows from this that a chain reaction with slow neutrons is in principle possible on natural uranium. In principle, because to actually implement a chain reaction, you need to be able to slow down neutrons with low losses.
For fast neutrons ν = 2.65, 2 barn, 0.1 barn. If we take into account fission only on the 235 U isotope, we obtain

But we must also take into account that fast neutrons with energies greater than 1 MeV can, with noticeable relative intensity, divide the nuclei of the 238 U isotope, which is very abundant in the natural mixture. For division by 238 U, the coefficient is approximately 2.5. In the fission spectrum, approximately 60% of neutrons have energies above the effective threshold of 1.4 MeV fission by 238 U. But of these 60%, only one neutron out of 5 manages to fission without slowing down to an energy below the threshold due to elastic and especially inelastic scattering. From here, for the coefficient 238 (fast) we get the estimate

Thus, on fast neutrons a chain reaction cannot occur in a natural mixture (235 U + 238 U). It has been experimentally established that for pure metallic uranium the multiplication factor reaches a value of unity with an enrichment of 5.56%. In practice, it turns out that the reaction with fast neutrons can only be maintained in an enriched mixture containing at least 15% of the 235 U isotope.
A natural mixture of uranium isotopes can be enriched with the 235 U isotope. Enrichment is a complex and expensive process due to the fact that Chemical properties both isotopes are almost the same. It is necessary to take advantage of small differences in the rates of chemical reactions, diffusion, etc., arising due to differences in the masses of isotopes. The chain reaction at 235 U is almost always carried out in an environment with high content 238 U. A natural mixture of isotopes is often used, for which η = 1.32 in the thermal neutron region, since 238 U is also useful. The 238 U isotope is fissile by neutrons with energies above 1 MeV. This fission results in a small additional multiplication of neutrons.
Let's compare fission chain reactions with thermal and fast neutrons.
For thermal neutrons, the capture cross sections are large and vary greatly when passing from one nucleus to another. On the nuclei of some elements (for example, cadmium), these cross sections are hundreds or more times higher than the cross sections on 235 U. Therefore, high purity requirements are imposed on the core of thermal neutron installations in relation to certain impurities.
For fast neutrons, all capture cross sections are small and not so different from each other, so the problem of high purity of materials does not arise. Another advantage of fast reactions is a higher reproduction rate.
Important distinctive property thermal reactions is that in the core the fuel is much more diluted, i.e., per fuel core there are significantly more nuclei that do not participate in fission than in a fast reaction. For example, in a thermal reaction on natural uranium, there are 140 nuclei of 238 U raw material per 235 U fuel core, and in a fast reaction, there can be no more than five to six 238 U nuclei per 235 U nucleus. The dilution of fuel in a thermal reaction leads to the fact that one and the same energy in a thermal reaction is released in a much larger volume of matter than in a rapid reaction. Thus, it is easier to remove heat from the active zone of a thermal reaction, which allows this reaction to be carried out with greater intensity than a fast one.
The lifetime of one generation of neutrons for a fast reaction is several orders of magnitude shorter than for a thermal one. Therefore, the rate of a fast reaction can change noticeably within a very short time after a change in the physical conditions in the core. At normal operation In a reactor, this effect is insignificant, since in this case the operating mode is determined by the lifetimes of delayed rather than prompt neutrons.
In a homogeneous medium consisting only of fissile isotopes of one type, the multiplication factor would be equal to η. However, in real situations, in addition to fissile nuclei, there are always other, non-fissionable ones. These extraneous nuclei will capture neutrons and thereby affect the multiplication factor. It follows that the third quantity determining the coefficients k ∞ , k, is the probability that the neutron will not be captured by one of the non-fissile nuclei. In real installations, “foreign” capture occurs on the moderator cores, on the cores of various structural elements, as well as on the cores of fission products and capture products.
To carry out a chain reaction with slow neutrons, special substances are introduced into the core - moderators, which convert fission neutrons into thermal ones. In practice, the slow neutron chain reaction is carried out on natural or slightly enriched uranium with the 235 U isotope. The presence of a large amount of the 238 U isotope in the core complicates the moderation process and makes it necessary to place high demands on the quality of the moderator. The life of one generation of neutrons in a core with a moderator can be approximately divided into two stages: moderation to thermal energies and diffusion. thermal rates before absorption. In order for the majority of neutrons to have time to slow down without absorption, the condition must be met

where σ control, σ capture are the energy-averaged cross sections for elastic scattering and capture, respectively, and n is the number of neutron collisions with moderator nuclei required to achieve thermal energy. The number n increases rapidly with increasing mass number of the moderator. For uranium 238 U, the number n is of the order of several thousand. And the ratio σ control /σ capture for this isotope, even in the relatively favorable energy region of fast neutrons, does not exceed 50. The so-called resonance region from 1 keV to 1 eV is especially “dangerous” in relation to neutron capture. In this region, the total cross section for the interaction of a neutron with 238 U nuclei has big number intense resonances (Fig. 2). At low energies, the radiation widths exceed the neutron widths. Therefore, in the resonance region, the ratio σ control/σ capture becomes even less than unity. This means that when a neutron enters the region of one of the resonances, it is absorbed with almost one hundred percent probability. And since the slowdown on such a heavier nucleus as uranium occurs in “small steps,” then when passing through the resonant region, the slowing down neutron will definitely “bump into” one of the resonances and be absorbed. It follows that a chain reaction cannot be carried out on natural uranium without foreign impurities: on fast neutrons the reaction does not occur due to the smallness of the coefficient η, and slow neutrons cannot be formed. In order to avoid resonant neutron capture, it is necessary to use very light nuclei to slow them down , in which the slowdown occurs in “large steps,” which sharply increases the probability of a neutron successfully “skipping” through the resonant energy region. The best moderating elements are hydrogen, deuterium, beryllium, and carbon. Therefore, the moderators used in practice are mainly limited to heavy water, beryllium, beryllium oxide, graphite, and ordinary water, which slows down neutrons no worse than heavy water, but absorbs them in much larger quantities. The retarder must be well cleaned. Note that to carry out a slow reaction, the moderator must be tens or even hundreds of times more than uranium in order to prevent resonant collisions of neutrons with 238 U nuclei.

The moderating properties of the active medium can be approximately described by three quantities: the probability of a neutron avoiding absorption by a moderator during moderation, the probability p of avoiding resonant capture by 238 U nuclei, and the probability f of a thermal neutron being absorbed by a fuel nucleus rather than a moderator. The value f is usually called the thermal utilization coefficient. Accurate calculation of these quantities is difficult. Usually, approximate semi-empirical formulas are used to calculate them.

The values ​​of p and f depend not only on the relative amount of the moderator, but also on the geometry of its placement in the core. The active zone, consisting of a homogeneous mixture of uranium and moderator, is called homogeneous, and the system of their alternating blocks of uranium and moderator is called heterogeneous (Fig. 4). A qualitatively heterogeneous system is distinguished by the fact that in it the fast neutron formed in uranium manages to go into the moderator without reaching resonant energies. Further deceleration occurs in a pure moderator. This increases the probability p of avoiding resonant capture

p het > p homo.

On the other hand, on the contrary, having become thermal in the moderator, the neutron must, in order to participate in the chain reaction, diffuse, without being absorbed in the pure moderator, to its boundary. Therefore, the thermal utilization factor f in a heterogeneous environment is lower than in a homogeneous one:

f get< f гом.

To estimate the multiplication factor k ∞ of a thermal reactor, an approximate four factor formula

We have already considered the first three factors earlier. The quantity ε is called fast neutron multiplication factor . This coefficient is introduced in order to take into account that some fast neutrons can fission without having time to slow down. In its meaning, the coefficient ε always exceeds one. But this excess is usually small. Typical for thermal reactions is the value ε = 1.03. For fast reactions, the formula of four factors is not applicable, since each coefficient depends on energy and the energy spread in fast reactions is very large.
Since the value of η is determined by the type of fuel, and the value of ε for slow reactions almost does not differ from unity, the quality of a particular active medium is determined by the product pf. Thus, the advantage of a heterogeneous medium over a homogeneous medium is quantitatively manifested in the fact that, for example, in a system in which there are 215 graphite nuclei per natural uranium nucleus, the product pf is equal to 0.823 for a heterogeneous medium and 0.595 for a homogeneous one. And since for a natural mixture η = 1.34, we get that for a heterogeneous medium k ∞ > 1, and for a homogeneous medium k ∞< 1.
For the practical implementation of a stationary chain reaction, one must be able to control this reaction. This control is greatly simplified due to the emission of delayed neutrons during fission. The overwhelming majority of neutrons escape from the nucleus almost instantly (i.e., in a time that is many orders of magnitude shorter than the lifetime of a generation of neutrons in the core), but several tenths of a percent of neutrons are delayed and escape from fragment nuclei after a fairly large period of time - from fractions seconds to several and even tens of seconds. The effect of delayed neutrons can be qualitatively explained as follows. Let the multiplication factor instantly increase from a subcritical value to such a supercritical value that k< 1 при отсутствии запаздывающих нейтронов. Тогда, очевидно, цепная реакция начнется не сразу, а лишь после вылета запаздывающих нейтронов. Тем самым процесс течения реакции будет регулируемым, если время срабатывания регулирующих устройств будет меньше сравнительно большого времени задержки запаздывающих нейтронов, а не очень малого времени развития цепной реакции. Доля запаздывающих нейтронов в ядерных горючих колеблется от 0.2 до 0.7%. Среднее время жизни запаздывающих нейтронов составляет приблизительно 10 с. При небольшой степени надкритичности скорость нарастания интенсивности цепной реакции определяется только запаздывающими нейтронами.
The capture of neutrons by nuclei not participating in the chain reaction reduces the intensity of the reaction, but can be beneficial in relation to the formation of new fissile isotopes. Thus, when neutrons are absorbed from the isotopes of uranium 238 U and thorium 232 Th, the isotopes of plutonium 239 Pu and uranium 233 U are formed (through two successive β-decays), which are nuclear fuel:

These two reactions open up a real possibility reproduction of nuclear fuel during a chain reaction. In the ideal case, i.e., in the absence of unnecessary losses of neutrons, an average of 1 neutron can be used for reproduction for each act of absorption of a neutron by a fuel nucleus.

Nuclear (nuclear) reactors

A reactor is a device in which a controlled fission chain reaction is maintained. When the reactor operates, heat is released due to the exothermic nature of the fission reaction. The main characteristic of a reactor is its power - the amount of thermal energy released per unit time. The reactor power is measured in megawatts (10 6 W). A power of 1 MW corresponds to a chain reaction in which 3·1016 fission events occur per second. Available a large number of different types reactors. One of the typical schemes of a thermal reactor is shown in Fig. 5.
The main part of the reactor is core, in which a reaction occurs and thereby releases energy. In thermal and intermediate neutron reactors, the core consists of a fuel, usually mixed with a non-fissile isotope (usually 238 U), and a moderator. There is no moderator in the core of fast neutron reactors.
The core volume varies from tenths of a liter in some fast neutron reactors to tens of cubic meters in large thermal reactors. To reduce neutron leakage, the core is given a spherical or nearly spherical shape (for example, a cylinder with a height approximately equal to the diameter, or a cube).
Depending on the relative location of the fuel and moderator, homogeneous and heterogeneous reactors are distinguished. An example of a homogeneous active zone is a solution of uranyl sulfate salt and U 2 SO 4 in ordinary or heavy water. Heterogeneous reactors are more common. In heterogeneous reactors, the core consists of a moderator in which cassettes containing fuel are placed. Since energy is released in these cassettes, they are called fuel elements or for short fuel rods. The active zone with reflector is often enclosed in a steel casing.

• The role of delayed neutrons in nuclear reactor control

Chain reaction

Chain reaction- a chemical and nuclear reaction in which the appearance of an active particle (a free radical or atom in a chemical process, a neutron in a nuclear process) causes a large number (chain) of successive transformations of inactive molecules or nuclei. Free radicals and many atoms, unlike molecules, have free unsaturated valences (unpaired electron), which leads to their interaction with the original molecules. When a free radical (R) collides with a molecule, one of the valence bonds of the latter is broken and, thus, as a result of the reaction, a new free radical is formed, which, in turn, reacts with another molecule - a chain reaction occurs.

Chain reactions in chemistry include the processes of oxidation (combustion, explosion), cracking, polymerization and others, which are widely used in the chemical and oil industries.

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See what “Chain reaction” is in other dictionaries:

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