Nuclear reactor physics
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Nuclear reactor physics is the field of
physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science is that depar ...
that studies and deals with the applied study and engineering applications of chain reaction to induce a controlled rate of fission in a nuclear reactor for the production of energy.van Dam, H., van der Hagen, T. H. J. J., & Hoogenboom, J. E. (2005). ''Nuclear reactor physics''. Retrieved from http://www.janleenkloosterman.nl/reports/ap3341.pdf Most
nuclear reactor A nuclear reactor is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. Heat from nu ...
s use a
chain reaction A chain reaction is a sequence of reactions where a reactive product or by-product causes additional reactions to take place. In a chain reaction, positive feedback leads to a self-amplifying chain of events. Chain reactions are one way that syst ...
to induce a controlled rate of
nuclear fission Nuclear fission is a nuclear reaction, reaction in which the atomic nucleus, nucleus of an atom splits into two or more smaller atomic nucleus, nuclei. The fission process often produces gamma ray, gamma photons, and releases a very large ...
in fissile material, releasing both
energy In physics, energy (from Ancient Greek: wikt:ἐνέργεια#Ancient_Greek, ἐνέργεια, ''enérgeia'', “activity”) is the physical quantity, quantitative physical property, property that is #Energy transfer, transferred to a phy ...
and free
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the atomic nucleus, nuclei of atoms. Since protons and ...
s. A reactor consists of an assembly of nuclear fuel (a reactor core), usually surrounded by a
neutron moderator In nuclear engineering, a neutron moderator is a medium that reduces the speed of Neutron temperature#Fast, fast neutrons, ideally without neutron capture, capturing any, leaving them as Neutron temperature#Thermal, thermal neutrons with only Ther ...
such as regular water, heavy water,
graphite Graphite () is a crystalline A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in al ...
, or zirconium hydride, and fitted with mechanisms such as control rods which control the rate of the reaction. The physics of
nuclear fission Nuclear fission is a nuclear reaction, reaction in which the atomic nucleus, nucleus of an atom splits into two or more smaller atomic nucleus, nuclei. The fission process often produces gamma ray, gamma photons, and releases a very large ...
has several quirks that affect the design and behavior of nuclear reactors. This article presents a general overview of the physics of nuclear reactors and their behavior.


Criticality

In a nuclear reactor, the
neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than that of a proton. Protons and neutrons constitute the atomic nucleus, nuclei of atoms. Since protons and ...
population at any instant is a function of the rate of neutron production (due to fission processes) and the rate of neutron losses (due to non-fission absorption mechanisms and leakage from the system). When a reactor’s neutron population remains steady from one generation to the next (creating as many new neutrons as are lost), the fission chain reaction is self-sustaining and the reactor's condition is referred to as "critical". When the reactor’s neutron production exceeds losses, characterized by increasing power level, it is considered "supercritical", and when losses dominate, it is considered "subcritical" and exhibits decreasing power. The " Six-factor formula" is the neutron life-cycle balance equation, which includes six separate factors, the product of which is equal to the ratio of the number of neutrons in any generation to that of the previous one; this parameter is called the effective multiplication factor k, also denoted by Keff, where k = Є ''L''f ρ ''L''th ''f'' η, where Є = "fast-fission factor", ''L''f = "fast non-leakage factor", ρ = " resonance escape probability", ''L''th = "thermal non-leakage factor", ''f'' = "thermal fuel utilization factor", and η = "reproduction factor". This equation's factors are roughly in order of potential occurrence for a fission born neutron during critical operation. As already mentioned before, k = (Neutrons produced in one generation)/(Neutrons produced in the previous generation). In other words, when the reactor is critical, k = 1; when the reactor is subcritical, k < 1; and when the reactor is supercritical, k > 1. '' Reactivity'' is an expression of the departure from criticality. δk = (k − 1)/k. When the reactor is critical, δk = 0. When the reactor is subcritical, δk < 0. When the reactor is supercritical, δk > 0. Reactivity is also represented by the lowercase Greek letter rho (ρ). Reactivity is commonly expressed in decimals or percentages or pcm (per cent mille) of Δk/k. When reactivity ρ is expressed in units of delayed neutron fraction β, the unit is called the ''
dollar Dollar is the name of more than 20 Currency, currencies. They include the Australian dollar, Brunei dollar, Canadian dollar, Hong Kong dollar, Jamaican dollar, Liberian dollar, Namibian dollar, New Taiwan dollar, New Zealand dollar, Singapore d ...
''. If we write 'N' for the number of free neutrons in a reactor core and \tau for the average lifetime of each neutron (before it either escapes from the core or is absorbed by a nucleus), then the reactor will follow the
differential equation In mathematics, a differential equation is an functional equation, equation that relates one or more unknown function (mathematics), functions and their derivatives. In applications, the functions generally represent physical quantities, the der ...
(''evolution equation'') :\frac = \frac where \alpha is a constant of proportionality, and dN/dt is the rate of change of the neutron count in the core. This type of differential equation describes
exponential growth Exponential growth is a process that increases quantity over time. It occurs when the instantaneous Rate (mathematics)#Of change, rate of change (that is, the derivative) of a quantity with respect to time is proportionality (mathematics), propor ...
or
exponential decay A quantity is subject to exponential decay if it decreases at a rate Proportionality (mathematics), proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where is the quantity and ...
, depending on the sign of the constant \alpha, which is just the expected number of neutrons after one average neutron lifetime has elapsed: :\alpha = P_P_ n_ - P_ - P_ Here, P_ is the probability that a particular neutron will strike a fuel nucleus, P_ is the probability that the neutron, having struck the fuel, will cause that nucleus to undergo fission, P_ is the probability that it will be absorbed by something other than fuel, and P_ is the probability that it will "escape" by leaving the core altogether. n_ is the number of neutrons produced, on average, by a fission event—it is between 2 and 3 for both 235U and 239Pu. If \alpha is positive, then the core is ''supercritical'' and the rate of neutron production will grow exponentially until some other effect stops the growth. If \alpha is negative, then the core is "subcritical" and the number of free neutrons in the core will shrink exponentially until it reaches an equilibrium at zero (or the background level from spontaneous fission). If \alpha is exactly zero, then the reactor is ''critical'' and its output does not vary in time (dN/dt = 0, from above). Nuclear reactors are engineered to reduce P_ and P_. Small, compact structures reduce the probability of direct escape by minimizing the
surface area The surface area of a solid object is a measure of the total area Area is the quantity that expresses the extent of a region on the plane or on a curved surface. The area of a plane region or ''plane area'' refers to the area of a s ...
of the core, and some materials (such as
graphite Graphite () is a crystalline A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in al ...
) can reflect some neutrons back into the core, further reducing P_. The probability of fission, P_, depends on the nuclear physics of the fuel, and is often expressed as a cross section. Reactors are usually controlled by adjusting P_. Control rods made of a strongly neutron-absorbent material such as
cadmium Cadmium is a chemical element with the Symbol (chemistry), symbol Cd and atomic number 48. This soft, silvery-white metal is chemically similar to the two other stable metals in group 12 element, group 12, zinc and mercury (element), mercury. Li ...
or
boron Boron is a chemical element with the Chemical symbol, symbol B and atomic number 5. In its crystalline form it is a brittle, dark, lustrous metalloid; in its amorphous form it is a brown powder. As the lightest element of the ''boron g ...
can be inserted into the core: any neutron that happens to impact the control rod is lost from the chain reaction, reducing \alpha. P_ is also controlled by the recent history of the reactor core itself ( see below).


Starter sources

The mere fact that an assembly is supercritical does not guarantee that it contains any free neutrons at all. At least one neutron is required to "strike" a chain reaction, and if the
spontaneous fission Spontaneous fission (SF) is a form of radioactive decay that is found only in very heavy chemical elements. The nuclear binding energy of the elements reaches its maximum at an atomic mass number of about 56 (e.g., iron-56); spontaneous breakdow ...
rate is sufficiently low it may take a long time (in 235U reactors, as long as many minutes) before a chance neutron encounter starts a chain reaction even if the reactor is supercritical. Most nuclear reactors include a "starter"
neutron source A neutron source is any device that emits neutrons, irrespective of the mechanism used to produce the neutrons. Neutron sources are used in physics, engineering, medicine, nuclear weapons, petroleum exploration, biology, chemistry, and nuclear p ...
that ensures there are always a few free neutrons in the reactor core, so that a chain reaction will begin immediately when the core is made critical. A common type of startup neutron source is a mixture of an
alpha particle Alpha particles, also called alpha rays or alpha radiation, consist of two protons and two neutron The neutron is a subatomic particle, symbol or , which has a neutral (not positive or negative) charge, and a mass slightly greater than tha ...
emitter such as 241Am (
americium-241 Americium-241 (, Am-241) is an Isotopes of americium, isotope of americium. Like all isotopes of americium, it is radioactive, with a half-life of . is the most common isotope of americium as well as the most prevalent isotope of americium in nu ...
) with a lightweight isotope such as 9Be ( beryllium-9). The primary sources described above have to be used with fresh reactor cores. For operational reactors, secondary sources are used; most often a combination of
antimony Antimony is a chemical element with the Symbol (chemistry), symbol Sb (from la, wiktionary:stibium#Latin, stibium) and atomic number 51. A lustrous gray metalloid, it is found in nature mainly as the sulfide mineral stibnite (Sb2S3). Antimony ...
with
beryllium Beryllium is a chemical element with the Symbol (chemistry), symbol Be and atomic number 4. It is a steel-gray, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with other ...
. Antimony becomes activated in the reactor and produces high-energy gamma photons, which produce photoneutrons from beryllium.
Uranium-235 Uranium-235 (235U or U-235) is an Isotopes of uranium, isotope of uranium making up about 0.72% of natural uranium. Unlike the predominant isotope uranium-238, it is fissile, i.e., it can sustain a nuclear chain reaction. It is the only fissile ...
undergoes a small rate of natural spontaneous fission, so there are always some neutrons being produced even in a fully shutdown reactor. When the
control rod Control rods are used in nuclear reactors to control the rate of fission of the nuclear fuel – uranium or plutonium. Their compositions include chemical elements such as boron, cadmium, silver, hafnium, or indium, that are capable of absorbing ...
s are withdrawn and criticality is approached the number increases because the absorption of neutrons is being progressively reduced, until at criticality the chain reaction becomes self-sustaining. Note that while a neutron source is provided in the reactor, this is not essential to start the chain reaction, its main purpose is to give a shutdown neutron population which is detectable by instruments and so make the approach to critical more observable. The reactor will go critical at the same control rod position whether a source is loaded or not. Once the chain reaction is begun, the primary starter source may be removed from the core to prevent damage from the high neutron flux in the operating reactor core; the secondary sources usually remains in situ to provide a background reference level for control of criticality.


Subcritical multiplication

Even in a subcritical assembly such as a shut-down reactor core, any stray neutron that happens to be present in the core (for example from spontaneous fission of the fuel, from radioactive decay of fission products, or from a
neutron source A neutron source is any device that emits neutrons, irrespective of the mechanism used to produce the neutrons. Neutron sources are used in physics, engineering, medicine, nuclear weapons, petroleum exploration, biology, chemistry, and nuclear p ...
) will trigger an exponentially decaying chain reaction. Although the chain reaction is not self-sustaining, it acts as a multiplier that increases the equilibrium number of neutrons in the core. This ''subcritical multiplication'' effect can be used in two ways: as a probe of how close a core is to criticality, and as a way to generate fission power without the risks associated with a critical mass. If k is the neutron multiplication factor of a subcritical core and S_0 is the number of neutrons coming per generation in the reactor from an external source, then at the instant when the neutron source is switched on, number of neutrons in the core will be S_0. After 1 generation, this neutrons will produce k \times S_0 neutrons in the reactor and reactor will have a totality of k \times S_0 + S_0 neutrons considering the newly entered neutrons in the reactor. Similarly after 2 generation, number of neutrons produced in the reactor will be k \times (k \times S_0 + S_0) + S_0 and so on. This process will continue and after a long enough time, the number of neutrons in the reactor will be, : S_0 +k \times S_0 + k \times k \times S_0 + \ldots This series will converge because for the subcritical core, 0 < k < 1 . So the number of neutrons in the reactor will be simply, : \frac The fraction \frac is called subcritical multiplication factor. Since power in a reactor is proportional to the number of neutrons present in the nuclear fuel material (material in which fission can occur), the power produced by such a subcritical core will also be proportional to the subcritical multiplication factor and the external source strength. As a measurement technique, subcritical multiplication was used during the
Manhattan Project The Manhattan Project was a research and development undertaking during World War II that produced the first nuclear weapons. It was led by the United States with the support of the United Kingdom and Canada. From 1942 to 1946, the project w ...
in early experiments to determine the minimum critical masses of 235U and of 239Pu. It is still used today to calibrate the controls for nuclear reactors during startup, as many effects (discussed in the following sections) can change the required control settings to achieve criticality in a reactor. As a power-generating technique, subcritical multiplication allows generation of nuclear power for fission where a critical assembly is undesirable for safety or other reasons. A subcritical assembly together with a neutron source can serve as a steady source of heat to generate power from fission. Including the effect of an external neutron source ("external" to the fission process, not physically external to the core), one can write a modified evolution equation: :\frac = \frac + R_ where R_ is the rate at which the external source injects neutrons into the core. In equilibrium, the core is not changing and dN/dt is zero, so the equilibrium number of neutrons is given by: :N = -\frac If the core is subcritical, then \alpha is negative so there is an equilibrium with a positive number of neutrons. If the core is close to criticality, then \alpha is very small and thus the final number of neutrons can be made arbitrarily large.


Neutron moderators

To improve P_ and enable a chain reaction, natural or low enrichment uranium-fueled reactors must include a
neutron moderator In nuclear engineering, a neutron moderator is a medium that reduces the speed of Neutron temperature#Fast, fast neutrons, ideally without neutron capture, capturing any, leaving them as Neutron temperature#Thermal, thermal neutrons with only Ther ...
that interacts with newly produced fast neutrons from fission events to reduce their kinetic energy from several
MeV In physics, an electronvolt (symbol eV, also written electron-volt and electron volt) is the measure of an amount of kinetic energy gained by a single electron accelerating from rest through an Voltage, electric potential difference of one volt i ...
to thermal energies of less than one eV, making them more likely to induce fission. This is because 235U has a larger cross section for slow neutrons, and also because 238U is much less likely to absorb a
thermal neutron The neutron detection temperature, also called the neutron energy, indicates a free neutron's kinetic energy In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its ...
than a freshly produced neutron from fission. Neutron moderators are thus materials that slow down neutrons. Neutrons are most effectively slowed by colliding with the nucleus of a light atom, hydrogen being the lightest of all. To be effective, moderator materials must thus contain light elements with atomic nuclei that tend to scatter neutrons on impact rather than absorb them. In addition to hydrogen, beryllium and carbon atoms are also suited to the job of moderating or slowing down neutrons. Hydrogen moderators include
water Water (chemical formula ) is an Inorganic compound, inorganic, transparent, tasteless, odorless, and Color of water, nearly colorless chemical substance, which is the main constituent of Earth's hydrosphere and the fluids of all known living ...
(H2O), heavy water ( D2O), and zirconium hydride (ZrH2), all of which work because a hydrogen nucleus has nearly the same mass as a free neutron: neutron-H2O or neutron-ZrH2 impacts excite rotational modes of the molecules (spinning them around).
Deuterium Deuterium (or hydrogen-2, symbol or deuterium, also known as heavy hydrogen) is one of two Stable isotope ratio, stable isotopes of hydrogen (the other being Hydrogen atom, protium, or hydrogen-1). The atomic nucleus, nucleus of a deuterium ato ...
nuclei (in heavy water) absorb kinetic energy less well than do light hydrogen nuclei, but they are much less likely to absorb the impacting neutron. Water or heavy water have the advantage of being transparent
liquid A liquid is a nearly Compressibility, incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of State of matter#Four fundamental states, the four fund ...
s, so that, in addition to shielding and moderating a reactor core, they permit direct viewing of the core in operation and can also serve as a working fluid for heat transfer. Carbon in the form of graphite has been widely used as a moderator. It was used in Chicago Pile-1, the world's first man-made critical assembly, and was commonplace in early reactor designs including the
Soviet The Soviet Union,. officially the Union of Soviet Socialist Republics. (USSR),. was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 to 1991. A flagship communist state, ...
RBMK The RBMK (russian: реактор большой мощности канальный, РБМК; ''reaktor bolshoy moshchnosti kanalnyy'', "high-power channel-type reactor") is a class of graphite-moderated nuclear power reactor designed and built ...
nuclear power plant A nuclear power plant (NPP) is a thermal power station in which the heat source is a nuclear reactor. As is typical of thermal power stations, heat is used to generate steam that drives a steam turbine connected to a electric generator, generato ...
s such as the Chernobyl plant.


Moderators and reactor design

The amount and nature of neutron moderation affects reactor controllability and hence safety. Because moderators both slow and absorb neutrons, there is an optimum amount of moderator to include in a given geometry of reactor core. Less moderation reduces the effectiveness by reducing the P_ term in the evolution equation, and more moderation reduces the effectiveness by increasing the P_ term. Most moderators become less effective with increasing temperature, so ''under-moderated'' reactors are stable against changes in temperature in the reactor core: if the core overheats, then the quality of the moderator is reduced and the reaction tends to slow down (there is a "negative temperature coefficient" in the reactivity of the core). Water is an extreme case: in extreme heat, it can boil, producing effective voids in the reactor core without destroying the physical structure of the core; this tends to shut down the reaction and reduce the possibility of a fuel meltdown. ''Over-moderated'' reactors are unstable against changes in temperature (there is a "positive temperature coefficient" in the reactivity of the core), and so are less inherently safe than under-moderated cores. Some reactors use a combination of moderator materials. For example, TRIGA type research reactors use ZrH2 moderator mixed with the 235U fuel, an H2O-filled core, and C (graphite) moderator and reflector blocks around the periphery of the core.


Delayed neutrons and controllability

Fission reactions and subsequent neutron escape happen very quickly; this is important for
nuclear weapons A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either nuclear fission, fission (fission bomb) or a combination of fission and nuclear fusion, fusion reactions (Thermonuclear weapon, thermonu ...
, where the objective is to make a nuclear pit release as much energy as possible before it physically explodes. Most neutrons emitted by fission events are prompt: they are emitted effectively instantaneously. Once emitted, the average neutron lifetime (\tau) in a typical core is on the order of a
millisecond A millisecond (from ''milli-'' and second; symbol: ms) is a unit of time in the International System of Units (SI) equal to one thousandth (0.001 or 10−3 or 1/1000) of a second and to 1000 microseconds. A unit of 10 milliseconds may be called ...
, so if the exponential factor \alpha is as small as 0.01, then in one second the reactor power will vary by a factor of (1 + 0.01)1000, or more than ten
thousand 1000 or one thousand is the natural number following 999 (number), 999 and preceding 1001 (number), 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period decimal mark#Digit grouping, separating ...
. Nuclear weapons are engineered to maximize the power growth rate, with lifetimes well under a millisecond and exponential factors close to 2; but such rapid variation would render it practically impossible to control the reaction rates in a nuclear reactor. Fortunately, the ''effective'' neutron lifetime is much longer than the average lifetime of a single neutron in the core. About 0.65% of the neutrons produced by 235U fission, and about 0.20% of the neutrons produced by 239Pu fission, are not produced immediately, but rather are emitted from an excited nucleus after a further decay step. In this step, further
radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive Decay chain, disintegration, or nuclear disintegration) is the process by which an unstable atomic nucleus loses energy by radiation. A material containing unstable nucl ...
of some of the fission products (almost always negative beta decay), is followed by immediate neutron emission from the excited daughter product, with an average life time of the beta decay (and thus the neutron emission) of about 15 seconds. These so-called
delayed neutron In nuclear engineering, a delayed neutron is a neutron emitted after a nuclear fission event, by one of the fission products (or actually, a fission product daughter after beta decay), any time from a few milliseconds to a few minutes after the fis ...
s increase the effective average lifetime of neutrons in the core, to nearly 0.1 seconds, so that a core with \alpha of 0.01 would increase in one second by only a factor of (1 + 0.01)10, or about 1.1: a 10% increase. This is a controllable rate of change. Most nuclear reactors are hence operated in a ''prompt subcritical'', ''delayed critical'' condition: the prompt neutrons alone are not sufficient to sustain a chain reaction, but the delayed neutrons make up the small difference required to keep the reaction going. This has effects on how reactors are controlled: when a small amount of control rod is slid into or out of the reactor core, the power level changes at first very rapidly due to ''prompt subcritical multiplication'' and then more gradually, following the exponential growth or decay curve of the delayed critical reaction. Furthermore, ''increases'' in reactor power can be performed at any desired rate simply by pulling out a sufficient length of control rod. However, without addition of a
neutron poison In applications such as nuclear reactors, a neutron poison (also called a neutron absorber or a nuclear poison) is a substance with a large Neutron cross section, neutron absorption cross-section. In such applications, absorbing neutrons is norma ...
or active neutron-absorber, ''decreases'' in fission rate are limited in speed, because even if the reactor is taken deeply subcritical to stop prompt fission neutron production, delayed neutrons are produced after ordinary beta decay of fission products already in place, and this decay-production of neutrons cannot be changed. The rate of change of reactor power is determined by the reactor period T, which is related to the reactivity \rho through the Inhour equation.


Kinetics

The kinetics of the reactor is described by the balance equations of neutrons and nuclei (fissile, fission products).


Reactor poisons

Any
nuclide A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state. The word ''nuclide'' was co ...
that strongly absorbs neutrons is called a reactor poison, because it tends to shut down (poison) an ongoing fission chain reaction. Some reactor poisons are deliberately inserted into fission reactor cores to control the reaction;
boron Boron is a chemical element with the Chemical symbol, symbol B and atomic number 5. In its crystalline form it is a brittle, dark, lustrous metalloid; in its amorphous form it is a brown powder. As the lightest element of the ''boron g ...
or
cadmium Cadmium is a chemical element with the Symbol (chemistry), symbol Cd and atomic number 48. This soft, silvery-white metal is chemically similar to the two other stable metals in group 12 element, group 12, zinc and mercury (element), mercury. Li ...
control rods are the best example. Many reactor poisons are produced by the fission process itself, and buildup of neutron-absorbing fission products affects both the fuel economics and the controllability of nuclear reactors.


Long-lived poisons and fuel reprocessing

In practice, buildup of reactor poisons in nuclear fuel is what determines the lifetime of nuclear fuel in a reactor: long before all possible fissions have taken place, buildup of long-lived neutron absorbing fission products damps out the chain reaction. This is the reason that
nuclear reprocessing Nuclear reprocessing is the chemical separation of fission products and actinides from spent nuclear fuel. Originally, reprocessing was used solely to extract plutonium for producing nuclear weapons. With commercialization of nuclear power, the ...
is a useful activity: spent nuclear fuel contains about 96% of the original fissionable material present in newly manufactured nuclear fuel. Chemical separation of the fission products restores the nuclear fuel so that it can be used again. Nuclear reprocessing is useful economically because chemical separation is much simpler to accomplish than the difficult isotope separation required to prepare nuclear fuel from natural uranium ore, so that in principle chemical separation yields more generated energy for less effort than mining, purifying, and isotopically separating new uranium ore. In practice, both the difficulty of handling the highly radioactive fission products and other political concerns make fuel reprocessing a contentious subject. One such concern is the fact that spent uranium nuclear fuel contains significant quantities of 239Pu, a prime ingredient in nuclear weapons (see breeder reactor).


Short-lived poisons and controllability

Short-lived reactor poisons in fission products strongly affect how nuclear reactors can operate. Unstable fission product nuclei transmute into many different elements (''secondary fission products'') as they undergo a
decay chain In nuclear science, the decay chain refers to a series of radioactive decay Radioactive decay (also known as nuclear decay, radioactivity, radioactive Decay chain, disintegration, or nuclear disintegration) is the process by which an unsta ...
to a stable isotope. The most important such element is
xenon Xenon is a chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical c ...
, because the isotope 135Xe, a secondary fission product with a half-life of about 9 hours, is an extremely strong neutron absorber. In an operating reactor, each nucleus of 135Xe becomes 136Xe (which may later sustain beta decay) by
neutron capture Neutron capture is a nuclear reaction in which an atomic nucleus The atomic nucleus is the small, dense region consisting of protons and neutrons at the center of an atom, discovered in 1911 by Ernest Rutherford based on the 1909 Geiger ...
almost as soon as it is created, so that there is no buildup in the core. However, when a reactor shuts down, the level of 135Xe builds up in the core for about 9 hours before beginning to decay. The result is that, about 6–8 hours after a reactor is shut down, it can become physically impossible to restart the chain reaction until the 135Xe has had a chance to decay over the next several hours. This temporary state, which may last several days and prevent restart, is called the iodine pit or xenon-poisoning. It is one reason why nuclear power reactors are usually operated at an even power level around the clock. 135Xe buildup in a reactor core makes it extremely dangerous to operate the reactor a few hours after it has been shut down. Because the 135Xe absorbs neutrons strongly, starting a reactor in a high-Xe condition requires pulling the control rods out of the core much farther than normal. However, if the reactor does achieve criticality, then the neutron flux in the core becomes high and 135Xe is destroyed rapidly—this has the same effect as very rapidly removing a great length of control rod from the core, and can cause the reaction to grow too rapidly or even become prompt critical. 135Xe played a large part in the
Chernobyl accident The Chernobyl disaster was a nuclear accident that occurred on 26 April 1986 at the No. 4 nuclear reactor, reactor in the Chernobyl Nuclear Power Plant, near the city of Pripyat in the north of the Ukrainian Soviet Socialist Republic, Ukrainia ...
: about eight hours after a scheduled maintenance shutdown, workers tried to bring the reactor to a zero power critical condition to test a control circuit. Since the core was loaded with 135Xe from the previous day's power generation, it was necessary to withdraw more control rods to achieve this. As a result, the overdriven reaction grew rapidly and uncontrollably, leading to steam explosion in the core, and violent destruction of the facility.


Uranium enrichment

While many
fissionable In nuclear engineering, fissile material is material capable of sustaining a nuclear fission Nuclear chain reaction#Fission chain reaction, chain reaction. By definition, fissile material can sustain a chain reaction with neutrons of thermal ene ...
isotopes exist in nature, the only usefully
fissile In nuclear engineering, fissile material is material capable of sustaining a nuclear fission Nuclear fission is a nuclear reaction, reaction in which the atomic nucleus, nucleus of an atom splits into two or more smaller atomic nucleu ...
isotope found in any quantity is 235U. About 0.7% of the uranium in most ores is the 235 isotope, and about 99.3% is the non-fissile 238 isotope. For most uses as a nuclear fuel, uranium must be ''enriched'' - purified so that it contains a higher percentage of 235U. Because 238U absorbs fast neutrons, the
critical mass In nuclear engineering, a critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its atomic nucleus, nuclear properties (specifically, it ...
needed to sustain a chain reaction increases as the 238U content increases, reaching infinity at 94% 238U (6% 235U). Concentrations lower than 6% 235U cannot go fast critical, though they are usable in a nuclear reactor with a
neutron moderator In nuclear engineering, a neutron moderator is a medium that reduces the speed of Neutron temperature#Fast, fast neutrons, ideally without neutron capture, capturing any, leaving them as Neutron temperature#Thermal, thermal neutrons with only Ther ...
. A nuclear weapon primary stage using uranium uses HEU enriched to ~90% 235U, though the secondary stage often uses lower enrichments. Nuclear reactors with water moderator require at least some enrichment of 235U. Nuclear reactors with heavy water or graphite moderation can operate with natural uranium, eliminating altogether the need for enrichment and preventing the fuel from being useful for nuclear weapons; the
CANDU The CANDU (Canada Deuterium Uranium) is a Canadian pressurized heavy-water reactor design used to generate electric power. The acronym refers to its deuterium oxide (heavy water) neutron moderator, moderator and its use of (originally, natural ...
power reactors used in
Canadian Canadians (french: Canadiens) are people identified with the country of Canada. This connection may be residential, legal, historical or cultural. For most Canadians, many (or all) of these connections exist and are collectively the source of ...
power plants are an example of this type. The
Uranium enrichment Enriched uranium is a type of uranium in which the percent composition of uranium-235 (written 235U) has been increased through the process of isotope separation. Naturally occurring uranium is composed of three major isotopes: uranium-238 (238U ...
is difficult because the chemical properties of 235U and 238U are identical, so physical processes such as gaseous diffusion, gas centrifuge,
laser A laser is a device that emits light through a process of optical amplification based on the stimulated emission of electromagnetic radiation. The word "laser" is an acronym for "light amplification by stimulated emission of radiation". The fi ...
, or the
mass spectrometry Mass spectrometry (MS) is an analytical technique that is used to measure the mass-to-charge ratio of ions. The results are presented as a ''mass spectrum'', a plot of intensity as a function of the mass-to-charge ratio. Mass spectrometry is us ...
must be used for isotopic separation based on small differences in mass. Because enrichment is the main technical hurdle to production of nuclear fuel and simple nuclear weapons, enrichment technology is politically sensitive.


Oklo: a natural nuclear reactor

Modern deposits of uranium contain only up to ~0.7% 235U (and ~99.3% 238U), which is not enough to sustain a chain reaction moderated by ordinary water. But 235U has a much shorter
half-life Half-life (symbol ) is the time required for a quantity (of substance) to reduce to half of its initial value. The term is commonly used in nuclear physics to describe how quickly unstable atoms undergo radioactive decay or how long stable ato ...
(700 million years) than 238U (4.5 billion years), so in the distant past the percentage of 235U was much higher. About two billion years ago, a water-saturated uranium deposit (in what is now the Oklo mine in
Gabon Gabon (; ; snq, Ngabu), officially the Gabonese Republic (french: République gabonaise), is a country on the west coast of Central Africa. Located on the equator, it is bordered by Equatorial Guinea to the northwest, Cameroon to the north, ...
,
West Africa West Africa or Western Africa is the westernmost region of Africa. The United Nations geoscheme for Africa#Western Africa, United Nations defines Western Africa as the 16 countries of Benin, Burkina Faso, Cape Verde, The Gambia, Ghana, Guinea, ...
) underwent a naturally occurring chain reaction that was moderated by
groundwater Groundwater is the water present beneath Earth's surface in rock and Pore space in soil, soil pore spaces and in the fractures of stratum, rock formations. About 30 percent of all readily available freshwater in the world is groundwater. A unit ...
and, presumably, controlled by the negative void coefficient as the water boiled from the heat of the reaction. Uranium from the Oklo mine is about 50% depleted compared to other locations: it is only about 0.3% to 0.7% 235U; and the ore contains traces of stable daughters of long-decayed fission products.


See also

* List of nuclear reactors *
Nuclear physics Nuclear physics is the field of physics that studies atomic nuclei and their constituents and interactions, in addition to the study of other forms of nuclear matter. Nuclear physics should not be confused with atomic physics, which studies the ...
*
Nuclear fission Nuclear fission is a nuclear reaction, reaction in which the atomic nucleus, nucleus of an atom splits into two or more smaller atomic nucleus, nuclei. The fission process often produces gamma ray, gamma photons, and releases a very large ...
*
Nuclear fusion Nuclear fusion is a reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles ( neutrons or protons). The difference in mass between the reactants and products is mani ...
* Void coefficient


References

*


External links

Fermi age theoryNotes on nuclear diffusion by Dr. Abdelhamid Dokhane
{{Nuclear Technology Nuclear technology + Pressure vessels + + Nuclear physics