Most nuclear reactors use a chain reaction to induce a controlled rate of nuclear fission in fissile material, releasing both energy and free neutrons. A reactor consists of an assembly of nuclear fuel (a reactor core), usually surrounded by a neutron moderator such as water, graphite, or zirconium hydride, and fitted with mechanisms such as control rods that control the rate of the reaction. Nuclear power station at Leibstadt, Switzerland. ... Several things have been named Chain Reaction, after the chain reaction process best known in connection with nuclear fission: Chain Reaction, a film Chain Reaction, a 1990s record label Chain Reaction, a 1980s game show Chain Reaction, a 1970s band A Square Dance Call on the A1 List A Series... Sketch of induced nuclear fission, a neutron (n) strikes a uranium nucleus which splits into similar products (F. P.), and releases more neutrons to continue the process, and energy in the form of gamma and other radiation. ... Properties In physics, the neutron is a subatomic particle with no net electric charge and a mass of 939. ... In nuclear engineering, a neutron moderator is a medium which reduces the velocity of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction. ... Water (from the Old English word wæter; c. ... Graphite (named by Abraham Gottlob Werner in 1789, from the Greek γραφειν: to draw/write, for its use in pencils) is one of the allotropes of carbon. ... A control rod is a rod made of a chemical element capable of absorbing many neutrons without decaying themselves. ...

The physics of nuclear fission 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. Sketch of induced nuclear fission, a neutron (n) strikes a uranium nucleus which splits into similar products (F. P.), and releases more neutrons to continue the process, and energy in the form of gamma and other radiation. ...

Criticality

In a nuclear reactor, most fission events are caused by neutrons impacting nuclear fuel. Hence, the power output (and neutron production) of a nuclear reactor at present depends on the number of neutrons that are already in the core from previous fissions, and on the expected value of how many fissions will occur as a result of each neutron before the neutron is absorbed or lost.

If the rate of production of new neutrons from fission in an assembly of nuclear fuel (a "core") is less than the rate of loss from absorption or escape, then the core is subcritical and will not support a self-sustaining chain reaction. If the rate of production exceeds the rate of loss, then the core is supercritical and the amount of neutrons produced will grow exponentially. The rate of growth depends on the ratio of neutron production to loss, and on the average lifetime of a neutron in the reactor core. In mathematics, a quantity that grows exponentially is one that grows at a rate proportional to its size. ...

If we write 'N' for the number of free neutrons in a reactor core and 'τ' 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 this differential equation (the evolution equation) In mathematics, a differential equation is an equation in which the derivatives of a function appear as variables. ...

dN / dt = αN / τ

where α 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 or exponential decay, depending on the sign of the constant α, which is just the expected number of neutrons after one average neutron lifetime has elapsed: In mathematics, a quantity that grows exponentially is one that grows at a rate proportional to its size. ... A quantity is said to be subject to exponential decay if it decreases at a rate proportional to its value. ...

α = P_impactP_fissionn_avg − P_absorb − P_escape

Here, P_impact is the probability that a particular neutron will strike a fuel nucleus, P_fission is the probability that the neutron, having struck the fuel, will cause that nucleus to undergo fission, P_absorb is the probability that it will be absorbed by something other than fuel, and P_escape is the probability that it will "escape" by leaving the core altogether. n_avg is the number of neutrons produced, on average, by a fission event -- it is between 2 and 3 for both ²³⁵U and ²³⁹Pu.

If α is positive, then the core is supercritical and the rate of neutron production will grow exponentially until some other effect stops the growth. If α 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 α is exactly zero, then the reactor is critical and its output does not vary in time (dN / dt = 0, from above). Equilibrium or balance is any of a number of related phenomena in the natural and social sciences. ...

Nuclear reactors are engineered to reduce P_escape and P_absorb. Small, compact structures reduce the probability of direct escape by minimizing the surface area of the core, and some materials (such as graphite) can reflect some neutrons back into the core, further reducing P_escape. Light metals such as aluminum that are not strong neutron absorbers are used to build the structure of reactor cores. This article explains the meaning of area as a Physical quantity. ... Graphite (named by Abraham Gottlob Werner in 1789, from the Greek γραφειν: to draw/write, for its use in pencils) is one of the allotropes of carbon. ... The term reflection (also spelt reflexion) can refer to several different concepts: In mathematics, reflection is the transformation of a space. ... Aluminum is a soft and lightweight metal with a dull silvery appearance, due to a thin layer of oxidation that forms quickly when it is exposed to air. ...

The probability of fission, P_fission, depends on the nuclear physics of the fuel, and is often expressed as a cross section. Reactors are usually controlled by adjusting P_absorb. control rods made of a strongly neutron-absorbent material such as cadmium or boron can be inserted into the core: any neutron that happens to impact the control rod is lost from the chain reaction, reducing α. P_absorb is also controlled by the recent history of the reactor core itself (see below). Cross section may refer to the following In geometry, Cross section is the intersection of a 3-dimensional body with a plane. ... A control rod is a rod made of a chemical element capable of absorbing many neutrons without decaying themselves. ... General Name, Symbol, Number cadmium, Cd, 48 Chemical series transition metals Group, Period, Block 12, 5, d Appearance silvery gray metallic Atomic mass 112. ... General Name, Symbol, Number boron, B, 5 Chemical series metalloids Group, Period, Block 13, 2, p Appearance black/brown Atomic mass 10. ...

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 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 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 neutron source is a mixture of an alpha particle emitter such as ²⁴¹Am (Americium-241) with a lightweight isotope such as ⁹Be (Beryllium-9). Once the chain reaction is begun, the starter source is removed from the core to prevent damage from the high neutron flux in the operating reactor core. A neutron source is a device, used in solid state physics (see neutron diffraction), particle physics and to start nuclear chain reactions, that emits neutrons. ... General Name, Symbol, Number americium, Am, 95 Chemical series actinides Group, Period, Block ?, 7, f Appearance silvery white Atomic mass (243) g/mol Electron configuration [Rn] 5f7 7s2 Electrons per shell 2, 8, 18, 32, 25, 8, 2 Physical properties Phase solid Density (near r. ... General Name, Symbol, Number beryllium, Be, 4 Chemical series alkaline earth metals Group, Period, Block 2, 2, s Appearance white-gray metallic Atomic mass 9. ...

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) 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. A neutron source is a device, used in solid state physics (see neutron diffraction), particle physics and to start nuclear chain reactions, that emits neutrons. ... Equilibrium or balance is any of a number of related phenomena in the natural and social sciences. ...

As a measurement technique, subcritical multiplication was used during the Manhattan Project 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. Control panels and operators for calutrons at the Y-12 Plant in Oak Ridge, Tennessee. ...

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:

dN / dt = αN / τ + R_ext

where R_ext 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: Equilibrium or balance is any of a number of related phenomena in the natural and social sciences. ...

N = τR_ext / ( − α)

If the core is subcritical, then α is negative so there is an equilibrium with a positive number of neutrons. If the core is close to criticality, then α is very small and thus the final number of neutrons can be made arbitrarily large.

Neutron moderators

To improve P_fission and enable a chain reaction, uranium-fueled reactors must include a neutron moderator that interacts with newly produced fast neutrons from fission events to reduce their kinetic energy from several MeV to several eV, making them more likely to induce fission. This is because ²³⁵U is much more likely to undergo fission when struck by one of these thermal neutrons than by a freshly-produced neutron from fission. In nuclear engineering, a neutron moderator is a medium which reduces the velocity of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction. ... A fast neutron is a free neutron with a kinetic energy level close to 1 MeV (10 TJ/kg, hence a speed of 14,000 km/s. ... An electronvolt (symbol: eV) is the amount of energy gained by a single unbound electron when it falls through an electrostatic potential difference of one volt. ... eV may stand for: electronvolt eingetragener Verein, i. ... A thermal neutron is a free neutron with a kinetic energy level of ca. ...

Neutron moderators are materials that interact weakly with the neutrons but absorb kinetic energy from them. Most moderators rely on either weakly bound hydrogen or a loose crystal structure of another light element such as carbon to transfer kinetic energy from the fast-moving neutrons. General Name, Symbol, Number hydrogen, H, 1 Chemical series nonmetals Group, Period, Block 1, 1, s Appearance colorless Atomic mass 1. ... General Name, Symbol, Number carbon, C, 6 Chemical series nonmetals Group, Period, Block 14, 2, p Appearance black (graphite) colorless (diamond) Atomic mass 12. ...

Hydrogen moderators include water (H₂O), heavy water(D₂O), and zirconium hydride (ZnH₂), all of which work because a hydrogen nucleus has nearly the same mass as a free neutron: neutron-H₂O or neutron-ZnH₂ impacts excite rotational modes of the molecules (spinning them around). Deuterium 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 liquids, 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. Water (from the Old English word wæter; c. ... Heavy water is dideuterium oxide, or D2O or 2H2O. It is chemically the same as normal water, H2O, but the hydrogen atoms are of the heavy isotope deuterium, in which the nucleus contains a neutron in addition to the proton found in the nucleus of any hydrogen atom. ... Deuterium, also called heavy hydrogen, is a stable isotope of hydrogen with a natural abundance of one atom in 6500 of hydrogen. ... See: transparency (optics) alpha compositing GIF#Transparency transparency (overhead projector) market transparency transparency (telecommunication) transparency (computing) For X11 pseudo-transparency, see pseudo-transparency. ... A liquid will assume the shape of its container. ...

Crystal structure moderators rely on a floppy crystal matrix to absorb phonons from neutron-crystal impacts. Graphite is the most common example of such 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 RBMK nuclear power plants, of which the Chernobyl plant was one. A phonon is a quantized mode of vibration occurring in a rigid crystal lattice, such as the atomic lattice of a solid. ... Graphite (named by Abraham Gottlob Werner in 1789, from the Greek γραφειν: to draw/write, for its use in pencils) is one of the allotropes of carbon. ... On December 2, 1942, the worlds first self-sustaining nuclear chain reaction, Chicago Pile-1, took place on a squash court beneath Stagg Field on the University of Chicago campus. ... Soviet redirects here. ... RBMK is an acronym for the Russian reaktor bolshoi moshchnosty kanalny which means reactor (of) large power (with) channels, and describes a now-obsolete class of nuclear power reactor which was built only in the Soviet Union. ... A nuclear power plant in Cattenom, France. ... The nuclear power plant at Chernobyl prior to the completion of the sarcophagus. ...

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_fission term in the evolution equation, and more moderation reduces the effectiveness by increasing the P_escape 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. Look up Void on Wiktionary, the free dictionary Void can refer to: The absence of matter, a vacuum. ... A nuclear meltdown occurs when the core of a nuclear reactor melts. ...

Most reactors in use today use a combination of moderator materials. For example, TRIGA type research reactors use ZnH₂ moderator mixed with the ²³⁵U fuel, an H₂O-filled core, and C (graphite) moderator and reflector blocks around the periphery of the core. TRIGA is a class of small nuclear reactor designed and manufactured by General Atomics of the USA. TRIGA is an acronym of Training, Research, Isotopes, General Atomics. This type of reactor can be installed without a containment building, and is designed for use by scientific institutions and universities for purposes...

Delayed neutrons and controllability

Fission reactions and subsequent neutron escape happen very quickly; this is important for nuclear weapons, where the object is to make a nuclear core release as much energy as possible before it physically explodes. Most neutrons emitted by fission events are prompt: they are emitted essentially instantaneously. Once emitted, the average neutron lifetime (τ) in a typical core is on the order of a millisecond, so if the exponential factor α 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. 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. The mushroom cloud of the atomic bombing of Nagasaki, Japan, 1945, rose some 18 km (11 mi) above the epicenter. ... Gasoline explosions, simulating bomb drops at an airshow. ... In nuclear engineering, a prompt neutron is a neutron immediately emitted by a nuclear fission event, as opposed to a delayed neutron which is emitted by one of the fission products anytime from a few milliseconds to a few minutes later. ... A millisecond is an SI-derived unit of time, equal to one thousandth of a second. ... For the techno single by Moby, see Thousand (single). ...

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 0.75% of the neutrons produced by ²³⁹Pu fission, are not produced immediately, but rather are emitted by radioactive decay of fission products, with an average lifetime of about 15 seconds. These delayed neutrons increase the effective average lifetime of neutrons in the core, to nearly 0.1 seconds, so that a core with α 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. Radioactive decay is the set of various processes by which unstable atomic nuclei (nuclides) emit subatomic particles (radiation). ... In nuclear engineering, a prompt neutron is a neutron immediately emitted by a nuclear fission event, as opposed to a delayed neutron which is emitted by one of the fission products anything from a few milliseconds to a few minutes later. ...

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. Further, increases in reactor power can be performed at any desired rate simply by pulling out a sufficient length of control rod -- but decreases are limited in speed, because even if the reactor is taken deeply subcritical, the delayed neutrons are produced by ordinary radioactive decay of fission products and that decay cannot be hastened. Radioactive decay is the set of various processes by which unstable atomic nuclei (nuclides) emit subatomic particles (radiation). ...

Reactor poisons

Any element 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 or cadmium 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 is a useful activity: spent nuclear fuel contains about 99% 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 separates any usable elements (e. ...

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). Isotope separation is the process of concentrating specific isotopes of a chemical element by removing other isotopes. ... The fast breeder or fast breeder reactor (FBR) is a type of fast neutron reactor that produces more fissile material than it consumes. ...

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 to a stable isotope. The most important such element is Xenon, 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 is destroyed by neutron capture 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 is one reason why nuclear power reactors are best operated at an even power level around the clock. Nearly all the decay products of radioactive decay are themselves radioactive. ... General Name, Symbol, Number xenon, Xe, 54 Chemical series noble gases Group, Period, Block 18, 5, p Appearance colorless Atomic mass 131. ... See r-process or s-process. ...

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. But if the reactor does achieve criticality, then the neutron flux in the core will become quite high and the ¹³⁵Xe will be 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. In nuclear engineering, an assembly is prompt critical if for each nuclear fission event, one or more of the immediate or prompt neutrons released causes an additional fission event. ...

¹³⁵Xe played a large part in the Chernobyl accident: about eight hours after a scheduled maintenance shutdown, workers tried to bring the the reactor to a zero power critical condition to test a control circuit, but because the core was loaded with ¹³⁵Xe from the previous day's power generation, the reaction rapidly grew uncontrollably, leading to steam explosion in the core, fire, and violent destruction of the facility. The nuclear power plant at Chernobyl prior to the completion of the sarcophagus. ...

Uranium enrichment

The only fissile isotope found in nature is ²³⁵U; about 0.7% of the uranium in most ores is the 235 isotope, and about 99.3% is the inert 238 isotope. For most uses as a nuclear fuel, uranium must be enriched - purified so that it contains a higher percentage of ²³⁵. Because ²³⁸U absorbs fast neutrons, uranium nuclear weapons require their uranium fuel to be ~90% ²³⁵U to work. Nuclear reactors with water moderation can operate with only moderate enrichment of ~5% ²³⁵U. Nuclear reactors with heavy water moderation can operate with natural uranium, eliminating altogether the need for enrichment and preventing the fuel from being useful for nuclear weapons; the CANDU power reactors used in Canadian power plants are an example of this type. General Name, Symbol, Number uranium, U, 92 Chemical series actinides Group, Period, Block ?, 7, f Appearance silvery gray metallic Atomic mass 238. ... Heavy water is dideuterium oxide, or D2O or 2H2O. It is chemically the same as normal water, H2O, but the hydrogen atoms are of the heavy isotope deuterium, in which the nucleus contains a neutron in addition to the proton found in the nucleus of any hydrogen atom. ... The CANDU reactor is a pressurized-heavy water, natural-uranium power reactor designed in the 1960s by a partnership between Atomic Energy of Canada Limited and the Hydro-Electric Power Commission of Ontario as well as several private industry participants. ...

Uranium enrichment is exremely difficult, because the chemical properties of ²³⁵U and ²³⁸U are identical, so physical processes such as gas diffusion or mass spectrometry must be used to separate the isotopes based on their slightly different mass. Because enrichment is the main technical hurdle to production of nuclear fuel and simple nuclear weapons, enrichment technology is politically sensitive. Enriched uranium is uranium whose uranium-235 content has been increased through the process of isotope separation. ... Mass spectrometry is a technique for separating ions by their mass-to-charge (m/z) ratios. ...

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 (70 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, West africa) underwent a naturally occuring chain reaction that was moderated by groundwater and, presumably, controlled by the negative void coeffficient as the water boiled from the heat of the reaction. Uranium from the Oklo mine is about 50% depleted compared to other locations: is is only about 0.3% ²³⁵U; and the ore contains traces of stable daughters of long-decayed fiission products. Half-Life For a quantity subject to exponential decay, the half-life is the time required for the quantity to fall to half of its initial value. ... Oklo is a place in the West African state of Gabon. ... Groundwater is water flowing within aquifers below the water table. ...