Nuclear reprocessing

From Wikipedia, the free encyclopedia

Nuclear reprocessing technology was developed to chemically separate and recover fissionable plutonium from spent nuclear fuel. Originally, reprocessing was used solely to extract plutonium for producing nuclear weapons. With commercialization of nuclear power, the reprocessed plutonium was recycled back into MOX nuclear fuel for thermal reactors. The reprocessed uranium, also known as the spent fuel material, can in principle also be re-used as fuel, but that is only economical when uranium supply is low and prices are high. A breeder reactor is not restricted to using recycled plutonium and uranium. It can employ all the actinides, closing the nuclear fuel cycle and potentially multiplying the energy extracted from natural uranium by about 60 times.

Reprocessing has been politically controversial because of the potential to contribute to nuclear proliferation, the potential vulnerability to nuclear terrorism, the political challenges of repository siting (a problem that applies equally to direct disposal of spent fuel), the environmental risks of the aqueous and organic waste streams, and because of its high cost compared to the once-through fuel cycle. In the United States, the Obama administration stepped back from President Bush's plans for commercial-scale reprocessing and reverted to a program focused on reprocessing-related scientific research. Nuclear fuel reprocessing is performed routinely in Europe, Russia and Japan.

Separated components and disposition

The potentially useful components dealt with in nuclear reprocessing comprise specific actinides (plutonium, uranium, and some minor actinides). The lighter elements components include fission products, activation products, and cladding.

History

The first large-scale nuclear reactors were built during World War II. These reactors were designed for the production of plutonium for use in nuclear weapons. The only reprocessing required, therefore, was the extraction of the plutonium (free of fission-product contamination) from the spent natural uranium fuel. In 1943, several methods were proposed for separating the relatively small quantity of plutonium from the uranium and fission products. The first method selected, a precipitation process called the bismuth phosphate process, was developed and tested at the Oak Ridge National Laboratory (ORNL) between 1943 and 1945 to produce quantities of plutonium for evaluation and use in the US weapons programs. ORNL produced the first macroscopic quantities (grams) of separated plutonium with these processes. 

The bismuth phosphate process was first operated on a large scale at the Hanford Site, in the later part of 1944. It was successful for plutonium separation in the emergency situation existing then, but it had a significant weakness: the inability to recover uranium. 

The first successful solvent extraction process for the recovery of pure uranium and plutonium was developed at ORNL in 1949. The PUREX process is the current method of extraction. Separation plants were also constructed at Savannah River Site and a smaller plant at West Valley Reprocessing Plant which closed by 1972 because of its inability to meet new regulatory requirements.

Reprocessing of civilian fuel has long been employed at the COGEMA La Hague site in France, the Sellafield site in the United Kingdom, the Mayak Chemical Combine in Russia, and at sites such as the Tokai plant in Japan, the Tarapur plant in India, and briefly at the West Valley Reprocessing Plant in the United States. 

In October 1976, concern of nuclear weapons proliferation (especially after India demonstrated nuclear weapons capabilities using reprocessing technology) led President Gerald Ford to issue a Presidential directive to indefinitely suspend the commercial reprocessing and recycling of plutonium in the U.S. On 7 April 1977, President Jimmy Carter banned the reprocessing of commercial reactor spent nuclear fuel. The key issue driving this policy was the risk of nuclear weapons proliferation by diversion of plutonium from the civilian fuel cycle, and to encourage other nations to follow the USA lead. After that, only countries that already had large investments in reprocessing infrastructure continued to reprocess spent nuclear fuel. President Reagan lifted the ban in 1981, but did not provide the substantial subsidy that would have been necessary to start up commercial reprocessing.

In March 1999, the U.S. Department of Energy (DOE) reversed its policy and signed a contract with a consortium of Duke Energy, COGEMA, and Stone & Webster (DCS) to design and operate a mixed oxide (MOX) fuel fabrication facility. Site preparation at the Savannah River Site (South Carolina) began in October 2005. In 2011 the New York Times reported "...11 years after the government awarded a construction contract, the cost of the project has soared to nearly $5 billion. The vast concrete and steel structure is a half-finished hulk, and the government has yet to find a single customer, despite offers of lucrative subsidies." TVA (currently the most likely customer) said in April 2011 that it would delay a decision until it could see how MOX fuel performed in the nuclear accident at Fukushima Daiichi.

Separation technologies

Water and organic solvents

PUREX

PUREX, the current standard method, is an acronym standing for Plutonium and Uranium Recovery by EXtraction. The PUREX process is a liquid-liquid extraction method used to reprocess spent nuclear fuel, to extract uranium and plutonium, independent of each other, from the fission products. This is the most developed and widely used process in the industry at present. 

When used on fuel from commercial power reactors the plutonium extracted typically contains too much Pu-240 to be considered "weapons-grade" plutonium, ideal for use in a nuclear weapon. Nevertheless, highly reliable nuclear weapons can be built at all levels of technical sophistication using reactor-grade plutonium. Moreover, reactors that are capable of refueling frequently can be used to produce weapon-grade plutonium, which can later be recovered using PUREX. Because of this, PUREX chemicals are monitored.

Plutonium Processing

Modifications of PUREX

UREX

The PUREX process can be modified to make a UREX (URanium EXtraction) process which could be used to save space inside high level nuclear waste disposal sites, such as the Yucca Mountain nuclear waste repository, by removing the uranium which makes up the vast majority of the mass and volume of used fuel and recycling it as reprocessed uranium. 

The UREX process is a PUREX process which has been modified to prevent the plutonium from being extracted. This can be done by adding a plutonium reductant before the first metal extraction step. In the UREX process, ~99.9% of the uranium and greater than 95% of technetium are separated from each other and the other fission products and actinides. The key is the addition of acetohydroxamic acid (AHA) to the extraction and scrub sections of the process. The addition of AHA greatly diminishes the extractability of plutonium and neptunium, providing somewhat greater proliferation resistance than with the plutonium extraction stage of the PUREX process.

TRUEX

Adding a second extraction agent, octyl(phenyl)-N, N-dibutyl carbamoylmethyl phosphine oxide(CMPO) in combination with tributylphosphate, (TBP), the PUREX process can be turned into the TRUEX (TRansUranic EXtraction) process. TRUEX was invented in the USA by Argonne National Laboratory and is designed to remove the transuranic metals (Am/Cm) from waste. The idea is that by lowering the alpha activity of the waste, the majority of the waste can then be disposed of with greater ease. In common with PUREX this process operates by a solvation mechanism.

DIAMEX

As an alternative to TRUEX, an extraction process using a malondiamide has been devised. The DIAMEX (DIAMide EXtraction) process has the advantage of avoiding the formation of organic waste which contains elements other than carbon, hydrogen, nitrogen, and oxygen. Such an organic waste can be burned without the formation of acidic gases which could contribute to acid rain (although the acidic gases could be recovered by a scrubber). The DIAMEX process is being worked on in Europe by the French CEA. The process is sufficiently mature that an industrial plant could be constructed with the existing knowledge of the process. In common with PUREX this process operates by a solvation mechanism.

SANEX

Selective ActiNide EXtraction. As part of the management of minor actinides it has been proposed that the lanthanides and trivalent minor actinides should be removed from the PUREX raffinate by a process such as DIAMEX or TRUEX. In order to allow the actinides such as americium to be either reused in industrial sources or used as fuel, the lanthanides must be removed. The lanthanides have large neutron cross sections and hence they would poison a neutron driven nuclear reaction. To date the extraction system for the SANEX process has not been defined, but currently several different research groups are working towards a process. For instance the French CEA is working on a bis-triazinyl pyridine (BTP) based process. Other systems such as the dithiophosphinic acids are being worked on by some other workers.

UNEX

The UNiversal EXtraction process was developed in Russia and the Czech Republic; it is designed to completely remove the most troublesome radioisotopes (Sr, Cs and minor actinides) from the raffinate remaining after the extraction of uranium and plutonium from used nuclear fuel. The chemistry is based upon the interaction of caesium and strontium with polyethylene glycol) and a cobalt carborane anion (known as chlorinated cobalt dicarbollide). The actinides are extracted by CMPO, and the diluent is a polar aromatic such as nitrobenzene. Other dilents such as meta-nitrobenzotrifluoride and phenyl trifluoromethyl sulfone have been suggested as well.

Electrochemical methods

An exotic method using electrochemistry and ion exchange in ammonium carbonate has been reported.

Obsolete methods

Bismuth phosphate

The bismuth phosphate process is an obsolete process that adds significant unnecessary material to the final radioactive waste. The bismuth phosphate process has been replaced by solvent extraction processes. The bismuth phosphate process was designed to extract plutonium from aluminium-clad nuclear fuel rods, containing uranium. The fuel was decladded by boiling it in caustic soda. After decladding, the uranium metal was dissolved in nitric acid. 

The plutonium at this point is in the +4 oxidation state. It was then precipitated out of the solution by the addition of bismuth nitrate and phosphoric acid to form the bismuth phosphate. The plutonium was coprecipitated with this. The supernatant liquid (containing many of the fission products) was separated from the solid. The precipitate was then dissolved in nitric acid before the addition of an oxidant (such as potassium permanganate) to produce PuO₂²⁺. The plutonium was maintained in the +6 oxidation state by addition of a dichromate salt. 

The bismuth phosphate was next re-precipitated, leaving the plutonium in solution, and an iron(II) salt (such as ferrous sulfate) was added. The plutonium was again re-precipitated using a bismuth phosphate carrier and a combination of lanthanum salts and fluoride added, forming a solid lanthanum fluoride carrier for the plutonium. Addition of an alkali produced an oxide. The combined lanthanum plutonium oxide was collected and extracted with nitric acid to form plutonium nitrate.

Hexone or redox

This is a liquid-liquid extraction process which uses methyl isobutyl ketone as the extractant. The extraction is by a solvation mechanism. This process has the disadvantage of requiring the use of a salting-out reagent (aluminium nitrate) to increase the nitrate concentration in the aqueous phase to obtain a reasonable distribution ratio (D value). Also, hexone is degraded by concentrated nitric acid. This process has been replaced by the PUREX process.

Pu⁴⁺ + 4 NO₃⁻ + 2 S → [Pu(NO₃)₄S₂]

Butex, β,β'-dibutyoxydiethyl ether

A process based on a solvation extraction process using the triether extractant named above. This process has the disadvantage of requiring the use of a salting-out reagent (aluminium nitrate) to increase the nitrate concentration in the aqueous phase to obtain a reasonable distribution ratio. This process was used at Windscale many years ago. This process has been replaced by PUREX.

Pyroprocessing

Pyroprocessing is a generic term for high-temperature methods. Solvents are molten salts (e.g. LiCl + KCl or LiF + CaF₂) and molten metals (e.g. cadmium, bismuth, magnesium) rather than water and organic compounds. Electrorefining, distillation, and solvent-solvent extraction are common steps. 

These processes are not currently in significant use worldwide, but they have been researched and developed at Argonne National Laboratory and elsewhere. 

Advantages

• The principles behind them are well understood, and no significant technical barriers exist to their adoption.
• Readily applied to high-burnup spent fuel and requires little cooling time, since the operating temperatures are high already.
• Does not use solvents containing hydrogen and carbon, which are neutron moderators creating risk of criticality accidents and can absorb the fission product tritium and the activation product carbon-14 in dilute solutions that cannot be separated later.
  • Alternatively, voloxidation can remove 99% of the tritium from used fuel and recover it in the form of a strong solution suitable for use as a supply of tritium.
• More compact than aqueous methods, allowing on-site reprocessing at the reactor site, which avoids transportation of spent fuel and its security issues, instead storing a much smaller volume of fission products on site as high-level waste until decommissioning. For example, the Integral Fast Reactor and Molten Salt Reactor fuel cycles are based on on-site pyroprocessing.
• It can separate many or even all actinides at once and produce highly radioactive fuel which is harder to manipulate for theft or making nuclear weapons. (However, the difficulty has been questioned.) In contrast the PUREX process was designed to separate plutonium only for weapons, and it also leaves the minor actinides (americium and curium) behind, producing waste with more long-lived radioactivity.
• Most of the radioactivity in roughly 10² to 10⁵ years after the use of the nuclear fuel is produced by the actinides, since there are no fission products with half-lives in this range. These actinides can fuel fast reactors, so extracting and reusing (fissioning) them increases energy production per kg of fuel, as well as reducing the long-term radioactivity of the wastes.

Disadvantages

• Reprocessing as a whole is not currently (2005) in favor, and places that do reprocess already have PUREX plants constructed. Consequently, there is little demand for new pyrometalurgical systems, although there could be if the Generation IV reactor programs become reality.
• The used salt from pyroprocessing is less suitable for conversion into glass than the waste materials produced by the PUREX process.
• If the goal is to reduce the longevity of spent nuclear fuel in burner reactors, then better recovery rates of the minor actinides need to be achieved.

Electrolysis

PYRO-A and -B for IFR

These processes were developed by Argonne National Laboratory and used in the Integral Fast Reactor project. 

PYRO-A is a means of separating actinides (elements within the actinide family, generally heavier than U-235) from non-actinides. The spent fuel is placed in an anode basket which is immersed in a molten salt electrolyte. An electric current is applied, causing the uranium metal (or sometimes oxide, depending on the spent fuel) to plate out on a solid metal cathode while the other actinides (and the rare earths) can be absorbed into a liquid cadmium cathode. Many of the fission products (such as caesium, zirconium and strontium) remain in the salt. As alternatives to the molten cadmium electrode it is possible to use a molten bismuth cathode, or a solid aluminium cathode.

As an alternative to electrowinning, the wanted metal can be isolated by using a molten alloy of an electropositive metal and a less reactive metal.

Since the majority of the long term radioactivity, and volume, of spent fuel comes from actinides, removing the actinides produces waste that is more compact, and not nearly as dangerous over the long term. The radioactivity of this waste will then drop to the level of various naturally occurring minerals and ores within a few hundred, rather than thousands of, years.

The mixed actinides produced by pyrometallic processing can be used again as nuclear fuel, as they are virtually all either fissile, or fertile, though many of these materials would require a fast breeder reactor in order to be burned efficiently. In a thermal neutron spectrum, the concentrations of several heavy actinides (curium-242 and plutonium-240) can become quite high, creating fuel that is substantially different from the usual uranium or mixed uranium-plutonium oxides (MOX) that most current reactors were designed to use. 

Another pyrochemical process, the PYRO-B process, has been developed for the processing and recycling of fuel from a transmuter reactor ( a fast breeder reactor designed to convert transuranic nuclear waste into fission products ). A typical transmuter fuel is free from uranium and contains recovered transuranics in an inert matrix such as metallic zirconium. In the PYRO-B processing of such fuel, an electrorefining step is used to separate the residual transuranic elements from the fission products and recycle the transuranics to the reactor for fissioning. Newly generated technetium and iodine are extracted for incorporation into transmutation targets, and the other fission products are sent to waste.

Voloxidation

Voloxidation (for volumetric oxidation) involves heating oxide fuel with oxygen, sometimes with alternating oxidation and reduction, or alternating oxidation by ozone to uranium trioxide with decomposition by heating back to triuranium octoxide. A major purpose is to capture tritium as tritiated water vapor before further processing where it would be difficult to retain the tritium. Other volatile elements leave the fuel and must be recovered, especially iodine, technetium, and carbon-14. Voloxidation also breaks up the fuel or increases its surface area to enhance penetration of reagents in following reprocessing steps.

Volatilization in isolation

Simply heating spent oxide fuel in an inert atmosphere or vacuum at a temperature between 700 °C and 1000 °C as a first reprocessing step can remove several volatile elements, including caesium whose isotope caesium-137 emits about half of the heat produced by the spent fuel over the following 100 years of cooling (however, most of the other half is from strontium-90 which remains).

Fluoride volatility

Blue elements have volatile fluorides or are already volatile; green elements do not but have volatile chlorides; red elements have neither, but the elements themselves or their oxides are volatile at very high temperatures. Yields at 10^0,1,2,3 years after fission, not considering later neutron capture, fraction of 100% not 200%. Beta decay Kr-85→Rb, Sr-90→Zr, Ru-106→Pd, Sb-125→Te, Cs-137→Ba, Ce-144→Nd, Sm-151→Eu, Eu-155→Gd visible.

In the fluoride volatility process, fluorine is reacted with the fuel. Fluorine is so much more reactive than even oxygen that small particles of ground oxide fuel will burst into flame when dropped into a chamber full of fluorine. This is known as flame fluorination; the heat produced helps the reaction proceed. Most of the uranium, which makes up the bulk of the fuel, is converted to uranium hexafluoride, the form of uranium used in uranium enrichment, which has a very low boiling point. Technetium, the main long-lived fission product, is also efficiently converted to its volatile hexafluoride. A few other elements also form similarly volatile hexafluorides, pentafluorides, or heptafluorides. The volatile fluorides can be separated from excess fluorine by condensation, then separated from each other by fractional distillation or selective reduction. Uranium hexafluoride and technetium hexafluoride have very similar boiling points and vapor pressures, which makes complete separation more difficult.

Many of the fission products volatilized are the same ones volatilized in non-fluorinated, higher-temperature volatilization, such as iodine, tellurium and molybdenum; notable differences are that technetium is volatilized, but caesium is not. 

Some transuranium elements such as plutonium, neptunium and americium can form volatile fluorides, but these compounds are not stable when the fluorine partial pressure is decreased. Most of the plutonium and some of the uranium will initially remain in ash which drops to the bottom of the flame fluorinator. The plutonium-uranium ratio in the ash may even approximate the composition needed for fast neutron reactor fuel. Further fluorination of the ash can remove all the uranium, neptunium, and plutonium as volatile fluorides; however, some other minor actinides may not form volatile fluorides and instead remain with the alkaline fission products. Some noble metals may not form fluorides at all, but remain in metallic form; however ruthenium hexafluoride is relatively stable and volatile. 

Distillation of the residue at higher temperatures can separate lower-boiling transition metal fluorides and alkali metal (Cs, Rb) fluorides from higher-boiling lanthanide and alkaline earth metal (Sr, Ba) and yttrium fluorides. The temperatures involved are much higher, but can be lowered somewhat by distilling in a vacuum. If a carrier salt like lithium fluoride or sodium fluoride is being used as a solvent, high-temperature distillation is a way to separate the carrier salt for reuse.

Molten salt reactor designs carry out fluoride volatility reprocessing continuously or at frequent intervals. The goal is to return actinides to the molten fuel mixture for eventual fission, while removing fission products that are neutron poisons, or that can be more securely stored outside the reactor core while awaiting eventual transfer to permanent storage.

Chloride volatility and solubility

Many of the elements that form volatile high-valence fluorides will also form volatile high-valence chlorides. Chlorination and distillation is another possible method for separation. The sequence of separation may differ usefully from the sequence for fluorides; for example, zirconium tetrachloride and tin tetrachloride have relatively low boiling points of 331 °C and 114.1 °C. Chlorination has even been proposed as a method for removing zirconium fuel cladding, instead of mechanical decladding.

Chlorides are likely to be easier than fluorides to later convert back to other compounds, such as oxides. 

Chlorides remaining after volatilization may also be separated by solubility in water. Chlorides of alkaline elements like americium, curium, lanthanides, strontium, caesium are more soluble than those of uranium, neptunium, plutonium, and zirconium.

Radioanalytical separations

In order to determine the distribution of radioactive metals for analytical purposes, Solvent Impregnated Resins (SIRs) can be used. SIRs are porous particles, which contain an extractant inside their pores. This approach avoids the liquid-liquid separation step required in conventional liquid-liquid extraction. For the preparation of SIRs for radioanalytical separations, organic Amberlite XAD-4 or XAD-7 can be used. Possible extractants are e.g. trihexyltetradecylphosphonium chloride(CYPHOS IL-101) or N,N0-dialkyl-N,N0-diphenylpyridine-2,6-dicarboxyamides (R-PDA; R = butyl, octy I, decyl, dodecyl).

Economics

The relative economics of reprocessing-waste disposal and interim storage-direct disposal was the focus of much debate over the first decade of the 2000s. Studies have modeled the total fuel cycle costs of a reprocessing-recycling system based on one-time recycling of plutonium in existing thermal reactors (as opposed to the proposed breeder reactor cycle) and compare this to the total costs of an open fuel cycle with direct disposal. The range of results produced by these studies is very wide, but all are agreed that under current (2005) economic conditions the reprocessing-recycle option is the more costly.

If reprocessing is undertaken only to reduce the radioactivity level of spent fuel it should be taken into account that spent nuclear fuel becomes less radioactive over time. After 40 years its radioactivity drops by 99.9%, though it still takes over a thousand years for the level of radioactivity to approach that of natural uranium. However the level of transuranic elements, including plutonium-239, remains high for over 100,000 years, so if not reused as nuclear fuel, then those elements need secure disposal because of nuclear proliferation reasons as well as radiation hazard.

On 25 October 2011 a commission of the Japanese Atomic Energy Commission revealed during a meeting calculations about the costs of recycling nuclear fuel for power generation. These costs could be twice the costs of direct geological disposal of spent fuel: the cost of extracting plutonium and handling spent fuel was estimated at 1.98 to 2.14 yen per kilowatt-hour of electricity generated. Discarding the spent fuel as waste would cost only 1 to 1.35 yen per kilowatt-hour.

In July 2004 Japanese newspapers reported that the Japanese Government had estimated the costs of disposing radioactive waste, contradicting claims four months earlier that no such estimates had been made. The cost of non-reprocessing options was estimated to be between a quarter and a third ($5.5–7.9 billion) of the cost of reprocessing ($24.7 billion). At the end of the year 2011 it became clear that Masaya Yasui, who had been director of the Nuclear Power Policy Planning Division in 2004, had instructed his subordinate in April 2004 to conceal the data. The fact that the data were deliberately concealed obliged the ministry to re-investigate the case and to reconsider whether to punish the officials involved.

Neutron moderator

From Wikipedia, the free encyclopedia

 

In nuclear engineering, a neutron moderator is a medium that reduces the speed of fast neutrons, thereby turning them into thermal neutrons capable of sustaining a nuclear chain reaction involving uranium-235 or a similar fissile nuclide.

 

Commonly used moderators include regular (light) water (roughly 75% of the world's reactors), solid graphite (20% of reactors) and heavy water (5% of reactors). Beryllium has also been used in some experimental types, and hydrocarbons have been suggested as another possibility.

Moderation

Neutrons are normally bound into an atomic nucleus, and do not exist free for long in nature. The unbound neutron has a half-life of 10 minutes and 11 seconds. The release of neutrons from the nucleus requires exceeding the binding energy of the neutron, which is typically 7-9 MeV for most isotopes. Neutron sources generate free neutrons by a variety of nuclear reactions, including nuclear fission and nuclear fusion. Whatever the source of neutrons, they are released with energies of several MeV. 

According to the equipartition theorem, the average kinetic energy, ${\displaystyle {\bar {E}}}$, can be related to temperature, ${\displaystyle T}$,via:

${\displaystyle {\bar {E}}={\frac {1}{2}}m_{n}\langle v^{2}\rangle ={\frac {3}{2}}k_{B}T}$,

where ${\displaystyle m_{n}}$ is the neutron mass, ${\displaystyle v}$ is the average neutron speed, and ${\displaystyle k_{B}}$ is the Boltzmann constant. The characteristic neutron temperature of several-MeV neutrons is several tens of billions kelvin. 

Moderation is the process of the reduction of the initial high speed (high kinetic energy) of the free neutron. Since energy is conserved, this reduction of the neutron speed takes place by transfer of energy to a material called a moderator. 

The probability of scattering of a neutron from a nucleus is given by the scattering cross section. The first couple of collisions with the moderator may be of sufficiently high energy to excite the nucleus of the moderator. Such a collision is inelastic, since some of the kinetic energy is transformed to potential energy by exciting some of the internal degrees of freedom of the nucleus to form an excited state. As the energy of the neutron is lowered, the collisions become predominantly elastic, i.e., the total kinetic energy and momentum of the system (that of the neutron and the nucleus) is conserved. 

Given the mathematics of elastic collisions, as neutrons are very light compared to most nuclei, the most efficient way of removing kinetic energy from the neutron is by choosing a moderating nucleus that has near identical mass. 

Elastic collision of equal masses

A collision of a neutron, which has mass of 1, with a ¹H nucleus (a proton) could result in the neutron losing virtually all of its energy in a single head-on collision. More generally, it is necessary to take into account both glancing and head-on collisions. The mean logarithmic reduction of neutron energy per collision, ${\displaystyle \xi }$, depends only on the atomic mass, ${\displaystyle A}$, of the nucleus and is given by: 

${\displaystyle \xi =\ln {\frac {E_{0}}{E}}=1+{\frac {(A-1)^{2}}{2A}}\ln \left({\frac {A-1}{A+1}}\right)}$.

This can be reasonably approximated to the very simple form ${\displaystyle \xi \simeq {\frac {2}{A+1}}}$. From this one can deduce ${\displaystyle n}$, the expected number of collisions of the neutron with nuclei of a given type that is required to reduce the kinetic energy of a neutron from ${\displaystyle E_{0}}$ to ${\displaystyle E_{1}}$

${\displaystyle n={\frac {1}{\xi }}(\ln E_{0}-\ln E_{1})}$.

In a system at thermal equilibrium, neutrons (red) are elastically scattered by a hypothetical moderator of free hydrogen nuclei (blue), undergoing thermally activated motion. Kinetic energy is transferred between particles. As the neutrons have essentially the same mass as protons and there is no absorption, the velocity distributions of both particles types would be well-described by a single Maxwell–Boltzmann distribution.

Choice of moderator materials

Some nuclei have larger absorption cross sections than others, which removes free neutrons from the flux. Therefore, a further criterion for an efficient moderator is one for which this parameter is small. The moderating efficiency gives the ratio of the macroscopic cross sections of scattering, ${\displaystyle \Sigma _{s}}$, weighted by ${\displaystyle \xi }$ divided by that of absorption, ${\displaystyle \Sigma _{a}}$: i.e., ${\displaystyle {\frac {\xi \Sigma _{s}}{\Sigma _{a}}}}$. For a compound moderator composed of more than one element, such as light or heavy water, it is necessary to take into account the moderating and absorbing effect of both the hydrogen isotope and oxygen atom to calculate ${\displaystyle \xi }$. To bring a neutron from the fission energy of ${\displaystyle E_{0}}$ 2 MeV to an ${\displaystyle E}$ of 1 eV takes an expected ${\displaystyle n}$ of 16 and 29 collisions for H₂O and D₂O, respectively. Therefore, neutrons are more rapidly moderated by light water, as H has a far higher ${\displaystyle \Sigma _{s}}$. However, it also has a far higher ${\displaystyle \Sigma _{a}}$, so that the moderating efficiency is nearly 80 times higher for heavy water than for light water.

The ideal moderator is of low mass, high scattering cross section, and low absorption cross section.

	Hydrogen	Deuterium	Beryllium	Carbon	Oxygen	Uranium
Mass of kernels	1	2	9	12	16	238
Energy decrement ${\displaystyle \xi }$	1	0.7261	0.2078	0.1589	0.1209	0.0084
Number of Collisions	18	25	86	114	150	2172

Distribution of neutron velocities once moderated

After sufficient impacts, the speed of the neutron will be comparable to the speed of the nuclei given by thermal motion; this neutron is then called a thermal neutron, and the process may also be termed thermalization. Once at equilibrium at a given temperature the distribution of speeds (energies) expected of rigid spheres scattering elastically is given by the Maxwell–Boltzmann distribution. This is only slightly modified in a real moderator due to the speed (energy) dependence of the absorption cross-section of most materials, so that low-speed neutrons are preferentially absorbed, so that the true neutron velocity distribution in the core would be slightly hotter than predicted.

Reactor moderators

In a thermal-neutron reactor, the nucleus of a heavy fuel element such as uranium absorbs a slow-moving free neutron, becomes unstable, and then splits ("fissions") into two smaller atoms ("fission products"). The fission process for ²³⁵U nuclei yields two fission products, two to three fast-moving free neutrons, plus an amount of energy primarily manifested in the kinetic energy of the recoiling fission products. The free neutrons are emitted with a kinetic energy of ~2 MeV each. Because more free neutrons are released from a uranium fission event than thermal neutrons are required to initiate the event, the reaction can become self-sustaining — a chain reaction — under controlled conditions, thus liberating a tremendous amount of energy.

Fission cross section, measured in barns (a unit equal to 10⁻²⁸ m²), is a function of the energy (so-called excitation function) of the neutron colliding with a ²³⁵U nucleus. Fission probability decreases as neutron energy (and speed) increases. This explains why most reactors fueled with ²³⁵U need a moderator to sustain a chain reaction and why removing a moderator can shut down a reactor.

 

The probability of further fission events is determined by the fission cross section, which is dependent upon the speed (energy) of the incident neutrons. For thermal reactors, high-energy neutrons in the MeV-range are much less likely to cause further fission. (Note: It is not impossible for fast neutrons to cause fission, just much less likely.) The newly released fast neutrons, moving at roughly 10% of the speed of light, must be slowed down or "moderated," typically to speeds of a few kilometres per second, if they are to be likely to cause further fission in neighbouring ²³⁵U nuclei and hence continue the chain reaction. This speed happens to be equivalent to temperatures in the few hundred Celsius range. 

In all moderated reactors, some neutrons of all energy levels will produce fission, including fast neutrons. Some reactors are more fully thermalised than others; for example, in a CANDU reactor nearly all fission reactions are produced by thermal neutrons, while in a pressurized water reactor (PWR) a considerable portion of the fissions are produced by higher-energy neutrons. In the proposed water-cooled supercritical water reactor (SCWR), the proportion of fast fissions may exceed 50%, making it technically a fast neutron reactor. 

A fast reactor uses no moderator, but relies on fission produced by unmoderated fast neutrons to sustain the chain reaction. In some fast reactor designs, up to 20% of fissions can come from direct fast neutron fission of uranium-238, an isotope which is not fissile at all with thermal neutrons. 

Moderators are also used in non-reactor neutron sources, such as plutonium-beryllium and spallation sources.

Form and location

The form and location of the moderator can greatly influence the cost and safety of a reactor. Classically, moderators were precision-machined blocks of high purity graphite with embedded ducting to carry away heat. They were in the hottest part of the reactor, and therefore subject to corrosion and ablation. In some materials, including graphite, the impact of the neutrons with the moderator can cause the moderator to accumulate dangerous amounts of Wigner energy. This problem led to the infamous Windscale fire at the Windscale Piles, a nuclear reactor complex in the United Kingdom, in 1957. 

Some pebble-bed reactors' moderators are not only simple, but also inexpensive: the nuclear fuel is embedded in spheres of reactor-grade pyrolytic carbon, roughly of the size of tennis balls. The spaces between the balls serve as ducting. The reactor is operated above the Wigner annealing temperature so that the graphite does not accumulate dangerous amounts of Wigner energy. 

In CANDU and PWR reactors, the moderator is liquid water (heavy water for CANDU, light water for PWR). In the event of a loss-of-coolant accident in a PWR, the moderator is also lost and the reaction will stop. This negative void coefficient is an important safety feature of these reactors. In CANDU the moderator is located in a separate heavy-water circuit, surrounding the pressurized heavy-water coolant channels. This design gives CANDU reactors a positive void coefficient, although the slower neutron kinetics of heavy-water moderated systems compensates for this, leading to comparable safety with PWRs."

Moderator impurities

Good moderators are also free of neutron-absorbing impurities such as boron. In commercial nuclear power plants the moderator typically contains dissolved boron. The boron concentration of the reactor coolant can be changed by the operators by adding boric acid or by diluting with water to manipulate reactor power. The Nazi Nuclear Program suffered a substantial setback when its inexpensive graphite moderators failed to work. At that time, most graphites were deposited on boron electrodes, and the German commercial graphite contained too much boron. Since the war-time German program never discovered this problem, they were forced to use far more expensive heavy water moderators. In the U.S., Leó Szilárd, a former chemical engineer, discovered the problem.

Non-graphite moderators

Some moderators are quite expensive, for example beryllium, and reactor-grade heavy water. Reactor-grade heavy water must be 99.75% pure to enable reactions with unenriched uranium. This is difficult to prepare because heavy water and regular water form the same chemical bonds in almost the same ways, at only slightly different speeds.

The much cheaper light water moderator (essentially very pure regular water) absorbs too many neutrons to be used with unenriched natural uranium, and therefore uranium enrichment or nuclear reprocessing becomes necessary to operate such reactors, increasing overall costs. Both enrichment and reprocessing are expensive and technologically challenging processes, and additionally both enrichment and several types of reprocessing can be used to create weapons-usable material, causing proliferation concerns. Reprocessing schemes that are more resistant to proliferation are currently under development.

The CANDU reactor's moderator doubles as a safety feature. A large tank of low-temperature, low-pressure heavy water moderates the neutrons and also acts as a heat sink in extreme loss-of-coolant accident conditions. It is separated from the fuel rods that actually generate the heat. Heavy water is very effective at slowing down (moderating) neutrons, giving CANDU reactors their important and defining characteristic of high "neutron economy".

Nuclear weapon design

Early speculation about nuclear weapons assumed that an "atom bomb" would be a large amount of fissile material, moderated by a neutron moderator, similar in structure to a nuclear reactor or "pile". Only the Manhattan project embraced the idea of a chain reaction of fast neutrons in pure metallic uranium or plutonium. Other moderated designs were also considered by the Americans; proposals included using uranium deuteride as the fissile material. In 1943 Robert Oppenheimer and Niels Bohr considered the possibility of using a "pile" as a weapon. The motivation was that with a graphite moderator it would be possible to achieve the chain reaction without the use of any isotope separation. In August 1945, when information of the atomic bombing of Hiroshima was relayed to the scientists of the German nuclear program, interred at Farm Hall in England, chief scientist Werner Heisenberg hypothesized that the device must have been "something like a nuclear reactor, with the neutrons slowed by many collisions with a moderator".

After the success of the Manhattan project, all major nuclear weapons programs have relied on fast neutrons in their weapons designs. The notable exception is the Ruth and Ray test explosions of Operation Upshot–Knothole. The aim of the University of California Radiation Laboratory designs was the exploration of deuterated polyethylene charge containing uranium as a candidate thermonuclear fuel, hoping that deuterium would fuse (becoming an active medium) if compressed appropriately. If successful, the devices could also lead to a compact primary containing minimal amount of fissile material, and powerful enough to ignite RAMROD a thermonuclear weapon designed by UCRL at the time. For a "hydride" primary, the degree of compression would not make deuterium to fuse, but the design could be subjected to boosting, raising the yield considerably. The cores consisted of a mix of uranium deuteride (UD₃), and deuterated polyethylene. The core tested in Ray used uranium low enriched in U²³⁵, and in both shots deuterium acted as the neutron moderator. The predicted yield was 1.5 to 3 kt for Ruth (with a maximum potential yield of 20 kt) and 0.5-1 kt for Ray. The tests produced yields of 200 tons of TNT each; both tests were considered to be fizzles.

The main benefit of using a moderator in a nuclear explosive is that the amount of fissile material needed to reach criticality may be greatly reduced. Slowing of fast neutrons will increase the cross section for neutron absorption, reducing the critical mass. A side effect is however that as the chain reaction progresses, the moderator will be heated, thus losing its ability to cool the neutrons. 

Another effect of moderation is that the time between subsequent neutron generations is increased, slowing down the reaction. This makes the containment of the explosion a problem; the inertia that is used to confine implosion type bombs will not be able to confine the reaction. The end result may be a fizzle instead of a bang. 

The explosive power of a fully moderated explosion is thus limited, at worst it may be equal to a chemical explosive of similar mass. Again quoting Heisenberg: "One can never make an explosive with slow neutrons, not even with the heavy water machine, as then the neutrons only go with thermal speed, with the result that the reaction is so slow that the thing explodes sooner, before the reaction is complete."

While a nuclear bomb working on thermal neutrons may be impractical, modern weapons designs may still benefit from some level of moderation. A beryllium tamper used as a neutron reflector will also act as a moderator.

Materials used

• Hydrogen, as in ordinary "light water". Because protium also has a significant cross section for neutron capture only limited moderation is possible without losing too many neutrons. The less-moderated neutrons are relatively more likely to be captured by uranium-238 and less likely to fission uranium-235, so light water reactors require enriched uranium to operate.
  • There are also proposals to use the compound formed by the chemical reaction of metallic uranium and hydrogen (uranium hydride—UH₃) as a combination fuel and moderator in a new type of reactor.
  • Hydrogen is also used in the form of cryogenic liquid methane and sometimes liquid hydrogen as a cold neutron source in some research reactors: yielding a Maxwell–Boltzmann distribution for the neutrons whose maximum is shifted to much lower energies.
  • Hydrogen combined with carbon as in paraffin wax was used in some early German experiments.
• Deuterium, in the form of heavy water, in heavy water reactors, e.g. CANDU. Reactors moderated with heavy water can use unenriched natural uranium.
• Carbon, in the form of reactor-grade graphite or pyrolytic carbon, used in e.g. RBMK and pebble-bed reactors, or in compounds, e.g. carbon dioxide . Lower-temperature reactors are susceptible to buildup of Wigner energy in the material. Like deuterium-moderated reactors, some of these reactors can use unenriched natural uranium.
  • Graphite is also deliberately allowed to be heated to around 2000 K or higher in some research reactors to produce a hot neutron source: giving a Maxwell–Boltzmann distribution whose maximum is spread out to generate higher energy neutrons.
• Beryllium, in the form of metal. Beryllium is expensive and toxic, so its use is limited.
• Lithium-7, in the form of a lithium fluoride salt, typically in conjunction with beryllium fluoride salt (FLiBe). This is the most common type of moderator in a Molten Salt Reactor.

Other light-nuclei materials are unsuitable for various reasons. Helium is a gas and it requires special design to achieve sufficient density; lithium-6 and boron-10 absorb neutrons.

Currently operating nuclear power reactors by moderator

Moderator	Reactors	Design	Country
none (fast)	1	BN-600	Russia (1)
graphite	25	AGR, Magnox, RBMK	United Kingdom (14), Russia (11)
heavy water	29	CANDU PHWR	Canada (17), South Korea (4), Romania (2), China (2), India (18), Argentina, Pakistan
light water	359	PWR, BWR	27 countries