Neutron moderator

Science with neutrons
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Water (sometimes called "light water" in this context) is the most commonly used moderator (roughly 75% of the world's reactors). Solid graphite (20% of reactors) and heavy water (5% of reactors) are the main alternatives.^[1] Beryllium has also been used in some experimental types, and hydrocarbons have been suggested as another possibility.

Moderation

Neutrons are normally bound into an

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, ${\displaystyle \langle v^{2}\rangle }$ is the average squared neutron speed, and ${\displaystyle k_{B}}$ is the Boltzmann constant.^[2][3] 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 few 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.

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:

${\displaystyle \xi =\ln {\frac {E_{0}}{E}}=1-{\frac {(A-1)^{2}}{2A}}\ln \left({\frac {A+1}{A-1}}\right)}$.^[4]

This can be reasonably approximated to the very simple form ${\displaystyle \xi \simeq {\frac {2}{A+2/3}}}$.^[5] 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 ${\displaystyle E_{1}}$

${\displaystyle n={\frac {1}{\xi }}(\ln E_{0}-\ln E_{1})}$.^[5]

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., ${\displaystyle {\frac {\xi \Sigma _{s}}{\Sigma _{a}}}}$.^[4] 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.^[4]

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 u	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

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 (though not unable) to cause further fission. 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

Moderators are also used in non-reactor neutron sources, such as plutonium-beryllium (using the ⁹
Be(α,n)¹²
C reaction) and spallation sources (using (p,xn) reactions with neutron rich heavy elements as targets).

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

The moderators of some

In

Moderator impurities

Good moderators are free of neutron-absorbing impurities such as

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

Early speculation about

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 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."^[19]

While a nuclear bomb working on

• 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 (
    a new type of reactor
    .
  • Hydrogen is also used in the form of cryogenic liquid
    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
    German experiments
    .
• CANDU. Reactors moderated with heavy water can use unenriched natural uranium
  .
• 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. Beryllium was used in the S2G reactor.^[22][23]
• 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.

See also

• Nuclear cross section
• Neutron reflector
• Neutron scattering
• Wigner effect

Notes