Substance that slows down particles with no electric charge
In
nuclear engineering
, a
neutron moderator
is a medium that reduces the speed of
fast neutrons
, ideally without
capturing
any, leaving them as
thermal neutrons
with only
minimal (thermal) kinetic energy
. These
thermal neutrons
are immensely more susceptible than
fast neutrons
to propagate a
nuclear chain reaction
of
uranium-235
or other
fissile
isotope
by colliding with their
atomic nucleus
.
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
[
edit
]
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
,
, can be related to
temperature
,
, via:
- ,
where
is the neutron mass,
is the average squared neutron speed, and
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
1
H 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
,
, depends only on the atomic mass,
, of the nucleus and is given by:
.
[4]
This can be reasonably approximated to the very simple form
.
[5]
From this one can deduce
, 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
to
- .
[5]
Choice of moderator materials
[
edit
]
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,
, weighted by
divided by that of absorption,
: i.e.,
.
[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
. To bring a neutron from the fission energy of
2 MeV to an
of 1 eV takes an expected
of 16 and 29 collisions for H
2
O and D
2
O, respectively. Therefore, neutrons are more rapidly moderated by light water, as H has a far higher
. However, it also has a far higher
, 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
.
Distribution of neutron velocities once moderated
[
edit
]
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,
[5]
[6]
so that the true neutron velocity distribution in the core would be slightly hotter than predicted.
Reactor moderators
[
edit
]
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
235
U
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 (see article
nuclear fission
).
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
235
U
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
(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
[
edit
]
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
[7]
[8]
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. In a carbon dioxide cooled graphite moderated reactor where coolant and moderator are in contact with one another, the
Boudouard reaction
needs to be taken into account. This is also the case if fuel elements have an outer layer of carbon ? as in some
TRISO
fuels ? or if an inner carbon layer becomes exposed by failure of one or several outer layers.
The moderators of some
pebble-bed reactors
are not only simple, but also inexpensive:
[
citation needed
]
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. The heavy water will slow down a significant portion of neutrons to the resonance integral of
238
U
increasing the neutron capture in this isotope that makes up over 99% of the uranium in CANDU fuel thus decreasing the amount of neutrons available for fission. As a consequence, removing some of the heavy water will increase reactivity until so much is removed that too little moderation is provided to keep the reaction going. 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.
[9]
In the light water cooled graphite moderated
RBMK
, a reactor type originally envisioned to allow both production of
weapons grade plutonium
and large amounts of usable heat while using natural uranium and foregoing the use of heavy water, the light water coolant acts primarily as a neutron absorber and thus its removal in a
Loss of Coolant Accident
or by conversion of water into steam will
increase
the amount of thermal neutrons available for fission. Following the
Chernobyl nuclear accident
the issue was remedied so that all still operating RBMK type reactors have a slightly negative void coefficient but they now require a higher degree of
uranium enrichment
in their fuel.
Moderator impurities
[
edit
]
Good moderators are 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 function. At that time, most graphites were deposited onto 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. This problem was discovered by famous physicist
Leo Szilard
[
citation needed
]
Non-graphite moderators
[
edit
]
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.
[
citation needed
]
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
". Unlike a light water reactor where adding water to the core in an accident might provide enough moderation to make a subcritical assembly go critical again, heavy water reactors will decrease their reactivity if light water is added to the core, which provides another important safety feature in the case of certain accident scenarios. However, any heavy water that becomes mixed with the emergency coolant light water will become too diluted to be useful without isotope separation.
Nuclear weapon design
[
edit
]
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".
[10]
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.
[11]
[12]
In 1943
Robert Oppenheimer
and
Niels Bohr
considered the possibility of using a "pile" as a weapon.
[13]
The motivation was that with a
graphite
moderator it would be possible to achieve the chain reaction without the use of any
isotope separation
. However, plutonium can be produced ("bred") sufficiently isotopically pure as to be usable in a bomb and then has to be "only" separated chemically, a much easier processes than isotope separation, albeit still a challenging one. 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".
[14]
The German program, which had been much less advanced, had never even considered the plutonium-option and didn't discover a feasible method of large scale isotope separation in uranium.
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
[15]
: chapter 15
as a candidate thermonuclear fuel,
[16]
: 203
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
[16]
: 149
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.
[17]
: 258
The
cores
consisted of a mix of
uranium deuteride
(UD
3
),
[16]
: 202
and deuterated polyethylene. The core tested in
Ray
used uranium low enriched in U
235
, and in both shots
deuterium
acted as the neutron moderator.
[17]
: 260
The predicted
yield
was 1.5 to 3 kt for
Ruth
(with a maximum potential yield of 20 kt
[18]
: 96
) and 0.5-1 kt for
Ray
. The tests produced yields of 200
tons of TNT
each; both tests were considered to be
fizzles
.
[11]
[12]
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 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
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.
[20]
[21]
Materials used
[
edit
]
- 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.
- 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
[7]
or
pyrolytic carbon
, used in e.g.
RBMK
and
pebble-bed reactors
, or in compounds, e.g.
carbon dioxide
. As carbon dioxide contains twice as many oxygen atoms as it does carbon atoms and both have moderating and neutron absorbing effects in a similar range (see above), a significant share of the moderation in a (yet to be built) carbon dioxide moderated reactor would actually come from the oxygen. 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.
- 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]
- 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
)
|
2
|
BN-600
,
BN-800
|
Russia (2)
|
graphite
|
25
|
AGR
,
Magnox
,
RBMK
|
United Kingdom (14), Russia (9)
|
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
|
See also
[
edit
]
Notes
[
edit
]
- ^
Miller, Jr., George Tyler (2002).
Living in the Environment: Principles, Connections, and Solutions
(12th ed.). Belmont:
The Thomson Corporation
. p. 345.
ISBN
0-534-37697-5
.
- ^
Kratz, Jens-Volker; Lieser, Karl Heinrich (2013).
Nuclear and Radiochemistry: Fundamentals and Applications
(3 ed.). John Wiley & Sons.
ISBN
9783527653355
. Retrieved
27 April
2018
.
- ^
De Graef, Marc; McHenry, Michael E. (2012).
Structure of Materials: An Introduction to Crystallography, Diffraction and Symmetry
. Cambridge University Press. p. 324.
ISBN
9781139560474
. Retrieved
27 April
2018
.
- ^
a
b
c
Stacey., Weston M (2007).
Nuclear reactor physics
.
Wiley-VCH
. pp. 29?31.
ISBN
978-3-527-40679-1
.
- ^
a
b
c
Dobrzynski, L.; K. Blinowski (1994).
Neutrons and Solid State Physics
. Ellis Horwood Limited.
ISBN
0-13-617192-3
.
- ^
Neutron scattering lengths and cross sections
V.F. Sears,
Neutron News
3, No. 3, 26-37 (1992)
- ^
a
b
Arregui Mena, J.D.; et al. (2016).
"Spatial variability in the mechanical properties of Gilsocarbon"
.
Carbon
.
110
: 497?517.
Bibcode
:
2016Carbo.110..497A
.
doi
:
10.1016/j.carbon.2016.09.051
.
S2CID
137890948
.
- ^
Arregui Mena, J.D.; et al. (2018).
"Characterisation of the spatial variability of material properties of Gilsocarbon and NBG-18 using random fields"
.
Journal of Nuclear Materials
.
511
: 91?108.
Bibcode
:
2018JNuM..511...91A
.
doi
:
10.1016/j.jnucmat.2018.09.008
.
S2CID
105291655
.
- ^
D.A. Meneley and A.P. Muzumdar, "Power Reactor Safety Comparison - a Limited Review", Proceedings of the CNS Annual Conference, June 2009
- ^
Nuclear Weapons Frequently Asked Questions - 8.2.1 Early Research on Fusion Weapons
- ^
a
b
Operation Upshot?Knothole
- ^
a
b
W48
- globalsecurity.org
- ^
"Atomic Bomb Chronology: 1942-1944"
. Archived from
the original
on 2008-05-28
. Retrieved
2008-12-16
.
- ^
Hans Bethe
in
Physics Today
Vol 53 (2001)
[1]
- ^
Herken, Gregg
(2003).
Brotherhood of the Bomb
.
- ^
a
b
c
Hansen, Chuck
(1995).
Swords of Armageddon
. Vol. III
. Retrieved
2016-12-28
.
- ^
a
b
Hansen, Chuck
(1995).
Swords of Armageddon
. Vol. I
. Retrieved
2016-12-28
.
- ^
Hansen, Chuck
(1995).
Swords of Armageddon
. Vol. VII
. Retrieved
2016-12-28
.
- ^
Paul Lawrence Rose
(1998).
Heisenberg and the Nazi Atomic Bomb Project: A Study in German Culture
.
University of California Press
. p.
211
.
ISBN
978-0-520-21077-6
. Retrieved
6 May
2017
.
- ^
Nuclear Weapons Frequently Asked Questions - 4.1.7.3.2 Reflectors
- ^
N Moderation
- ^
https://lynceans.org/wp-content/uploads/2020/02/Marine-Nuclear-Power-1939-2018_Part-2A_USA_submarines.pdf
- ^
"Naval Reactors Physics Handbook: The physics of intermediate spectrum ractors, edited by J.R. Stehn"
. 1964.
References
[
edit
]