In a
nuclear weapon
A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission or atomic bomb) or a combination of fission and fusion reactions (thermonuclear weapon), producing a nuclear exp ...
, a tamper is an optional layer of dense material surrounding the
fissile material. It is used in
nuclear weapon design
Nuclear weapons design are physical, chemical, and engineering arrangements that cause the physics package of a nuclear weapon to detonate. There are three existing basic design types:
# Pure fission weapons are the simplest, least technically de ...
to reduce the
critical mass and to delay the expansion of the reacting material through its
inertia
Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newto ...
, which delays the thermal expansion of the fissioning fuel mass, keeping it supercritical longer. Often the same layer serves both as tamper and as
neutron reflector. The weapon disintegrates as the reaction proceeds, and this stops the reaction, so the use of a tamper makes for a longer-lasting, more energetic and more efficient explosion. The
yield can be further enhanced using a fissionable tamper.
The first nuclear weapons used heavy
natural uranium or
tungsten carbide tampers, but a heavy tamper necessitates a larger
high-explosive implosion system and makes the entire device larger and heavier. The primary stage of a modern
thermonuclear weapon
A thermonuclear weapon, fusion weapon or hydrogen bomb (H-bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a lowe ...
may instead use a lightweight
beryllium
Beryllium is a chemical element; it has Symbol (chemistry), symbol Be and atomic number 4. It is a steel-gray, hard, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with ...
reflector, which is also transparent to
X-ray
An X-ray (also known in many languages as Röntgen radiation) is a form of high-energy electromagnetic radiation with a wavelength shorter than those of ultraviolet rays and longer than those of gamma rays. Roughly, X-rays have a wavelength ran ...
s when
ionized, allowing the primary's energy output to escape quickly to be used in compressing the secondary stage. More exotic tamper materials such as
gold
Gold is a chemical element; it has chemical symbol Au (from Latin ) and atomic number 79. In its pure form, it is a brightness, bright, slightly orange-yellow, dense, soft, malleable, and ductile metal. Chemically, gold is a transition metal ...
are used for special purposes like emitting large amounts of X-rays or altering the amount of
nuclear fallout
Nuclear fallout is residual radioactive material that is created by the reactions producing a nuclear explosion. It is initially present in the mushroom cloud, radioactive cloud created by the explosion, and "falls out" of the cloud as it is ...
.
While the effect of a tamper is to increase efficiency, both by reflecting
neutron
The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...
s and by delaying the expansion of the bomb, the effect on the critical mass is not as great. The reason for this is that the process of reflection is time-consuming. By the time reflected neutrons return to the
core, several generations of the
chain reaction have passed, meaning the contribution from the older generation is a tiny fraction of the neutron population.
Function
In ''
Atomic Energy for Military Purposes'' (1945), physicist
Henry DeWolf Smyth describes the function of a tamper in
nuclear weapon design
Nuclear weapons design are physical, chemical, and engineering arrangements that cause the physics package of a nuclear weapon to detonate. There are three existing basic design types:
# Pure fission weapons are the simplest, least technically de ...
as similar to the
neutron reflector used in a
nuclear reactor
A nuclear reactor is a device used to initiate and control a Nuclear fission, fission nuclear chain reaction. They are used for Nuclear power, commercial electricity, nuclear marine propulsion, marine propulsion, Weapons-grade plutonium, weapons ...
:
History
The concept of surrounding the
core of a
nuclear weapon
A nuclear weapon is an explosive device that derives its destructive force from nuclear reactions, either fission (fission or atomic bomb) or a combination of fission and fusion reactions (thermonuclear weapon), producing a nuclear exp ...
with a tamper was introduced by
Robert Serber in his ''
Los Alamos Primer'', a series of lectures given in April 1943 as part of the
Manhattan Project
The Manhattan Project was a research and development program undertaken during World War II to produce the first nuclear weapons. It was led by the United States in collaboration with the United Kingdom and Canada.
From 1942 to 1946, the ...
, which built the first nuclear weapons. He noted that since
inertia
Inertia is the natural tendency of objects in motion to stay in motion and objects at rest to stay at rest, unless a force causes the velocity to change. It is one of the fundamental principles in classical physics, and described by Isaac Newto ...
was the key, the densest materials were preferable, and he identified
gold
Gold is a chemical element; it has chemical symbol Au (from Latin ) and atomic number 79. In its pure form, it is a brightness, bright, slightly orange-yellow, dense, soft, malleable, and ductile metal. Chemically, gold is a transition metal ...
,
rhenium,
tungsten
Tungsten (also called wolfram) is a chemical element; it has symbol W and atomic number 74. It is a metal found naturally on Earth almost exclusively in compounds with other elements. It was identified as a distinct element in 1781 and first ...
and
uranium
Uranium is a chemical element; it has chemical symbol, symbol U and atomic number 92. It is a silvery-grey metal in the actinide series of the periodic table. A uranium atom has 92 protons and 92 electrons, of which 6 are valence electrons. Ura ...
as the best candidates. He believed they also had good
neutron
The neutron is a subatomic particle, symbol or , that has no electric charge, and a mass slightly greater than that of a proton. The Discovery of the neutron, neutron was discovered by James Chadwick in 1932, leading to the discovery of nucle ...
-reflecting properties, although he cautioned that a great deal more work needed to be done in this area. Using elementary
diffusion theory, he predicted that the
critical mass of a nuclear weapon with a tamper would be one-eighth that of an identical but untamped weapon. He added that in practice this would only be about a quarter instead of an eighth.
Serber noted that the neutron reflection property was not as good as it might first seem, because the neutrons returning from collisions in the tamper would take time to do so. He estimated that for a uranium tamper they might take about 10
−7 seconds. By the time reflected neutrons return to the core, several generations of the
chain reaction would have passed, meaning the contribution from the older generation is a tiny fraction of the neutron population. The returning neutrons would also be slowed by the collision. It followed that 15% more
fissile material was required to get the same energy release with a gold tamper compared to a uranium one, despite the fact that the critical masses differed by 50%. At the time, the critical masses of uranium (and more particularly
plutonium
Plutonium is a chemical element; it has symbol Pu and atomic number 94. It is a silvery-gray actinide metal that tarnishes when exposed to air, and forms a dull coating when oxidized. The element normally exhibits six allotropes and four ...
) were not precisely known. It was thought that uranium with a uranium tamper might be about 25 kg, while that of plutonium would be about 5 kg.
The
Little Boy uranium bomb used in the
atomic bombing of Hiroshima had a
tungsten carbide tamper. This was important not just for neutron reflection but also for its strength in preventing the projectile from blowing through the target. The tamper had a radius of and a thickness of , for a mass of . This was about 3.5 times the mass of the fissile material used. Tungsten carbide has a high density and a low neutron absorbency
cross section. Despite being available in adequate quantity during the Manhattan Project,
depleted uranium
Depleted uranium (DU), also referred to in the past as Q-metal, depletalloy, or D-38, is uranium with a lower content of the fissile isotope Uranium-235, 235U than natural uranium. The less radioactive and non-fissile Uranium-238, 238U is the m ...
was not used because it has a relatively high rate of
spontaneous fission of about 675 per kg per second; a 300 kg depleted uranium tamper would therefore have an unacceptable chance of initiating a
predetonation. Tungsten carbide was commonly used in
uranium-233
Uranium-233 ( or U-233) is a fissile isotope of uranium that is bred from thorium-232 as part of the thorium fuel cycle. Uranium-233 was investigated for use in nuclear weapons and as a Nuclear fuel, reactor fuel. It has been used successfully ...
gun-type nuclear weapons used with artillery pieces for the same reason.

There are advantages to using a fissionable tamper to increase the yield.
Uranium-238 will fission when struck by a neutron with , and about half the neutrons produced by the fission of
uranium-235
Uranium-235 ( or U-235) is an isotope of uranium making up about 0.72% of natural uranium. Unlike the predominant isotope uranium-238, it is fissile, i.e., it can sustain a nuclear chain reaction. It is the only fissile isotope that exists in nat ...
will exceed this threshold. However, a
fast neutron striking a uranium-238 nucleus is eight times as likely to be inelastically scattered as to produce a fission, and when it does so, it is slowed to the point below the fission threshold of uranium-238. In the
Fat Man type used in the
Trinity test and at Nagasaki, the tamper consisted of shells of natural uranium and
aluminium
Aluminium (or aluminum in North American English) is a chemical element; it has chemical symbol, symbol Al and atomic number 13. It has a density lower than that of other common metals, about one-third that of steel. Aluminium has ...
. It is estimated that up to 30% of the
yield came from fission of the
natural uranium tamper. An estimated of the yield was contributed by the
photofission of the tamper.
In a
boosted fission weapon or a
thermonuclear weapon
A thermonuclear weapon, fusion weapon or hydrogen bomb (H-bomb) is a second-generation nuclear weapon design. Its greater sophistication affords it vastly greater destructive power than first-generation nuclear bombs, a more compact size, a lowe ...
, the neutrons produced by a
deuterium-
tritium reaction can remain sufficiently energetic to fission uranium-238 even after three collisions with deuterium, but the ones produced by deuterium-deuterium fusion no longer have sufficient energy after even a single collision. A uranium-235 tamper will fission even with slow neutrons. A highly
enriched uranium tamper is therefore more efficient than a depleted uranium one, and a smaller tamper can be used to achieve the same yield. The use of enriched uranium tampers therefore became more common once enriched uranium became more plentiful.
An important development after World War II was the lightweight
beryllium
Beryllium is a chemical element; it has Symbol (chemistry), symbol Be and atomic number 4. It is a steel-gray, hard, strong, lightweight and brittle alkaline earth metal. It is a divalent element that occurs naturally only in combination with ...
tamper. In a boosted device the thermonuclear reactions greatly increase the production of neutrons, which makes the inertial property of tampers less important. Beryllium has a low slow neutron absorbency cross section but a very high scattering cross section. When struck by high energy neutrons produced by fission reactions, beryllium emits neutrons. With a beryllium reflector, the critical mass of highly enriched uranium is 14.1 kg, compared with 52.5 kg in an untamped sphere. A beryllium tamper also minimizes the loss of X-rays, which is important for a thermonuclear primary which uses its X-rays to compress the secondary stage.
The beryllium tamper had been considered by the Manhattan Project, but beryllium was in short supply, and experiments with a beryllium tamper did not commence until after the war. Physicist
Louis Slotin was killed in May 1946 in a
criticality accident involving one. A device with a beryllium tamper was successfully tested in the
Operation Tumbler–Snapper How shot on 5 June 1952, and since then beryllium has been widely used as a tamper in thermonuclear primaries. The secondary's tamper (or "pusher") functions to reflect neutrons, confine the fusion fuel with its inertial mass, and enhance the yield with its fissions produced by neutrons emitted from the thermonuclear reactions. It also helps drive the radiation implosion and prevent the loss of thermal energy. For this reason, the heavy tamper is still preferred.
Alternative materials
Thorium
Thorium is a chemical element; it has symbol Th and atomic number 90. Thorium is a weakly radioactive light silver metal which tarnishes olive grey when it is exposed to air, forming thorium dioxide; it is moderately soft, malleable, and ha ...
can also be used as a fissionable tamper. It has an atomic weight nearly as high as uranium and a lower propensity to fission, which means that the tamper has to be much thicker.
It is possible that a state seeking to develop nuclear weapons capability might add
reactor-grade plutonium to a natural uranium tamper. This would cause problems with neutron emissions from the plutonium, but it might be possible to overcome this with a layer of
boron-10,
which has a high neutron cross section for the absorption of the slow neutrons that fission uranium-235 and
plutonium-239, but a low cross-section for the absorption of the fast neutrons that fission uranium-238. It was used in thermonuclear weapons to protect the plutonium spark plug from stray neutrons emitted by the uranium-238 tamper. In the Fat Man type the natural uranium tamper was coated with
boron
Boron is a chemical element; it has symbol B and atomic number 5. In its crystalline form it is a brittle, dark, lustrous metalloid; in its amorphous form it is a brown powder. As the lightest element of the boron group it has three ...
.
Non-fissionable materials can be used as tampers. Sometimes these were substituted for fissionable ones in
nuclear tests where a high yield was unnecessary. The most commonly used non-fissionable tamper material is
lead
Lead () is a chemical element; it has Chemical symbol, symbol Pb (from Latin ) and atomic number 82. It is a Heavy metal (elements), heavy metal that is density, denser than most common materials. Lead is Mohs scale, soft and Ductility, malleabl ...
, which is both widely available and cheap. British designs often used a lead-
bismuth alloy. Bismuth has the highest atomic number of any non-fissionable tamper material. The use of lead and bismuth reduces
nuclear fallout
Nuclear fallout is residual radioactive material that is created by the reactions producing a nuclear explosion. It is initially present in the mushroom cloud, radioactive cloud created by the explosion, and "falls out" of the cloud as it is ...
, as neither produces isotopes that emit significant amounts of
gamma radiation when irradiated with neutrons.
The
W71 warhead used in the
LIM-49 Spartan anti-ballistic missile
An anti-ballistic missile (ABM) is a surface-to-air missile designed to Missile defense, destroy in-flight ballistic missiles. They achieve this explosively (chemical or nuclear), or via hit-to-kill Kinetic projectile, kinetic vehicles, which ma ...
had a gold tamper around its secondary to maximize its output of X-rays, which it used to incapacitate incoming nuclear warheads.
The irradiation of gold-197 produces gold-198, which has a
half-life Half-life is a mathematical and scientific description of exponential or gradual decay.
Half-life, half life or halflife may also refer to:
Film
* Half-Life (film), ''Half-Life'' (film), a 2008 independent film by Jennifer Phang
* ''Half Life: ...
of 2.697 days and emits gamma rays and
beta particles. It therefore produces short-lived but intense radiation, which may have battlefield uses, although this was not its purpose in the W71. Another element evaluated by the US for such a purpose was
tantalum
Tantalum is a chemical element; it has Symbol (chemistry), symbol Ta and atomic number 73. It is named after Tantalus, a figure in Greek mythology. Tantalum is a very hard, ductility, ductile, lustre (mineralogy), lustrous, blue-gray transition ...
. Natural tantalum is almost entirely tantalum-181, which when irradiated with neutrons become tantalum-182, a beta and gamma ray emitter with a half-life of 115 days.
In the theoretical
cobalt bomb,
cobalt
Cobalt is a chemical element; it has Symbol (chemistry), symbol Co and atomic number 27. As with nickel, cobalt is found in the Earth's crust only in a chemically combined form, save for small deposits found in alloys of natural meteoric iron. ...
is poor prospect for a tamper because it is relatively light and
ionizes at . Natural cobalt is entirely cobalt-59, which becomes
cobalt-60 when irradiated with neutrons. With a half-life of 5.26 years, this could produce long-lasting radioactive contamination.
The British
Tadje nuclear test at
Maralinga used cobalt pellets as a "tracer" for determining yield. This fuelled rumours that Britain had been developing a cobalt bomb.
Physics
The diffusion equation for the number of neutrons within a bomb core is given by:
:
where
is the number density of neutrons,
is the average neutron velocity,
is the number of secondary neutrons produced per fission,
is the fission
mean free path
In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...
and
is transport mean free path for neutrons in the core.
doesn't depend on the direction, so we can use this form of the
Laplace operator
In mathematics, the Laplace operator or Laplacian is a differential operator given by the divergence of the gradient of a Scalar field, scalar function on Euclidean space. It is usually denoted by the symbols \nabla\cdot\nabla, \nabla^2 (where \ ...
in spherical coordinates:
:
Solving the
separable partial differential equation gives us:
:
where
:
and
:
For the tamper, the first term in the first equation relating to the production of neutrons can be disregarded, leaving:
:
Set the separation constant as
. If
(meaning that the neutron density in the tamper is constant) the solution becomes:
:
Where
and
are
constants of integration.
If
(meaning that the neutron density in the tamper is growing) the solution becomes:
:
where
:
Serber noted that at the boundary between the core and the tamper, the diffusion stream of neutrons must be continuous, so if the core has radius
then:
:
If the neutron velocity in the core and the tamper is the same, then
and:
:
Otherwise each side would have to be multiplied by the relevant neutron velocity. Also:
:
For the case where
:
:
If the tamper is really thick, ie
this can be approximated as:
:
If the tamper (unrealistically) is a vacuum, then the neutron scattering cross section would be zero and
. The equation becomes:
:
which is satisfied by:
:
If the tamper is very thick and has neutron scattering properties similar to the core, ie:
:
Then the equation becomes:
:
which is satisfied when:
:
In this case, the critical radius is twice what it would be if no tamper were present. Since the volume is proportional to the cube of the radius, we reach Serber's conclusion that an eightfold reduction in the critical mass is theoretically possible.
Notes
References
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