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THE PHYSICS OF NUCLEAR WEAPONS
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Abstract
1995 saw the 50th anniversary of the first detonation of an atomic bomb. At the present
time the world is in a period of nuclear proliferation, where more and more nations
have the ability to develop their own atomic weapons. It is important to limit nuclear proliferation as far as is possible, because the probability of use increases as the number of nuclear powers rises. However, before you can take action to stop a proliferant nation's nuclear weapons programme, you first have to recognise the signs that one is
underway. This article outlines the main technical features of nuclear weapons, which
have now been published in open literature, in the belief that these facts should
be known to future physicists, so they can more easily recognise cases where work
they hear about or work they are being asked to perform might relate to a covert foreign nuclear weapons development programme, such as that run by Iraq.
The Trinity Test
It was 5:30 am on the 16th July 1945 at the Trinity test site north of Alamogordo,
New Mexico, when daylight came early. A new sun flared in the desert plain, then reddened and heaved upwards, becoming a boiling purple mushroom cloud of radioactive debris, two miles high. A few seconds after the flash, the blast wave and the din of a gigantic explosion reached the onlookers. J. Robert Oppenheimer, Technical Director of the Manhattan Project (the code-name of the wartime atom bomb programme) and sometimes known as the "Father of the Atom Bomb", quoted Hindu scripture: "Now I am become Death, the destroyer of worlds." This was the occasion, over half a century ago, that the awesome power of nuclear weaponry was first unleashed upon the Earth.
Einstein and Energy
An excellent place to begin to understand the physics of nuclear weapons is with
Einstein's most famous equation: E = m*c*c. This equation associates energy E with mass m. The constant of proportionality is the square of the speed of light c. Because c is rather large (3E8m/s), the equation suggests there is a lot of energy associated with even a small amount of matter. In fact one kilogram of matter contains 9E16 Joules of energy, which is roughly the amount of energy released by a hydrogen bomb. Chemical reactions, such as the combustion of petrol in car engines, free less than a billionth of the energy stored in the mass of the fuel, since they do not involve the atomic nuclei, where most of the mass is stored. However, in nuclear reactions the trick of releasing a large proportion of the bound up energy becomes possible.
Fission & Fusion
Two kinds of nuclear reaction may be used to release energy on a large scale. Fission
is the splitting of heavy atomic nuclei into pairs of lighter nuclei, whilst fusion
is the marriage of two light nuclei to form the nucleus of a heavier atom. When
(protons and neutrons) come together to form an atomic nucleus, the nucleus is found to weigh less than the sum of the masses of the nucleons. The difference is the mass of the energy released when the nucleons combine (the so-called "binding energy"). It turns out that the binding energy per nucleon, which is also known as the "mass defect", varies for different sizes of nuclei. The binding energy peaks for atoms about the size of iron. It can be seen that the fusion of light nuclei to form heavier ones generally increases the average binding energy per nucleon. The same is true of the fission of nuclei that are much heavier than iron. Certain kinds of heavy nuclei such as Uranium-235 and Plutonium-239 split very readily when hit by a free neutron. As well as the two lighter daughter nuclei, these fissions tend to produce two or three further free neutrons. If on average more than one of these product neutrons goes on to cause a further fission, then successive generations of fissions involve exponentially increasing numbers of atoms in a nuclear chain reaction.
A chain reaction can very quickly lead to the fission of a large fraction of the atoms in a block of uranium or plutonium. If the average number of neutrons from each fission which go on to initiate further fissions is k (called the k factor), then, starting with a single fission, the number of fissions in the nth subsequent generation is just k**n. The average number of neutrons produced by the fission of Uranium-235 is around 2.5 and the figure is about 3 for Plutonium-239 (Ref. 2). However, not all these neutrons will go on to cause further fissions, as some will be lost in other kinds of nuclear reaction and some will escape from the fissile material without reacting. For the purposes of a rough calculation, we can assume a k of 2.
The fission of a single Uranium-235 nucleus liberates about 3.36E-11J, whereas around 4.18E12J is produced by the detonation of 1000 tonnes (a kiloton) of TNT (a conventional high explosive), so about 1.24E23 Uranium-235 fissions yield the same amount of energy as a kiloton of TNT. You can check with your calculator that the number of fissions in the 77th generation (n=77) exceeds this number for k=2. The time between fission generations is only about 10 nanoseconds, so we can estimate that a nuclear chain reaction in an atom bomb takes around a microsecond from start to finish. The nuclei of certain light atoms will fuse together spontaneously with an accompanying release of energy, if they approach very close to one another. However,
all nuclei are positively charged, so they tend to repel each other. In order to
overcome this repulsion, the nuclei require a lot of kinetic energy. The most straightforward way of providing this energy is to heat the material to very high
temperatures. It also helps to compress the material, because the nuclei start off closer
together and collide due to their thermal motions more frequently at higher densities. The most favourable fusion reaction for nuclear weapons is that between deuterium and tritium nuclei, which are both "isotopes" of hydrogen (isotopes have the same number of protons, but differ in the number of neutrons). Ordinary hydrogen has just a single proton in its nucleus, whilst deuterium has a proton plus a neutron and tritium has
a proton together with two neutrons. The products of the fusion are a helium nucleus,
a single free neutron and 2.8E-12J of energy: D + T ---> He-3 + neutron + 2.8E12J
Atomic Bombs
If the k factor for a block of fissile material is exactly equal to one, then on
average one of the neutrons produced by each fission goes on to cause a further fission
and the reaction neither grows nor dies away. A block for which k=1 is called a critical
mass and blocks for which k is greater than 1 are said to be super critical. To create
an atomic bomb it is simply necessary very rapidly somehow to assemble a super-critical
mass of Uranium-235 or Plutonium-239 and to ensure that there are a few free neutrons
around at the same time in order to get the chain reaction going.
One of the most important factors affecting k is the surface area of the block. If
a block has a larger surface area relative to the number of fissile atoms which it
contains, then it tends to have a lower k, because more neutrons are able to escape through the surface. If you imagine cutting a large block into smaller pieces and moving them apart, then you can visualise that the total surface area of the pieces will be
greater than that of the original block, because of the extra area from the cut surfaces.
For this reason, if a large block of fissile material is assembled from smaller blocks,
it tends to have a larger k value than the parts. It is possible to arrange for a
super-critical mass to be assembled from two or more parts each of which have k factors
less than one. This is the principle used in the so-called "gun assembly"
approach, where a bullet of Uranium-235 is fired down a barrel into a second sub-critical
mass of the same material, thus forming a super-critical mass. The bullet has to
approach the target mass at very high speed or the chain reaction has time to start
while the bullet is still a little distance away and enough energy could be released
to blow the assembly apart before the bullet connected. This premature fission results
in a low yield explosion called a "fizzle". The gun assembly technique
was used in the "Little Boy" bomb which was dropped on Hiroshima by a B-29
bomber called the Enola Gay on August 6th 1945. In this device a cylindrical
slug of 25.2kg of Uranium-235 was blasted at 300m/s down a 7.6cm diameter barrel
into a series of rings made of 34.8kg of Uranium-235 in the tail of the bomb. The
yield was 14.5 kilotons. (Refs. 1, 2 & 3).
The Implosion Design
An implosion is the opposite of an explosion: the blast converges inwards towards
a point instead of travelling outwards from it. A spherical implosion can be used
to crush a sphere of fissile material so as uniformly to reduce its radius and therefore
its surface area. The consequential rapid increase in the k factor offers an attractive
means of starting a chain reaction, so this has become the most commonly used configuration. Plutonium-239 cannot easily be used in the gun assembly configuration, because the chain reaction is so rapid that there is a high risk of fizzle. However, in the implosion design assembly speeds of around 5000m/s are readily achievable (Ref. 2), so this design is almost always used for plutonium bombs. In order to implode a sphere of plutonium you might think all you need to do is wrap a layer of explosive around the sphere, place many detonators at evenly spaced points over the outer surface of the explosive and trigger them all simultaneously. However, it turns out that this simply isn't good enough. The main problem is that the ignition waves overlap before they touch the plutonium sphere and where they overlap they reinforce one another causing the sphere surface to dimple like a golf ball and the plutonium can jet up between the dimples. The net result may actually be an increase in the surface area of the plutonium. Clearly a much smoother implosion wave is necessary to maintain the sphericity of the plutonium during its compression.
Explosive Lenses
By using a special configuration of different explosives, it is possible to modulate
the shape of the convex waves from the detonators to make them concave, such that
they fit the surface of the plutonium core precisely. This configuration is called
an explosive lens, because it works according to the same principles as an optical
lens. A glass lens slows down the light waves as they enter it and this has the effect
of deflecting the wavefront according to the law of refraction. In an explosive lens
a block of slow burn explosive bends the detonation wave at its convex interface
with the block of fast burn explosive in which the detonation is triggered, thus
transforming the diverging wave from the detonator into the converging wave required
to compress the plutonium core. It is known (Ref. 3) that the Trinity device used lenses made from three explosive castings and a total of 96 castings were required. Ref. 2 describes an "advanced" device design where the lenses are arranged according to the 20 hexagons and 12 pentagons used to make some soccer balls. Interestingly,
96 = 3 x (20 +12).
The Tamper/Reflector
A fairly thick shell of neutron reflecting material, called the tamper, surrounds
the core in most designs. This needs to be made of atoms which have a low probability
of reacting with neutrons from the core, but a high probability of knocking neutrons which hit their nuclei back into the core. This reduces the critical mass by cutting down on the number of neutrons which escape the chain reaction. The tamper can also be designed to help in profiling the detonation wave to ensure that the energy of the implosion is used efficiently to compress the core. Beryllium-9 is the best tamper (it can react with neutrons to emit two neutrons), but another isotope of uranium, Uranium-238, also performs adequately and was used in the Trinity device (Ref. 3).
The Driver
In some designs the lenses surround a shell of heavy metal (e.g. Uranium-238), called
the driver. There is an air gap between the driver and the tamper. The implosion
accelerates the driver across the air gap giving it an inexorable momentum, so that
it compresses the core very rapidly and efficiently. Its inertia also helps to keep
the core compressed long enough for the chain reaction to fission a large proportion
of the plutonium atoms.
The Initiator
Although there are usually a few neutrons present in fissile material at any given
time, due to occasional spontaneous fissions for example, it is necessary to be sure
that there are plenty of neutrons near the centre of the core at precisely the right moment in order to be sure of initiating an optimal chain reaction. In the Trinity device this was achieved by placing a grape-sized device at the centre of the core. This initiator device contained Polonium-210 and beryllium separated by metal foils. Polonium-210 is radioactive and emits copious alpha particles, whilst beryllium emits neutrons when irradiated by alpha particles. It was arranged that the implosion of the core should break the foils so that alphas from the Polonium-210 could reach the beryllium (Ref. 3). More modern bombs are said (Ref. 1) to use a neutron gun mounted outside the main bomb assembly to fire a burst of neutrons into the core at the right moment.
Fat Man
At 11:02 on the morning of August 9th 1945 a plutonium implosion weapon called Fat
Man of the same design as the Trinity device was dropped on Nagasaki. It exploded
500m above the city with a yield estimated at 22 or 23 kilotons. It contained 6.2kg
of plutonium of which 21% was fissioned (Ref. 1). Fusion Boosting Of Fission Weapons
The first implosion weapons reportedly (Ref. 3) had solid spherical plutonium cores
about the size of an orange with a central grape-sized cavity for the initiator.
However, a more dramatic and efficient implosion is possible, if a spherical shell
of plutonium containing a larger central cavity is used. The existence of the central
cavity can be exploited to further advantage by injecting a pressurised mix of deuterium
and tritium into it during the implosion. The temperatures and pressures reached
in the core as the chain reaction develops are sufficient to produce a significant amount of fusion in this mixture. In turn, the neutrons generated by this fusion help to accelerate
the chain reaction, allowing a larger fraction of the core atoms to undergo fission,
before the assembly blows itself apart.
Hydrogen Bombs
Boosted fission weapons have an upper limit on their yield of about a megaton (1000
kilotons). For larger yields, Edward Teller and a team of US scientists first of
all considered various ways of packing more fusion fuel around the outside of an
implosion weapon. However, these studies ended in dismal failure in 1950, when computer calculations demonstrated that the fusion fuel would be blown
apart before the temperatures and pressures required to ignite it could be achieved.
It was not until February 1951 that Stanislaw Ulam had an interesting idea.
The Radiation Implosion
When an iron bar is heated, first of all you can feel heat radiating from it, which
is the infrared radiation given out by the hot atoms. As it gets hotter, it starts
to glow, first dull red, then bright orange and finally almost white as it becomes
molten. The electromagnetic radiation given out by hot objects is called blackbody radiation and it shifts to shorter and shorter wavelengths as the temperature
increases. The Sun has a surface temperature of around 5000K, so its blackbody radiation
is in the visible part of the spectrum, a little hotter than the white-hot iron bar.
The debris in a nuclear explosion is initially much hotter and glows in the X-ray
region. These X-rays travel outwards about a hundred times faster than the debris
itself (Ref. 4) at nearly the speed of light. They carry around 70% of the energy liberated
by the explosion (Ref. 5), but they are not very penetrating and can be contained
for a while by a dense, heavy outer casing. Ulam suggested to Edward Teller that
these X-rays might be used to implode and heat a separate capsule of fusion fuel mounted next to the implosion weapon, if both units were contained within the same casing.
The Teller-Ulam Configuration
Ulam's idea turned out to be the crucial breakthrough, though Teller needed to contribute
at least one other major innovation before the design became practicable. In its
finalised form the invention is known as the Teller-Ulam configuration. Oppenheimer
called it "technically...sweet." It certainly has a kind of terrible beauty.
A version of this design, which is loosely based on the US Mark 17 device that was
the first deliverable hydrogen bomb (Refs. 1 & 3). The containment vessel is cylindrical, but rounded at the end where the plutonium implosion device (called the primary) sits, since this is found to help in scattering the X-ray flash down the tube.
This containment vessel is made of some thick, dense metal such as Uranium-238.
The fusion fuel capsules are also cylindrical and are mounted in Styrofoam. The fuel capsules are surrounded by a blanket of Uranium-238 (or Uranium-235).
This blanket is thickened to act as a radiation shield on the side of the capsules
facing the primary. The fusion fuel is likely to consist of Lithium-6 Deuteride and
possibly some Lithium-6 Tritide. These are chemically stable solid compounds
of lithium with deuterium and tritium respectively. Lithium-6 has the special property
of being readily transformed into Helium-4 and tritium, when its nucleus is struck by a neutron:-Li-6 + neutron ---> He-4 + T + 7.5E-13 J This reaction provides additional tritium for the fusion reaction. The X-rays from the primary rapidly burn down through the Styrofoam turning it to a high pressure plasma, which compresses the first fuel capsule in a cylindrical implosion. However, the fuel is still not hot enough to undergo fusion. This is where the second major design innovation comes in. A cylindrical rod of either Uranium-235 or Plutonium-239 is located on the axis of the fuel capsule
and it is arranged for the cylindrical implosion to send this rod super-critical.
A small aperture in the radiation shield allows neutrons from the primary to initiate
a chain reaction in the rod, which then supplies neutrons to transmute the lithium
into helium and tritium and the extra energy required to spark off the fusion reaction.
By analogy with the device used to ignite the fuel in a car engine, this rod is called
the "spark plug". The very high energy neutrons released by the fusion
reaction are capable of inducing additional fissions in the Uranium-238 blanket and
the confinement casing. 
Since each individual fission produces more than ten times
the energy of an individual fusion, these fissions can significantly augment the
yield of the weapon. It is possible to extend the yield of the device to virtually any desired value by adding additional fusion capsules. The first true hydrogen bomb was detonated in a test, code-named Mike, on 1st November 1952. It yielded 10.4 Megatons
and vaporised the island of Elugelab, leaving a crater 800m deep and 3000m wide, which filled with sea water.
Iraqi Developments
Morality
Nuclear weapons are in themselves morally neutral: they can be used to do good as well as evil, for instance, by destroying or deflecting an asteroid, which threatens to collide with the Earth. It is my personal view that their possession by the UK is an important guarantee of our freedom and security. However, in the hands of irresponsible people nuclear weapons present a great threat to the future well being of the world. An improved awareness and vigilance among scientists is one of the ways in which this threat may be countered.
REFERENCES
(c) Andrew Michael Chugg 1995
This article is a copyright document in which the author retains all rights under
applicable law. You are licenced to reproduce it for non-commercial purposes on condition
that it is always clearly attributed to the author and that it is not re-edited.
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