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4.4 Elements of Thermonuclear Weapon Design

In the previous subsection (4.3) I discussed weapon designs that employ the 
easy-to-ignite D-T reaction. In principle large fusion explosions could be 
created using this reaction, if sufficient tritium were available. The fact 
that tritium must be made through neutron reactions (or other even more 
expensive charged particle reactions) makes its cost prohibitively high for 
this. A neutron expended in breeding Pu-239 or U-233 would make ten times as 
much energy available for a nuclear explosion. Even if the fusion neutrons 
were used efficiently in causing U-238 fast fission (requiring a massive 
fusion tamper as in the Alarm Clock/Layer Cake design), the energy gain 
would still not be dramatically greater than breeding fissile material 
directly. For at most a modest energy gain, this design would have 
considerable penalties. First, there is the added complexity compared to a 
pure fission bomb. Second, and more important, is the natural decay of 
tritium. If the weapon is intended to be kept in stockpile rather than used 
immediately (which fortunately, has been the case since 1945), then 
maintaining a given tritium inventory means duplicating the initial 
investment in tritium production every 17.8 years (sic, this is not a typo, 
the half-life is 12.33 years but continuously replacing decayed tritium 
requires duplicating production over 12.33/ln 2 years).

4.4.1       Development of Thermonuclear Weapon Concepts
The design and functioning of these weapons is complex, I have decided to 
introduce the physics and design of these weapons by discussing the 
evolution of thermonuclear weapon design concepts, instead of plunging 
directly in to a description of modern hydrogen bomb design principles. This 
has the advantage of allowing the introduction of important design ideas 
piecemeal, within a framework which gives the reader a sense of the 
significance of each.

4.4.1.1     Early Work
In the summer of 1942, quite early in the development of nuclear weapons (3 
years before the first fission weapon test), the possibility was noticed of 
igniting self-supporting thermonuclear combustion in pure deuterium, a 
naturally available and comparatively cheap material. If the D-D reaction 
could be initiated then explosions of practically unlimited power could be 
created inexpensively. An additional possibility was that such weapons might 
be much lighter than other designs of comparable yield.

Preliminary investigation made the idea seem promising, but more detailed 
analysis soon showed that the feasibility of a self-sustaining D+D reaction 
in deuterium at achievable densities was marginal at best. In fact the 
better part of a decade (until mid 1950) was spent refining calculations to 
conclusively determine its feasibility one way or the other. In the end, it 
was shown to be impossible under the conditions then deemed to be 
achievable.

It was not until early 1951 that a series of conceptual breakthroughs made 
by Stanislaw Ulam and Edward Teller discovered a way of creating the 
necessary conditions for solving the "ignition problem". These discoveries 
led to the detonation of the first hydrogen bomb in November 1952, some 20 
months later.

4.4.1.2     The Ignition Problem
Stated as generally as possible, the ignition problem is finding a means of 
achieving the following requirements.
1. Creating conditions so that the fusion reaction proceeds at a high rate;
2. Maintaining these conditions for a period of time, such that:
3. The total energy produced (rate*time) exceeds the externally supplied 
energy consumed in creating and maintaining the reaction conditions.

The formula for the rate of a fusion reaction between two types of particles 
A and B is:
     R = N_A * N_B * f_AB(T)
where R is reactions/sec-cm^3, N_A and N_B are the particle densities of A 
and B in particles/cm^3, and f_AB(T) is a function the gives the reaction 
cross section (in cm^2) at temperature T. Since particle energies at 
equilibrium follow a Maxwellian distribution, the function is actually an 
average of the cross section values for specific energies over the 
distribution. In the fusion physics literature, T is normally given in 
electron volts (eV or KeV). One electron volt of temperature is equal to 
11,606 degrees K.

For a given fuel mixture both N_A and N_B are proportional to density. Since 
the rate at a given temperature is determined by the product of N-A and N_B, 
it is proportional to the square of the density. A high density can thus 
greatly enhance the reaction rate.

Note that the effect on the reaction rate in a fixed quantity of fusion fuel 
only increases linearly with density. This because while the reaction rate 
(per unit volume) goes up as the square of density, the actual volume 
decreases linearly with density offsetting this.

The reaction rate is highly dependent on temperature also, as can be seen 
from the table below:

       Reaction Cross Sections (cm^2)
T (KeV)    D/T         D/D       D/He-3
 1.0   5.5x10^-21  1.5x10^-22  3  x10^-26
 2.0   2.6x10^-19  5.4x10^-21  1.4x10^-23
 5.0   1.3x10^-17  1.8x10^-19  6.7x10^-21
 6.0   2.6x10^-17  2.3x10^-19  3.3x10^-20
 7.0   4.1x10^-17  3.5x10^-19  5.3x10^-20
 8.0   6.0x10^-17  5.0x10^-19  8.0x10^-20
 9.0   8.2x10^-17  6.7x10^-19  1.3x10^-19
10.0   1.1x10^-16  1.2x10^-18  2.3x10^-19
15.0   2.6x10^-16  1.9x10^-18  1.3x10^-18
20.0   4.2x10^-16  5.2x10^-18  3.8x10^-18
30.0   6.6x10^-16  6.3x10^-18  1.0x10^-17
40.0   7.9x10^-16  1.0x10^-17  2.3x10^-17
50.0   8.7x10^-16  2.1x10^-17  5.4x10^-17

The primary means by which energy is lost from a fully ionized plasma is 
through bremsstrahlung radiation. The rate of energy emission per unit 
volume is energy emitted is:

 e = 1.42 x 10^-27 Z^3 n_i^2 T^0.5 ergs/cm^3-sec

where n_i is the ion density, Z is the ion atomic number, and T is in 
degrees K. 

Note that the dependence on density for bremsstrahlung emission is the same 
as that of the fusion reaction rate. Its increase with temperature is 
comparatively sluggish, varying only with the square root.

4.4.1.3     The Classical Super
The original concept for creating a thermonuclear explosion was to create a 
thermonuclear combustion wave in a mass of liquid deuterium. The idea was to 
heat a portion of the mass to ignition conditions with an atomic bomb. The 
energy released by the burning region would be sufficient to heat an 
adjacent region to the point of ignition, allowing the region of burning to 
spread throughout the mass. 

This process has been described as "thermonuclear detonation" but 
"thermonuclear combustion" is more accurate. Unlike a high explosive, the 
fusion reaction will not go to completion in a narrow zone behind the 
ignition front, instead the fuel would continue to burn until quenched by 
the expansion of the fuel mass. Since a large mass takes longer to expand 
than a small one, it seemed clear that such a bomb must be fairly large for 
he combustion to be reasonably efficient (one cubic meter of deuterium 
yielding 10 megatons was the nominal figure used).

Developing this approach (originally called the Super, later the Classical 
Super) actually required solving two different ignition problems: 
establishing the initial ignition conditions, and determining whether the 
combustion wave would be self-supporting once established. 

Despite the enormous temperatures and energy densities in a fission bomb, 
the first problem was not straightforward. Some 80% of the energy in an 
exploding bomb core is in the form of soft x-rays, but ionized hydrogen at 
normal densities is virtually transparent to this high temperature radiation 
(the mean free path is measured in hundreds of meters). The thermal 
radiation escaping from the bomb core thus cannot heat a localized region of 
deuterium to ignition. Most the remaining energy is present in the form of 
kinetic energy of ions and electrons. This energy, transferred as a shock 
wave by the expanding bomb core, was a possibility. However the primary 
means to heat the fuel that was chosen seems to have been the neutron flux 
from the core, which carried a mere 1% or so of the explosion energy. The 
reason was that the neutrons travel very rapidly and quickly deposit their 
energy in a manageably small region (roughly 8 cm thick) through moderation 
by the hydrogen. Very large explosions were required for sufficient heating 
to occur (hundreds of kilotons).

The second problem, determining whether thermonuclear combustion would 
propagate and lead to efficient combustion, was very difficult to solve. A 
large number of physical processes are involved: questions of energy 
production rates, energy transport by various reaction products (different 
types of ions and neutrons of various energies), energy transport by 
electrons, energy loss from photons through bremsstrahlung and inverse 
Compton scattering, etc. 

Early on it became apparent that direct heating of deuterium could not 
establish ignition conditions, even fission bombs are not hot enough for 
this. Adding extremely costly tritium to the ignition zone as a "starter 
fuel" was required, the easily combustible tritium could in principal raise 
the fuel to deuterium-deuterium fusion temperatures. Since it is impractical 
to use tritium as the principal fusion fuel, it was essential that the 
detonation wave be able to propagate itself into pure deuterium. Determining 
whether or not this was even possible proved extremely difficult.

Study of the problem began during WWII, and continued until late 1950. The 
basic problems were the balance of energy production to energy loss, and 
spread of combustion conditions. In the burning zone, energy emitted as 
bremsstrahlung (and to a lesser extent the inverse Compton effect) was 
effectively lost to the fuel mass since it was very unlikely to be 
reabsorbed (the MFP for these high temperature photons was measured in 
kilometers!). The fuel mass was thus out of equilibrium with thermal 
radiation. To make the ratio between production and loss favorable, and the 
rate of deuterium combustion reasonably rapid, very high temperatures were 
needed. The energy loss of course tended to damp the temperature rise, 
making the conditions difficult to achieve and maintain.

The fact that most of the fusion energy was released as neutron kinetic 
energy was no doubt problematic also. This meant that most of the energy was 
deposited in a fairly large region outside of the combustion zone, making 
propagation of the zone more difficult.

Solving these problems required intensive numerical computations to simulate 
the propagation and combustion process. As computations became more refined 
during 1949-1950 the ignition problem became worse, requiring ever larger 
amounts of tritium to reach ignition conditions (eventually it was estimated 
that 3-5 kilograms were needed - basically filling the entire ignition zone 
with a 50:50 D-T mixture, corresponding to lost production of 220-500 kg of 
plutonium). But even this did not solve the propagation and combustion 
efficiency questions.

Eventually in mid-1950 (after 8 years of study) it became clear that despite 
large amounts of tritium starter fuel, at best very low combustion 
efficiencies could be obtained with bombs of reasonable size. The reaction 
cross sections of the deuterium-deuterium reactions were simply too low by a 
factor of 2 to 3 to make a Classical Super feasible.

4.4.1.4     The Teller-Ulam Design
Here the matter rested until January 1951. No viable technical approach for 
exploding deuterium was available. At this time Stanislaw Ulam was 
considering ways of improving fission bombs. Since these weapons generally 
rely on compression, he contemplated whether the energy of a small fission 
bomb could be used to compress a larger amount of fissile material. Since 
the energy of fissile material exceeds that of a conventional explosive by 
six orders of magnitude, if this energy could be harnessed to drive an 
implosion much more rapid compression and much higher densities could be 
achieved.

Very quickly he realized that this idea could be extended to compressing 
deuterium, to make a fusion explosion possible. This is the origin of the 
key ideas of separation and staging: separating fuels into physically 
discrete units, and using the explosion of one stage to drive the second 
stage.

It is not immediately evident from a cursory examination of the physics of 
thermonuclear detonation waves that this is really of any help. At a 
constant temperature, the reaction rate in a fusion fuel mass increases 
linearly with compression, but so does the emission rate of thermal energy 
through bremsstrahlung. The balance of energy production to energy loss 
remains the same. For this reason Teller had long regarded compression as 
being futile for enhancing the classical Super.

However not all physical factors scale similarly. While the rates of energy 
generation and emission are linear with density, the scale of the whole 
system varies inversely with the cube root of density just as it does in 
fission cores. Compressing the fuel by a factor of 1000 (for example), 
reduces the dimensions by a factor of 10. This has several important 
consequences. First, the fuel has greater opportunity to burn before 
disassembly. Second, the MFPs for neutrons decrease by a factor of 1000, and 
for photons by a factor of a million. Neutron heating thus occurs in a 
narrower zone, assisting the propagation of the burn region, while photon 
absorption becomes an important heating mechanism - effectively eliminating 
bremsstrahlung loss.

The net result is that compression does indeed make a big difference in the 
feasibility of propagating a thermonuclear combustion wave.

Ulam was the key figure involved with the detailed computations that killed 
the Classical Super concept, he was thus well positioned to realize the 
benefits of compression. The fact that he did not propose compression as a 
solution earlier can be explained by the fact that chemical explosives are 
too weak to be helpful. Much higher compressions are needed. Once he thought 
of nuclear driven implosion, the idea of harnessing it to fusion was 
immediate. He quickly persuaded Teller of the fundamental soundness of the 
idea.

The next problem was determining how the second stage implosion should 
actually be carried out. Ulam's concept did not specify how an implosion 
could be successfully produced using the nuclear explosion energy. His 
initial idea was to use the kinetic energy in the shock wave of expanding 
fission trigger debris. Reflecting and concentrating this shock wave on the 
second stage is possible in principle, but likely to be exceedingly 
difficult in practice.

Teller soon conceived of a better idea. He had been studying radiation 
transport in fission explosions and was well acquainted with the physics 
involved. He knew that most of the energy is in the form of thermal 
radiation, not kinetic energy, and furthermore that the shock front rapidly 
emits this energy into the bomb casing. He also recognized that this thermal 
energy could be harnessed to perform work on the second stage much more 
easily and efficiently than the kinetic shock.

The idea Teller developed is now known as radiation implosion. The thermal 
radiation escaping from the primary stage (also called simply the "primary" 
or "trigger") flows along a gap between the fusion fuel and the opaque bomb 
casing (known as the radiation channel) until the interior of the casing is 
heated to a uniform temperature. The blackbody radiation emission from the 
casing evaporates material from an opaque pusher/tamper around the fusion 
fuel. The expansion of this heated material acts like a rocket engine turned 
inside out -  the inward directed reaction force drives the fuel capsule 
inward, imploding it.

Once the idea of separation and staging have been developed, the idea of 
radiation implosion is actually rather difficult to avoid. The thermal 
radiation arrives well ahead of the shock, and must be dealt with in some 
way. It is very unfavorable to allow it to heat the fusion fuel prior to 
compression, since entropic heating makes compression much less effective. 
If an opaque radiation shield is placed around the fuel to protect it from 
heating, the evaporation of the shield and a resulting implosion is 
inevitable.

A final additional question remains to making this scheme work. How to heat 
the compressed fuel to ignition temperature? One possibility is achieving 
sufficient heating from the compression process itself, reminiscent of a 
diesel engine. Adiabatic compression raises the temperature, but even with 
extreme compression not by a large enough factor. The extremely rapid 
implosion necessarily generates an intense convergent shock wave in the 
fuel. When this shock converges at the center, the extreme heating can be 
sufficient to ignite the fuel (this approach is used in the radiation 
imploded fuel capsules used in inertial confinement fusion experiments).

Teller thought of an additional element to the design to accomplish 
ignition. He proposed placing a sub-critical fissile mass (called the "spark 
plug") at the center of the fusion fuel. The implosion process would 
compress this mass to a high level of criticality, causing an extremely 
rapid fission reaction. This would directly heat the highly compressed fuel, 
initiating a thermonuclear burn. 

As J. Carson Mark points out, the spark plug idea is a fairly obvious 
addition. After all, it was the idea of compressing fissile material that 
set Ulam upon this path in the first place, and heating fusion fuel in 
direct contact with a fission explosion is the same approach as the original 
Super concept.

Taken together these ideas form the basis of the "Teller-Ulam" design, more 
technically described as "staged radiation implosion". So far as is known 
all high yield nuclear weapons today (>50 kt or so) use this design. It is 
striking that once Ulam's initial insight regarding the use of a nuclear 
explosion to compress the fuel was made, the other parts of the concept seem 
to develop almost inevitably from the effort to translate the concept to 
practice (which partly explains its reinvention by the Soviets, British, 
French, and Chinese).

Although the prospect of making possible a self-supporting thermonuclear 
detonation wave appears to have been the initial attraction to both Ulam and 
Teller, it turns out that once the final Teller-Ulam concept was developed 
the character of the ignition problem was so completely changed that this 
issue ceased to be of major importance.

To permit radiation implosion, and prevent premature heating of the fusion 
fuel, an opaque tamper is placed around the fuel mass to keep thermal 
radiation out. By the same token it acts as a radiation container to keep 
thermal radiation in. Because of this, the issue of balancing energy 
production and radiation loss is no longer important. The energy produced by 
the fusion reactions remains trapped inside the tamper, allowing the 
temperature and reaction rate to rise continuously. This is in fact 
essential in making the fissile spark plug viable. The very high Z fissile 
material radiates thermal energy at an extraordinary rate (over seven 
hundred thousand times faster than hydrogen), and would quench the fusion 
reaction if the energy could escape.

The ignition problem for the radiation implosion approach now resembles the 
efficiency problem in fission bombs. The efficiency of the fusion burn is 
determined by the fusion rate, integrated over the duration of confinement. 
The fusion process is usually shut down when the fuel capsule undergoes 
explosive disassembly in a manner similar to that of a fission core. If the 
reaction is highly efficient it may burn up so of the much fuel that the 
rate drops off to a negligible value despite the increasing temperature 
before disassembly occurs.

Unlike the fission bomb though, convenient efficiency equations cannot be 
analytically derived. The energy release in a fission reaction is governed 
by a simple exponential function of time. In contrast fusion reactions are 
not chain reactions, and the way reaction rate varies with temperature is 
not simple. Further the energy release in deuterium is due to three 
different reactions, each with a different rate, and the composition of the 
fuel continuously changes. An adequate treatment of efficiency necessarily 
relies on numerical simulations.

The fully developed Teller-Ulam design was dubbed the "equilibrium 
thermonuclear" or "equilibrium super". The meaning of this term is open to 
question. Some writers (Rhodes in _Dark Sun_ for example) have interpreted 
it to mean that a dynamical equilibrium is established between the exploding 
spark plug and the collapsing fuel mass, bringing the fusion fuel to its 
highest state of compression. This is possible, but I believe the term most 
likely simply refers to the fact that the burning fusion fuel remains in 
equilibrium with thermal energy, unlike the Classical Super.

This short overview provides an understanding of the components of 
thermonuclear weapon designs, and an understanding of the role of each 
component. It scarcely does justice to the physical processes involved. This 
requires a more detailed look at each part of the system.

4.4.2       Schematic of a Thermonuclear Device
Below is a representative deptiction of how a Teller-Ulam device is 
constructed. This schematic is based on a cylindrical design for the 
secondary (mostly because it was easy to create using ASCII graphics). This 
illustration is probably most representative of the large, high yield 
designs developed in the early fifties. Many variations , such as spherical 
secondary designs and other geometric variants, are possible, and 
undoubtedly many have been tried. 

Teller Ulam Diagram

Components of the Teller-Ulam design:

4.4.3       Radiation Implosion
4.4.3.1     The Role of Radiation
At the temperatures achievable in the fission core of the primary (up to 
10^8 degrees K) nearly all of the energy is present as a thermal radiation 
field (up to 95%) with average photon energies around 10 KeV (moderately 
energetic X-rays). Most of this thermal energy is rapidly radiated away from 
the surface of the "X-ray fireball", composed of the expanding X-ray opaque 
material of the core and tamper. It is this powerful flux of energy in the 
form of X-rays that is harnessed to compress the fusion fuel.

To do useful work, the radiant energy from the primary must be kept from 
escaping from the bomb before the work is completed. This is accomplished by 
the radiation case - a container made of X-ray opaque (high-Z, or high 
atomic number) material that encloses both the primary and secondary. The 
gap between the radiation case and other parts of the bomb (mostly the 
secondary) is called the radiation channel since thermal radiation travels 
from to other parts of the bomb through this gap.

The X-ray flux from the primary actually penetrates a short distance into 
the casing (a few microns) and is absorbed, heating a very thin layer lining 
the casing to high temperatures and turning it into a plasma. This plasma 
re-radiates thermal energy, heating other parts of the radiation channel 
farther from the primary.

The radiant energy emitted by the primary is blackbody radiation: a 
continuous spectrum of photons whose energy distribution is determined 
solely by the temperature of the radiating surface. The average photon 
energy, and the energy of the peak photon intensity are proportional to the 
temperature. Similarly, the photons re-radiated by the surfaces lining the 
radiation channel form a blackbody spectrum. 

As energy flows down the radiation channel, the energy density drops since 
the photon gas is now filling a greater volume. This means the temperature 
of the photon gas, and the average photon energy must drop as well. From an 
initial average energy of 10 KeV, the X-rays soften to around 1-2 KeV. This 
corresponds to a temperature in the casing of some 10-25 million degrees K.

[Note: Many descriptions in the open literature exist dating back to the 
late seventies claiming that energetic X-rays from the primary are absorbed 
by the radiation casing (or plastic foam), and are re-emitted at a lower 
energy - implying that some sort of energy down-shifting mechanism (like X-
ray fluorescence) is at work. This is a misconception. The lining of the 
casing is in local thermal equilibrium with the energy flux impinging on it, 
and re-radiates X-rays with the same spectrum. The X-ray spectrum softens 
simply because the photon gas cools as it expands to fill the entire 
radiation channel.]

In physics a closed container of radiation, like the radiation case, is 
called a "hohlraum". This German word for "cavity" (which has the obvious 
English cognates "hole" and "room") has been attached to the study of the 
thermodynamics of radiation since the last century in connection with 
blackbody radiation. German physicists early in this century used it as a 
theoretical model for deriving the blackbody radiation laws from quantum 
mechanics. Energy in a hohlraum necessarily comes into thermal equilibrium 
and assumes a blackbody spectrum. This is important for obtaining the 
necessary symmetry for an efficient implosion. Regardless of how uneven the 
initial energy distribution within the casing is, the radiation field will 
quickly establish thermal equilibrium throughout the casing - heating all 
parts to the same temperature.
4.4.3.2     Opacity of Materials in Thermonuclear Design
Since the emission, transport, and absorption of thermal radiation is 
critical to all phases of operation of a thermonuclear device the opacity of 
various materials to this radiation is critically important. The interaction 
between a given element and an X-ray photon is dependent on the atomic 
number, atom density, and ionization state of the element, and the energy of 
the photon. Since the X-ray flux has a continuous spectrum, we are really 
interested in the average interaction across that spectrum. We are also 
especially interested in the situation where the average photon energy (the 
radiation temperature) and the average kinetic energy of atoms/ions are the 
same. This situation is called local thermodynamic equilibrium (LTE), and is 
found almost everywhere inside a thermonuclear device.

The terms "high-Z" and "low-Z" come up frequently in discussing the 
interaction between thermal radiation and physical materials. These terms 
are relative - whether a material qualifies as having high or low atomic 
number depends on the temperature under discussion. The two terms can also 
be taken as approximate synonyms for "opaque" and "transparent". This is not 
universally true, however. As explained below, at extremely high pressure 
this distinction may become unimportant.

An ion strongly interacts with the X-ray spectrum (is opaque to it) when it 
possesses several electrons, because it then has many possible excitation 
states, and can absorb and emit photon of many different frequencies. A 
material where the atomic nuclei are completely stripped of electrons must 
interact with X-ray photons primarily through the much weaker processes of 
bremsstrahlung or Thomson scattering. High atomic number atoms hold on to 
their last few electrons very strongly (the ionization energy of the last 
electron is proportional to Z^2), resisting both thermal ionization and high 
pressure dissociation, which is the primary reason they are opaque.

Even when comparing two different fully ionized materials, the higher Z 
material will more readily absorb photons since bremsstrahlung absorption is 
proportional to Z^2 (at equal particle density, if it is the ion densities 
that are the same then it is proportional to Z^3). See Sections 3.2.5 Matter 
At High Temperatures, and 3.3 Interaction of Radiation and Matter for more 
discussion of these are related issues.

To summarize: a material qualifies as opaque or "high-Z" if it possesses 
some electrons at the temperature under consideration. A transparent or 
"low-Z" material will be completely ionized. Since electrons are removed by 
ion/particle collisions, the ionization state will depend on the 
temperature, which is determined by the average kinetic energy (kT) of a 
particle. At a minimum, all electrons with ionization energies less than or 
equal kT will be removed, and at the densities of matter encountered here 
electrons with ionization energies up 3 or 4 kT will often be removed as 
well.  

An important caveat to the above is that at the very high pressures that 
exist in a fully compressed secondary, essentially any element will become 
opaque. The density of Fermi degenerate matter under some specific pressure 
is determined by the density of free electrons. Under the enormous 
compressive forces generated during secondary implosion the electron density 
becomes so high that even the "weak" Thomson scattering effect becomes 
strong enough to render matter opaque. This is important for the energy 
confinement needed during the thermonuclear burn.

Different temperatures are encountered in different parts of a thermonuclear 
device - approaching 10 KeV in the primary, 1-2.5 KeV in the radiation 
channel, and up to 35 KeV inside the secondary. We can make a general guide 
showing which materials qualify as opaque or transparent at these 
temperatures by finding Z such that the last (Zth) ionization state has an 
ionization energy I(Z) approximately equal to kT and 4kT. Any element with 
I(Z) of around kT will certainly be completely ionized at temperature T. An 
element will need I(Z) to be significantly greater than 4kT to be highly 
opaque.

It should be noted that a significant proportion of Planck spectrum energy 
to be carried by photons with energies even higher than 4kT (10% of it is 
carried by photons with energies above 6.55 kT). It is possible then at 
temperatures where the radiation field dominates for the flux of photons to 
be so intense that photo-ionization of electrons with energies well above 7 
kT may occur. 

Temperature      Low Z (I(Z)~kT)        High Z (I(Z)~4kT)
              Z Symbol  Actual I(Z)   Z Symbol  Actual I(Z)
1 KeV         9    F     1.10 KeV    18   Ar      4.41 KeV
2.5 KeV      13   Al     2.30 KeV    28   Ni     10.7  KeV
10 KeV       28   Ni    10.7  KeV    55   Cs     41.1  KeV
35 KeV       51   Sb    35.4  KeV   101   Md    139.   KeV

From the table we can make some general statements about the materials we 
want in different parts of the device. We want thermal radiation to escape 
rapidly from the primary, so it is important to keep the atomic number of 
materials present in the explosive layer to no higher that Z=28. The use of 
baratol (containing barium with Z=56) is thus very undesirable. Since the 
radiation channel needs to be transparent, keeping materials with Z above 9-
13 out of the channel is desirable. Radiation case linings should have Z 
significantly higher than 55, as should the fusion tamper and radiation 
shield.

Due to the complexity of the interacting processes that determine the 
opacity of incompletely ionized material at LTE, theoretical prediction of 
these properties is extremely difficult. In fact accurate predictions based 
on first principles is impossible, experimental study is required. It is 
interesting to note that opacity data for elements with Z > 71 remain 
classified in the US. This is a clear indication of the materials used in 
thermonuclear weapon design for containing and directing radiation. The fact 
that elements with Z > 71 are used as radiation case linings has recently 
been declassified in the US. 

There are 14 plausible elements with atomic number of 72-92 that may be used 
for this purpose. Of these 14 elements, 5 are definitely known to have been 
used in radiation case or secondary pusher/tamper designs in actual nuclear 
devices: tungsten (74), gold (79), lead (82), bismuth (83), and uranium 
(92). There is evidence that rhenium (75) and thorium (90) may have been 
used as well, and tantalum (73) has been used in ICF pusher designs. Two 
others, mercury (80) and thallium (81) are also known to have been 
incorporated in thermonuclear weapons in classified uses (in addition to 
declassified uses, such as electrical switches).

The optimal material for radiation confinement should have maximum optical 
thickness per unit mass. Opacity increases with atomic number, but for a 
given radiation temperature the increase with Z probably declines at some 
point. Since atomic mass also increases with Z, there is probably an optimal 
element for any given radiation temperature that has a maximum opacity per 
unit mass. 

4.4.3.3     The Ablation Process
The thin hot plasma layer lining the radiation channel not only radiates 
heat back into the channel, it also radiates heat deeper into the material 
lining the channel creating a flow of thermal radiation into the radiation 
case and the secondary pusher/tamper. The hot plasma also has tremendous 
internal kinetic pressure and expands into the radiation channel.

This rapid evaporation and expansion (ablation) of the radiation channel 
lining is unavoidable. Due to the conservation of momentum, the expanding 
material creates a reaction force called "ablation pressure" that pushes in 
the opposite direction - blowing the walls of the radiation case outward, 
and the pusher/tamper of the secondary inward. It is this inward force, 
analogous to the force exerted by the exhaust of a rocket, that compresses 
the secondary.

We can calculate representative parameters for the implosion process. To 
span a range of designs and parameter values let us consider the Mike 
device, a high yield design that was the first (and undoubtedly physically 
largest) radiation implosion device ever exploded, and the W-80 cruise 
missile warhead which is a modern light weight design. 

The casing of the Mike device was a steel cylinder 20 ft. (6.1 m) long and 
80 in. (2.0 m) wide, with walls 12 in. (30 cm) thick. It used a TX-5 fission 
primary, with a yield probably no larger than 50 kt, and produced a total 
yield of 10.4 Mt. The W-80 is a cylinder 80 cm long, and 30 cm wide, it has 
a primary with a yield in the low kiloton range (call it 5 kt for the sake 
of the discussion), and a total yield of 150 kt. The thickness of the W-80 
casing is unknown, but given its weight (130 kg) it must be less than 2 cm.

Once equilibrium is established, the energy density in the radiation channel 
will be roughly the energy released by the primary, divided by the volume 
inside the radiation case (this neglects the kinetic energy in the primary 
remnants, and the volume of the secondary, but these are comparatively small 
and offset each other). This gives radiation densities of 2.2 x 10^14 
erg/cm^3 for Mike and 4.3 x 10^15 erg/cm^3 for the W-80, a energy density 
ratio of 1:20. By applying the blackbody radiation laws (see Section 3.1.6 
Properties of Blackbody Radiation) we can determine the corresponding 
radiation intensities and temperatures:  9.8 x 10^6 K and 5.3 x 10^16 W/cm^2 
for Mike; and 2 x 10^7 K and 1.0 x 10^18 W/cm^2 for the W-80. The radiation 
pressures are 73 and 1400 megabars respectively.

The ablation pressure is determined by mass evaporation rate, and the 
effective exhaust velocity of the evaporated material:
     P = m_evap_rate * V_ex
If the evaporation rate is in g/cm^2-sec, and V_ex is in cm/sec, then the 
result is in dynes/cm^2, applying the conversion factor of 10^6 dynes/cm^2 
per bar gives the result in bars.

The ultimate implosion velocity is determined by the rocket equation:
     V_imp = V_ex * ln(m_initial/m_final)
where m_initial is the initial mass of the pusher/tamper and m_final is the 
mass after ablation is complete. Peak efficiency (in terms of energy 
expended) of an ideal rocket is reached when the ratio (m_initial/m_final) 
is around 5.

In a rocket maximum force is extracted from hot reaction gases by allowing 
them to expand as they exit the rocket nozzle, which cools and accelerates 
the exhaust. The effective exhaust velocity is the velocity of the cooled 
and expanded gas at the nozzle's mouth. In contrast, ablation is generated 
by an energy flow that must penetrate the exhaust gas which prevents the gas 
from cooling. The effective exhaust velocity here is the gas velocity at the 
sonic point, the point where the gas is moving at the local speed of sound 
relative to the ablation front, where the material is actually evaporating. 
Since changes to the exhaust flow beyond the sonic point cannot propagate 
back to the ablation front, as far as the secondary is concerned the exhaust 
effectively disappears at this point.

[Note that many descriptions in the open literature ascribe the driving 
force in implosion to the plasma pressure created by a plastic foam that is 
known to fill the radiation channel in many weapon designs. Since 
hydrodynamic effects that occur beyond the sonic point cannot propagate back 
to the imploding secondary, this is impossible.]

Since the exhaust gases beyond the sonic point absorb heat and carry it away 
from the secondary, and also reradiate significant amounts of thermal energy 
back into the radiation channel, the ablation driven acceleration process is 
less efficient than an ideal rocket as judged in terms of the incident 
radiation intensity.

The efficiency for an ideal rocket (the percentage of the kinetic energy in 
the exhaust-rocket system ending up in the rocket at burnout) is given by:
 eff = (x (ln x)^2)/(1 - x)
where x if the ratio between the final mass and the initial mass:
    x = m_final/m_initial
This has a peak efficiency of 64.8% at x = 0.203.

The heating of the exhaust limits the ablation driven rocket to a maximum 
efficiency of approximately 15-20% when x is in the range of 0.1 to 0.6 
(with peak efficiency around 0.25). Above 0.6 it drops off to about 7% at 
0.85. It thus desirable to ablate off most of the pusher/tamper mass so that 
x < 0.5. [Note: This is based on ICF data which uses radiation driven 
implosions at a few hundred eV. The higher temperature X-rays of nuclear 
implosion systems penetrate to the ablation front more efficiently and may 
actually do better than this.]

Scaling laws for the relationships between temperature or energy density and 
the ablation rate and exhaust velocity can be determined by dimensional 
analysis. The sonic-point temperature (and average kinetic energy) is 
proportional to (~=) the temperature in the radiation channel, and since
v ~= KE^(1/2), 
then 
V_ex ~= T^(1/2).

Because the incident energy flux I between the ablation front and the sonic 
point must be proportional to the kinetic energy carried away we have:
I ~= m_evap_rate * V_ex^2 ~= m_evap_rate * T
and since
I ~= T^4
we get 
m_evap_rate ~= T^3.

Finally:
P = m_evap_rate * V_ex ~= T^3 * T^(1/2) ~= T^3.5

It is possible to estimate the values of the constants to convert these 
proportionalities into equations from physical data, but the process is 
rather elaborate. We can borrow some relationships that have appeared in the 
inertial confinement fusion literature in connection with radiation 
implosion to get some estimates of the magnitudes:
     P (bars) = 0.3 T^3.5
and
     m_evap_rate (g/cm^2-sec) = 0.3 T^3
where T is in electron volts. From this we get:
V_ex (cm/sec) = P/m_evap_rate =  0.3 T^3.5 (10^6 dynes/cm^2 /bar)/0.3 T^3 
              = 10^6 T^0.5

For the Mike device this gives:
P = 5.3 x 10^9 bars
m_evap_rate = 0.18 g/cm^2-nanosecond
V_ex = 2.9 x 10^7 cm/sec = 290 km/sec

For the W-80:
P = 6.4 x 10^10 bars
m_evap_rate = 1.5 g/cm^2-nanosecond
V_ex = 4.1 x 10^7 cm/sec = 410 km/sec

The ablation pressures for the Mike and W-80 devices are much greater than 
the corresponding radiation pressures, by factors of 73 and 46 respectively. 
This shows that the force exerted by radiation pressure is comparatively 
small.

From the classical rocket equation given above we can estimate V_imp at 
maximum efficiency (where 75% of the mass is ablated off) at 400 km/sec 
(Mike) and 570 km/sec (W-80). 

4.4.3.3.1   The Ablation Shock
There is a short "settling" period early in the implosion process when the 
initial ablation pressures are propagating through the pusher/tamper. When 
the radiation flux begins ablating the pusher, a strong shock wave 
propagates through the pusher/tamper. This shock compresses and accelerates 
the tamper inward.

When the shock reaches the inner surface of the tamper, the tamper is (more 
or less) uniformly compressed and at its minimum thickness. The material 
beyond the tamper has a much lower density, so the shock compressed 
material, which is under extremely high pressure, immediately begins to 
expand and form a release wave (see Section 3.6.1.1 Release Waves). This 
release wave has two edges, a forward edge where the expanding gas meets the 
low density material, and a rear edge where the pressure drop begins in the 
shock compressed gas.

At the forward edge of this wave most of the internal energy of the gas has 
been converted to kinetic energy. This means that the gas velocity is at a 
maximum and the pressure has dropped to a minimum. The actual pressure and 
velocity of the forward edge depends on the density of the low density 
material. If the density is greater than zero, then this forward edge will 
be a low pressure shock front. 

Behind this leading edge gas velocity decreases, and pressure and density 
both increase. These changes are continuous, increasing in magnitude with 
distance from the leading edge until the original state of the shocked gas 
is reached at the rear edge of the release wave. Eventually this rear edge 
(which travels at the local speed of sound) will reach the ablation front at 
which point the pressure, density, and velocity distribution in the tamper 
reaches its final overall form, with a continuously decreasing pressure and 
density gradient from the ablation front forward to the leading edge of the 
tamper.

This pressure gradient is responsible for the inward acceleration of all of 
the material that has passed through the inner implosion shock front. The 
general pressure and density profile, once established, remains stable 
throughout the implosion process, until the inner front collides with itself 
at the center.

It is likely that while the initial shock is moving through the tamper, the 
pressure at the ablation front will continue to climb, creating a pressure 
and density gradient behind the shock. The pressure gradient created by the 
release wave will merge with this compression wave to create the continuous 
pressure and density gradient.  

The velocities of the shock waves generated in a uranium pusher/tamper by 
these pressures is on the order of 150 km/sec (for Mike) and 550 km/sec for 
the W-80. These shocks are powerful enough to dissociate electrons from 
their nuclei by pressure alone, but they also strongly heat the tamper 
(causing thermal ionization) and prevent the achievement of true Fermi 
degenerate compression (see below). Still, with the effects of ionization, 
the density increase can be greater than a factor of 10. If the rise in 
ablation pressure can be moderated by appropriate design techniques (see 
Implosion System Design below) so that the shock front can traverse the 
tamper ahead of the full pressure jump, this can be substantially improved 
upon. The temperatures produced are in the order of several million degrees 
K, considerably lower than the radiation channel temperature. The pressure 
behind the shock front is predominantly due to particle kinetic pressure not 
radiation pressure, so these are simple supercritical radiative shocks.

4.4.3.4     Principles of Compression

4.4.3.4.1   Purpose of Compression
The fundamental purpose of compressing the fusion fuel is to allow the 
reaction to proceed swiftly enough for a large part of the fuel to burn 
before it disassembles from its own expansion, or from the expansion of the 
trigger fireball. Compression promotes the fusion reaction in several ways.

In Section 4.4.1.2 (The Ignition Problem) it was seen that the reaction rate 
of a quantity of fuel will increase in direct proportion to its density if 
it is compressed at constant temperature.

But we can expect the temperature to increase as well, and with it the 
cross-sections of the thermonuclear reactions. In dense thermonuclear fuel 
nearly all of the energy  present exists as a photon gas. Since the 
radiation energy density in a sealed container is dependent only on 
temperature, confining the energy to a smaller volume increases the 
temperature. According to the blackbody radiation law (Section 3.1.6 
Properties of Blackbody Radiation) this increase is rather slow though, 
being proportional to the fourth root of the energy density. This is offset 
by the fact that throughout most of the temperature range of interest the 
increase in cross section with temperature is rapid.

To illustrate the relative importance of these effects, suppose a quantity 
of fuel were compressed 16-fold. This would increase the reaction rate 16 
times due to the density increase alone. This compression would double the 
temperature (16^(1/4) = 2). If the temperature were initially 5 KeV (58 
million degrees K), the cross-section increase for the pace-setting D-D 
reaction would be 6.7 fold (although this factor would decline as the 
temperature rises).

These are not the only advantages however. Just as it does with a fissile 
core, compression of the fusion fuel increases the dimension of the fuel 
mass as measured by neutron collision mean free paths. The neutrons released 
by the fusion reactions will thus undergo many more collisions with fuel 
nuclei before they can reach the tamper. In the early stages of combustion 
of pure deuterium fuel (before the temperature rise and buildup of He-3 make 
the He-3 + D reaction significant) 66.3% of all the energy produced is 
released in the form of neutron kinetic energy. Deuterium is a very light 
atom (only hydrogen-1 is lighter) so it has a very strong moderating effect. 
On average a neutron will lose 51.6% of its energy with each collision (see 
Section 4.1.7.3.2.1 Moderation and Inelastic Scattering). After several 
collisions then, almost all the energy released as neutron kinetic energy 
will be transferred to heating the fusion fuel.

The MFP in liquid deuterium for the 14.1 MeV neutrons produced by the D+T 
reaction is 22 cm. A 1 kg sphere of liquid deuterium would be 22.4 cm 
across, most 14.1 MeV neutrons generated within this mass would escape 
without even a single collision. If this sphere were compressed 125-fold, 
its diameter would shrink to 4.49 cm but the MFP would now be only 0.18 cm. 
Few neutrons would escape without depositing most of their energy in the 
fuel mass.

The effects of multiple neutron collisions are even more important in 
lithium deuteride fuel. 75% of the mass of Li-6 D fuel consists of lithium. 
To use this mass as fuel, the lithium nuclei must each capture a neutron. 
The fuel must be compressed sufficiently for a large part of the neutrons 
produced to participate in this reaction.

To illustrate how compression affects the rate of burn up, I have run a 
simple computer model of deuterium fusion at varying densities. The model 
assumes constant density during the fusion reaction and no energy escape 
from the fuel. 

With the same amount of energy deposited in the fuel for ignition (0.1 
kilotons/kg) the time to burn up 75% of the deuterium at normal liquid 
density (0.16 g/cm^3) is 1.3 milliseconds. At 288 g/cm^3 the time shrinks to 
only 4.4 nanoseconds. The graph of density versus time is nearly a straight 
line on a log-log plot, so intermediate values can be easily estimated using 
a scientific calculator (or log-log graph paper).

The reduction in burn up time is partly due to the higher initial 
temperature of the denser fuel (12 million degrees K at 0.16 g/cm^3, and 55 
million degrees K at 288 g/cm^3) but even at constant initial temperature 
the comparative burn up rates are much the same.

4.4.3.4.2   The Fermi Pressure 
From the ablation pressures calculated earlier, we can determine the maximum 
densities that can be produced. Maximum density is achieved if the heating 
during compression is negligible, that is, the counterbalancing pressure in 
the compressed material is simply the Fermi pressure produced by a 
completely degenerate Fermi gas (see 3.2.4 Matter At High Pressures). 

Since:
P_Fermi (bars) = 2.34 x 10^-33 * n^(5/3)
where n is the electron density (electrons/cm^3), we can calculate the 
electron densities of 2.6 x 10^25 electrons/cm^3 for 5.3 gigabars (the Mike 
device) and 1.2 x 10^26 electrons/cm^3 for 64 gigabars (the W-80). The 
limiting mass density based on the calculated ablation pressure for the Mike 
device is thus 86 g/cm^3 (deuterium or Li6D) and 290 g/cm^3 (U-238 at 38% 
dissociation). The corresponding values for the W-80 are 380 g/cm^3 
(deuterium or Li6D) and 1200 g/cm^3 (U-238 at 41% dissociation). The 
inevitable shock induced entropy increase in the tamper will reduce the 
achievable densities of a U-238 tamper to values well below this.

Now the energy densities due to degeneracy pressure implied by these 
electron densities is given by:
   E_density (erg/cm^3) = 3.50 x 10^-27 n^(5/3)
or 8.0 x 10^15 erg/cm^3 for 5.3 gigabars, and 1.0 x 10^17 erg/cm^3 for 64 
gigabars. The Fermi energy per mass at 5.3 gigabars is 9.3 x 10^9 J/kg (D or 
Li6D) and <7.3 x 10^9 J/kg (U-238), or 2.2 and <1.7 tonnes of explosive 
energy per kg respectively. At 64 gigabars the energy per unit mass is 2.6 x 
10^10 J/kg (D or Li6D) and <2.0 x 10^10 J/kg (U-238), or 6.2 and <4.8 tonnes 
per kg. These figures show the minimum energy investment required to achieve 
the maximum density.

The corresponding Fermi temperatures, given by:
  T_Fermi = (5 P_Fermi)/(2 nk)
are 3.7 x 10^6 K (5.3 gigabars), and 9.7 x 10^6 K (64 gigabars). In 
efficient (i.e. Fermi degenerate) compression the final temperatures of the 
compressed fuel most be substantially lower than the Fermi temperature.

4.4.3.4.3   Efficient Compression
Now the question arises as to how these tremendous pressure can be applied 
to actually generate densities close to these maximum values. Simply 
applying these ablation pressures suddenly to the thermonuclear fuel will 
not actually compress it very much. Sudden pressure jumps produce intense 
shock waves that expend shock energy about equally between heat and kinetic 
energy, with a negligible portion going to compression. The density increase 
will limited by the effective value of gamma. Such a violent shock would be 
radiation dominated so no more than a 7-fold compression occurs in this 
case.

There are two ways this can be done. The pressure increment can divided into 
a series of shock waves, each providing a modest pressure increase ratio, 
and minimal entropic heating. Alternatively, an appropriately shaped 
continuous pressure rise can produce true adiabatic compression. Actually 
there is not much difference between these two options. Continuous adiabatic 
compression is the limiting case of an infinitely large number of infinitely 
weak shocks producing no entropic heating. And in practice, any continuous 
pressure gradient of this magnitude will tend to break up into a sequence of 
discrete shocks (see 3.7.5 Methods for Extreme Compression for further 
discussion of this).

In any case, propagating an initial shock of considerable strength into the 
fuel is unavoidable. This is because the bomb will typically disassemble on 
a time scale of no more than a microsecond or so, and the compression of the 
fuel must be complete well before this occurs. Even if the fuel layer to be 
compressed is only a few centimeters thick, then an initial shock of at 
least some tens of kilometers per second is necessary to traverse the fuel.

We can make some useful observations about the compression of the secondary 
rather easily. 

If A denotes the area of the fuel capsule surface, then the total force 
being exerted on the capsule is:
     F = P*A
From the Newtonian law:
     work = force*distance
we can determine the work done on the capsule by:
     W = P*A*d = P * (change in volume)
for small values of d. More generally we can say:
     W = Integral[P] dV

Now we consider two possible implosion geometries - cylindrical and 
spherical (variants of these, such as tapered cylinders and ellipsoids are 
possible but the principles are the same). Since V is proportional to r^2 
(for cylindrical geometry) or r^3 (for spherical geometry), it follows that 
most of the work done on the capsule occurs during the early stages of 
implosion when the net change in radius is fairly small.

By the time the capsule volume has been reduced by half, then half of all 
the work that is done on the capsule has been completed (assuming constant 
ablation pressure). This corresponds to a radius reduction (measured from 
the outside surface of the pusher/tamper) of:
 1 - 0.5^(1/2) = 29.3% (cylindrical geometry)
or
or 1 - 0.5^(1/3) = 20.6% (spherical geometry).

Another way to look at it is that as the capsule implodes, its surface area 
shrinks. Since the pressure (which is the force per unit area) is constant, 
the total force, and the ability to do work, on the capsule shrinks also 
with decreasing radius.

At this point the imploding capsule has acquired half of its final kinetic 
energy, and 70% (0.5^0.5) of its final implosion velocity. The remaining 
part of the implosion can be termed "free fall", during which the 
pusher/tamper travels inward at essentially constant velocity. This maximum 
velocity depends on the ablation pressure, mass of the pusher/tamper, and 
the volume of secondary, as well as the geometry.

We should observe that the ablation process soaks up a lot of energy. A 
simplistic computation of the work done in imploding a 10 liter secondary in 
the "W-80", assuming constant ablation pressure, shows that 6.4 x 10^13 J 
(15 kt) is put into the secondary. This is more energy than we assumed that 
the primary actually produced (5 kt), and also ignores the limits of rocket 
efficiency. Clearly as implosion proceeds the available energy in the 
channel decreases, as does the ablation pressure. We can expect the final 
implosion velocity to be in the range of 300-800 km/sec however.

By the same geometric argument used above, if the compression wave 
propagates only 30% of the way into a cylindrical fuel mass, or 20% of the 
way into a spherical one, then half the fusion fuel will have been 
compressed. Thus the compression process only needs to be efficient in the 
outer layers of fuel. Even if excessive heating and poor compression occur 
at significantly smaller radii, overall fuel compression will still be 
efficient.

From the equations given in Methods of Extreme Compression, and assuming an 
initial 50 megabar shock though the outer layers of fuel which compresses 
liquid deuterium or Li6D fuel 12-fold (a 200 km/sec shock in deuterium, a 90 
km/sec shock in LiD), we can estimate final compressions and densities for 
our two illustration cases. The compression for Mike (5.4 gigabars and 
liquid deuterium) is 197-fold (33.3 g/cm^3); for the W-80 (64 gigabars and 
Li6D) it is 878 fold (720 g/cm^3). The calculated compression for Mike is 
well short of the limit imposed by the Fermi pressure, with a lower initial 
shock pressure than the one I assumed the density could be increased by a 
factor of two or more. The density calculations for the W-80 (which were 
done without considering degeneracy effects) is higher than the Fermi 
pressure. We can conclude then that this system can achieve compressions 
near the Fermi pressure limited density. [Note that to more properly 
calculate the effects of compression on dense tamper material at pressures 
lying between those achieved by high explosives, and the Fermi degenerate 
state requires use of more complicated theoretical models like the Thomas-
Fermi theory.]

4.4.3.5     Ignition
Efficient compression can raise the temperature of the fuel to a few million 
degrees K. This is hot enough to create a measurable D-D fusion reaction in 
the compressed fuel, but by itself it does not result in a thermonuclear 
reaction that is rapid enough to be useful. 

To achieve efficient fuel burn up the fuel most be heated to the point where 
the rate of self-heating becomes significant, triggering a rapidly 
accelerating combustion process. The denser the fuel mass, the less energy 
is required to reach this point.

How hot the fuel must be is determined by the density, and the achievable 
confinement time of the fuel - which in turn is governed by a number of 
weapon design factors, including the size of the secondary. Using the same 
simple deuterium fusion model mentioned above, we find an effective ignition 
temperature of 30 million degrees K. At this temperature the reaction rate 
and fuel temperature immediately begin a rapid rise, causing accelerating 
fuel burn-up. The reaction is essentially complete (80% burnup) in 20 
nanoseconds when the fuel density is 100 g/cm^3. Lower temperatures create a 
latency period where the temperature rises very slowly, before abruptly 
climbing upwards (once 30 million K is reached). At an initial temperature 
of 12 million degrees, this latency period is 60 nanoseconds after which the 
fuel burns to near completion in the same 20 nanosecond period. 
Investigating other densities in the range of 50-300 g/cm^3 gives much the 
same picture regarding the ignition temperature, although the density does 
strongly affect how long the fuel burn up takes.

In any case, it is clear that the temperatures prevailing in the ablation-
induced shock are much too low to ignite efficient fuel burning.

The energy required to heat the fuel to 3 x 10^7 K is in the range of 2.8 to 
4.1 x 10^11 J/kg (67 to 98 tonnes of explosive energy) for deuterium and 
Li6D fuel with densities between 50 and 200 g/cm^3. This is a factor of 5 
times (200 g/cm^3, Li6D fuel) to 15 times (50g/cm^3, D fuel) higher than the 
energy in the fuel due to degeneracy pressure. Heating the fuel to ignition 
is thus energetically more expensive than efficient compression.

At least two different mechanisms are possible for igniting the main fusion 
reaction:
* The first method to be used was suggested by Teller - the use of a fission 
spark plug in the center of the fuel mass.
* A second method is used in laboratory scale fusion explosions (inertially 
confined fusion experiments, that is) - allowing the compression shock to 
converge in the center of the fuel, creating extremely high temperatures and 
in a very small volume of fuel. A combustion wave then spreads from the 
center to the remaining fuel. A variant on this to place a tritium-deuterium 
spark plug in the center of the secondary. Since this reaction ignites at 
much lower temperatures, it is much easier to achieve the necessary ignition 
conditions. In ICF experiments D-T mixtures are the only fuel used.

4.4.3.5.1   Fission Spark Plugs
A subcritical fissile mass placed in the center of the fuel will be rapidly 
compressed upon arrival of the imploding shock. At such a small radius (a 
few centimeters), the pressure gradient or shock sequence will probably have 
merged into a single extremely energetic shock. This shock will have been 
further augmented by the effects of shock convergence, and the final stages 
of implosion - where the compressed fuel mass decelerates the high velocity 
tamper - may have generated pressures even higher than the ablation 
pressure. This shock will have velocities in the range of several hundreds 
of kilometers a second. When this shock arrives at the interface between the 
fusion fuel and the higher density spark plug, it will drive an even higher 
pressure (but slower) shock into the fissile material. The implosion 
velocity achieved will be at least 100 km/sec in any case - more than an 
order of magnitude higher than the highest velocities achieved by practical 
high explosive implosion systems.

In principal a shock of this intensity could compress the spark plug to a 
density of perhaps 16 times normal, but here too the effects of 
predetonation intervene to prevent this from being reached. If neutrons are 
present at the outset of supercritical insertion, the energy release from 
fission will halt the implosion well short of this density. But - here the 
much higher velocity of implosion makes a *big* difference in the practical 
effect of predetonation.

First the enormous kinetic energy and pressures in the imploding mass 
requires energy releases in the order of a few kilotons simply to halt the 
implosion process, unlike the high explosive case where the energy release 
required is negligible compared to the final yield. Second, the compression 
that is achieved at this point, while much lower than the maximum that the 
shock is capable of producing, is still probably at least a factor of 3.5 to 
4 - as good as that achieved by the best conventional implosion systems 
under optimum conditions. The result is that an efficient fission explosion 
should always result. 

This is important because neutrons are inevitably present in abundance. 
First, even though the production of energy in the compressed fusion fuel is 
negligible at this point, its production of neutrons should be quite 
significant. Second, and even more important, are neutrons from the trigger 
explosion. These are leftover stragglers from the primary explosion, now 
long past (300 nanoseconds or more, such are the time scales with which we 
are dealing). All of the excess neutrons from the primary (on the order of 
10^24) have long since escaped from the expanding primary fireball, and if 
nothing has slowed them down they are now well outside the bomb casing.

A substantial fraction of them have, however, have entered the fuel capsule.  
Unless an absorber has been intentionally placed between the capsule and the 
primary this neutron population would be on the order of 10^22. The average 
scattering mean free path for fission spectrum neutrons in liquid deuterium 
is 7.8 cm, and 4.2 cm in lithium-6 deuteride, so once a neutron enters it 
will usually scatter repeatedly.  Both fuels are very good moderators. With 
each collision a neutron is robbed of nearly half its energy, on average. 
Now after a collision, a neutron may escape the capsule or be absorbed by 
the lithium (the chances of capture by deuterium is negligible) so the 
population of neutrons declines with time. But since they are losing energy, 
the time scale for absorption and escape keeps getting longer and longer. 
The time for complete thermalization is several microseconds, but in the 
time available before the spark plug fires the neutron energies would still 
be in the KeV range, and the number of collisions that would have occurred 
would number scarcely more than a dozen. Even if half of the neutrons were 
lost after each collision (a high estimate), the neutron population in the 
fuel capsule would still be astronomically high (>10^17). Since a neutron 
absorber would have to be implausibly thick (the order of 40 mean free 
paths) to reduce this to a negligible level, we can assume that many fission 
neutrons will remain present.

Energy is transmitted from the spark plug to the fuel by both neutrons and 
photons. The neutron MFP in the Mike model is reduced to 7.8 cm/197 = 0.040 
cm, and to 0.0048 cm for the W-80, thus allowing strong neutron mediated 
heating of the fuel in a thin layer around the spark plug.

From the electron densities calculated above, we can compute the mean free 
path for Thomson scattering in the compressed secondary at 0.058 cm (5.4 
gigabars) and 0.013 cm (64 gigabars). These values are much smaller than the 
radius of the compressed spark plug, or the thickness of the fuel or tamper 
layers. The can see that the entire secondary is opaque, strongly scattering 
the emitted photons and causing photon transport to occur by diffusion. 
Thomson scattering by itself does not cause fuel heating, the photons must 
be absorbed before this can occur. The due to the high densities, the 
spectrum averaged MFPs for the photons flux from the spark plug is quite 
short also. Assuming a nominal fuel temperature of 10^6 K from compression 
heating, for the lower compression, low-Z deuterium fuel in Mike we can 
estimated an absorption MFP of 0.3 cm. For the lithium-containing W-80 fuel 
it is less than 0.001 cm. 

The energy produced by fission will thus be transmitted through the fuel by 
means of a radiation dominated shock or pure Marshak wave. The fuel will 
ignite ahead of the full shock heating zone by the leading thermal diffusion 
zone. Although a spark plug can easily be designed to directly supply 
sufficient energy to ignite the entire fuel mass, the fact that the heating 
travels outward by a Marshak wave may allow much smaller spark plugs since 
the ignition wave may be self-sustaining. The emission of fusion neutrons 
ahead of the ignition zone may also play a significant role in the growth of 
the ignition region.

The use of fission spark plugs appears to be the most common (if not 
exclusive) means of igniting secondaries in deployed designs.

4.4.3.5.2   Shock Heating Induced Ignition
It was noted in Section 3.7.3 Convergent Shock Waves that considerable 
heating occurs near the center of an implosion, where the shock wave 
converges in principal to a mathematical point or line. In principal, the 
temperatures reached at the very center are unlimited.

It is possible to ignite a small mass of fusion fuel in this central region 
of strong heating. The fusion reactions occurring here can then spread 
outward through the entire fuel mass as a thermonuclear combustion wave as 
described above for spark plugs.

It is not clear from present evidence whether this approach has ever 
actually been used in a real design - either deployed or merely tested. If 
so, it is likely that a deuterium-tritium mixture would be deliberately 
introduced at the center to provide a "match" to more easily ignite the 
fuel. It is known that lithium tritide has been used by the U.S. in 
thermonuclear secondaries. Since tritium is far too expensive to use in a 
weapon unless its energy yield is greatly magnified in some way (similar to 
its use in fusion boosted fission bombs), this may be evidence of the use of 
this type of ignition system.

4.4.3.6     Burn and Disassembly
Once ignited, the thermonuclear reaction is self-heating. Since the reaction 
rate increases with temperature, feed-back is established that causes the 
power output of the secondary to rises steeply. When more than half of the 
fuel has burned the temperature cannot rise much more since most of the 
energy has already been released. The depletion of fuel then catches up, and 
the power output levels off, then begins a somewhat less rapid decline. The 
period during which the majority of the fuel is burned amounts to a mere 20 
nanoseconds or so. All this assumes of course that the disassembly of the 
secondary hasn't yet intervened to quench the reaction.

At fuel densities on the order of 100 g/cm^3, the maximum temperature can 
rise to about 350 million degrees K. Under these conditions the pressure 
tops 100 terabars (100 million megabars, 10^14 bars, or 100 trillion 
atmospheres). This tremendous temperature and pressure is initially confined 
to the fusion fuel. It propagates into the tamper as a Marshak wave (a 
radiation driven compression wave), compressing and accelerating the tamper 
material outward.

Pressures of this magnitude are capable of generating an outgoing 
compression wave in the tamper with a velocity of several millimeters per 
nanosecond. This rate of expansion is so fast that even during the extremely 
short period when the thermonuclear reaction is near its peak, the density 
of the fuel could drop significantly and impair overall efficiency. It helps 
considerably if the tamper is still imploding rapidly when the reaction 
ignites, since pressure of a few terabars will be necessary to simply to 
bring the implosion to a halt. 

The picture is much the same even in secondary designs where most of the 
energy is released by fast fission of the surrounding tamper. The pressure 
in the fusion fuel should be considerably higher than in the tamper, since 
the fuel energy density of the fissile tamper is substantially lower and it 
lags behind the fusion reaction slightly (due to the finite velocity of the 
escaping neutrons). The pressure in a fissioning tamper can have a 
substantial confining effect however. The tamper itself will start expanding 
outward into the radiation channel as it fissions in manner very similar to 
a disassembling fission bomb core.

Note that the use of fast fission to produce energy in a bomb involves the 
tamper surrounding the fuel, *not* the bomb casing as is sometimes reported. 
The highly compressed imploded tamper has an extremely high mass density per 
unit area and is almost inevitably many mean free paths thick. This makes it 
an excellent neutron absorber. The bomb casing is not compressed in the same 
sense, and would have to be extremely thick and heavy to capture many 
neutrons. 

4.4.4       Implosion Systems
The discussion above (and in Section 3.7.5 Methods for Extreme Compression) 
it has been made clear that efficient compression requires creating and 
maintaining a relatively low pressure for a relatively long time, with the 
pressure rise accelerating rapidly near the end of the compression process. 
But so far, I have not discussed at any length how this might be 
accomplished.

To make this problem clear consider the required duration of relatively low 
pressure. For a typical fuel layer thickness of 2 to 8 cm (depending on 
weapon size), it would take the weak initial shock (travelling at ca. 100 
km/sec) something like 200-800 nanoseconds to traverse it. During most of 
this time, perhaps 80% of it, the pressure at the fuel surface can be 
permitted to rise no higher than a few tens of megabars. The remaining 
pressure increase - to a value perhaps a thousand times higher than the 
average pressure of the initial shock - can occur no sooner than this final 
20%.

But the source of this pressure - the primary - typically generates its 
energy output on a much shorter time scale. This time scale is determined by 
the length of the multiplication interval, 1/alpha, which may be no more 
than a few nanoseconds. Within a time period of a few times 1/alpha, say 3-4 
multiplication periods, >98% of the fission reactions occur and we can think 
of essentially all of the fission explosion occurring during this time. Thus 
nearly all of the energy and excess neutrons produced by the primary are 
released within perhaps 10-15 nanoseconds for a pure fission primary, and as 
little as 3-4 nanoseconds for a fusion boosted primary.

Clearly some cleverness is required to stretch out the rate at which this 
brief burst of energy arrives at the fusion fuel. 

4.4.4.1     Techniques for Controlled Implosion
A number of techniques for doing this can be identified which may be used 
alone or (probably more typically) in combination to achieve the desired 
pressure vs. time history.

4.4.4.1.1   Release Waves
The development of a release wave when the ablation shock completes its 
passage through the tamper (see Section 4.4.3.2.1 The Ablation Shock above) 
is an inherent feature of radiation implosion which significantly 
contributes to achieving efficient compression. The release wave converts 
the sudden intense pressure jump of the ablation shock front into a lower 
pressure, higher velocity shock in the fusion fuel which is followed by a 
gradient of increasing pressure.

We previously estimated the ablation shock velocity for Mike at 160 km/sec, 
and 570 km/sec for the W-80. The release wave driven shock must be even 
faster. This indicates the release wave driven shock will be much faster, 
and its pressure much higher, than the relatively weak 50 megabar bar shock 
(travelling at 100-200 km sec) described earlier. We can conclude then that 
unless the ablation shock pressure is very low, this mechanism does not by 
itself reduce the shock jump sufficiently to give efficient compression.

4.4.4.1.2   Standoff Gaps
A standoff gap is a void between the fusion fuel and the tamper. The effect 
of a standoff is to allow the release wave to unload to zero pressure and 
full escape velocity (see Section 3.6.1.1 Release Waves), converting the 
internal energy of the gas entirely into kinetic energy. The forward edge of 
the wave then runs far ahead of the bulk of the imploding tamper without 
heating any fuel in the process.

When it reaches the fusion fuel, the release wave will be decelerated and 
begin piling up at the void/fuel interface, driving a low pressure shock 
into the fuel. As the rest of the release wave arrives the pressure keeps 
climbing, driving a compression wave of increasing strength.

The velocity of the release wave front is given by:
     u_escape = (2*c_s)/(gamma - 1) + u_particle
where c_s is the speed of sound in the shocked tamper, and u_particle is the 
velocity acquired by the tamper from the shock wave. Thus for a perfect 
monatomic gas, with a gamma of 5/3, this velocity is equal to three times 
the speed of sound in the shock compressed gas plus the velocity the gas 
acquired by passing through the shock front. In a dense tamper under extreme 
pressure the effective value of gamma may be significantly lower than 5/3 
due to ionization effects, making the escape velocity four or more times 
faster than the speed of sound.

If the tamper were not accelerating, then the larger the standoff gap the 
greater the elapsed time between the arrival of the release wave and bulk of 
the tamper, which is desirable for efficient compression. But the tamper is 
actually accelerating, so in time it will tend to catch up with the release 
wave front. For a given geometry, ablation pressure, and tamper mass, there 
is an optimum standoff that will maximize the elapsed time.

The use of use of a standoff seems to have been the major (perhaps only) 
method for creating the desired compression wave in Mike, the first 
radiation implosion device ever tested. From the available specifications, 
we can estimate that the standoff may have been in the order of 25 cm, with 
a fuel mass radius of 20 cm. Calculating u_escape at around 600 km/sec 
(gamma = 1.5, c_s = 100 km/sec), the elapsed time between the arrival of the 
release wave and the rest of tamper at the initial fuel surface radius would 
be about 300 nanoseconds. At an average shock velocity of 200 km/sec, the 
initial shock could traverse 8 cm of fuel before the tamper finally catches 
up, far enough to efficiently compress 64% of the fuel.

4.4.4.1.3   Compartmented Radiation Cases
A second technique is to divide the interior of the weapon into two 
compartments that separate the primary and secondary. A barrier between the 
compartments made of opaque (high-Z) material controls the rate at which 
energy flows from the primary to the secondary.

Since a small amount of energy is needed to begin the implosion, the barrier 
would have tiny apertures (narrow slits perhaps) that would allow photons to 
enter the secondary compartment at a slow rate. The barrier material ablates 
away, driving an ablation shock through the wall. The ablation shock is 
luminous (though much less intense than the unobstructed flux from the 
primary compartment would be) so when it arrives at the opposite side, a 
significant additional thermal flux into the secondary compartment would 
occur.

By far the largest increase in radiation flux would occur when the ablation 
front arrived at the opposite side of the barrier (i.e. when it completely 
ablates away). Then radiation at the full temperature of the primary 
compartment would flow into the secondary compartment.

Of course the barrier would be driven forward at a very high velocity by the 
ablation shock, and preventing it from damaging the secondary would be a 
significant problem. One possible technique for addressing this problem 
would be to place a shield made of X-ray transparent low-Z material 
(lithium, beryllium, or boron for example) between the barrier and the 
secondary to absorb the impact of the barrier remnants.

Many variations on this idea are possible. Varying the thickness or the 
composition of different parts of the barrier could provide a more carefully 
tailored release of energy. Thermal energy could be diverted into "radiation 
bottles" by unimpeded flow through a duct or pipe before release to the 
secondary. Multiple barriers or baffles could be used to control the rate of 
energy flow. 

4.4.4.1.4   Modulated Primary Energy Production
The idea here is to tailor the energy production in the primary so that the 
desired pressure-time curve is produced directly. The functional form of 
fission energy release (an exponential function) actually does match the 
desired functional form of the pressure-time curve fairly well. The problem 
is that the time constant of a reasonably efficient fission system is simply 
to short. By the time a low pressure shock created by an early stage of 
fission has propagated a substantial distance (a few millimeters, say) the 
intense shock from the final stages of fission will have caught up with it. 
If the value of alpha is reduced to the point where the rate of increase is 
tolerably slow (10-20 per microsecond), the core has time to disassemble 
without producing much energy - leading to a very inefficient primary.

It may be possible to use fusion boosting to overcome this problem. Since 
boosting can be initiated at a fairly low fission yield and accelerates as 
the temperature rises, it may be possible to use boosting to still achieve 
high efficiency. Boosting would kick in after the slow, low pressure phase 
and drive the rapidly rising high pressure end of the curve. 

A design of his kind would have several advantages. The low alpha of the 
fission process would mean that a small quantity of fissile material and/or 
weak compression would be adequate for the primary, leading to light and 
compact primaries. The requirements for radiation containment would be 
reduced as well, leading to reduced overall weapon weight.

A disadvantage is that the idea could not be extended to weapons of 
unlimited yield.  Larger yields require thicker fuel layers, slower initial 
compression, lower alpha values in the primary, and reduced fission yield. 
The approach would fail (if it can be made to work at all) when the reduced 
alpha value allows the primary to disassemble before initiating the boosting 
process.

A primary using this approach would be designed with a beryllium reflector, 
but with no tamper between the fissile material and the reflector so that 
radiation escaped as readily as possible. U.S. primaries are known to 
contain plutonium bonded directly to beryllium, suggesting this design 
approach.

4.4.4.1.5   Multiple Staging
In weapons with more than two stages, the efficient compression of tertiary 
(or, in principal, later stages) can be conveniently arranged with the aid 
of the sequenced energy release of the earlier stages. This is fundamentally 
the same general idea of modulated energy release just described, using a 
different mechanism.

The secondary stage releases much more energy than the primary (as much as 
200 times more has been demonstrated, but more typically 10-50 times more), 
and does so hundreds of nanoseconds later. 

A portion of the primary energy can be used to create an initial low 
pressure shock in the tertiary stage, even as it compresses the secondary. 
The third stage which would generally be larger and have a greater radius 
that must be traversed by the initial shock, requiring a longer compression 
period in any case. The sudden burst of energy from the secondary would be 
quite effective in creating the rapid rise in pressure desired at the end of 
the tertiary compression period.

This technique is obviously of limited general usefulness, since only 
relatively large weapons would have three stages (all known three stage 
tests have been in the megaton range, very few three stage designs appear to 
have been actually fielded).

4.4.4.1.6   Selection of Pusher Materials
Another possible technique for creating a time varying pressure in the fuel 
is to modify the ablation process itself. The amount of ablation pressure 
generated by radiant heating depend on the properties of the material being 
ablated.

If the ablation surface has a very high atomic number, then the ablated gas 
will still be quite opaque to X-rays. This means that the radiation will 
have to reach the ablation front by diffusion - each X-ray being captured 
and re-emitted multiple times. Radiation diffusion is a relatively slow 
process. Also, the hot ablated gas will radiate energy back into the 
radiation channel, reducing the net flux reaching the ablation front.

A lower Z material, which completely ionizes at the radiation channel 
temperature, will become nearly transparent to X-rays when heated. The X-ray 
flux will thus reach the cold ablation surface unimpeded. Neither the cold 
surface, nor the hot gas, will radiate significant amounts of energy back 
into the channel so the thermal energy will be absorbed by the ablator very 
rapidly (with a correspondingly high mass loss rate).

The effective particle mass of a completely ionized low-Z material will be 
much lower than that of a partially ionized high-Z material. This gives a 
higher escape velocity, and a larger ablation pressure per unit of mass 
lost. 

These factors give the designer a range of materials and effects to choose 
from to tailor the ablation rate and pressure. Using multiple layers of 
different materials offers the possibility of creating a time-varying 
ablation pressure even with constant radiation temperature.

No information is available indicating that this technique has been ever 
actually been used.

4.4.4.2     Radiation Containment and Transport
The thermal radiation that drives the implosion process must be kept from 
escaping until it has completed its work. This is the function of the 
radiation case.

The radiation must also be transported rapidly and effectively to the 
secondary (when it is time). The conduit through which the radiation flows 
is the radiation channel.

4.4.4.2.1   Radiation Case
The radiation case may be integral with, or identical to, the external bomb 
casing; or it may be a separate component nested inside of the bomb casing. 
There may in fact be more than one radiation case, especially in a multi-
compartment design. Radiation cases may also be nested inside each other, to 
provide different degrees of confinement during different phases of bomb 
operation.

To fulfill its role, the wall of the radiation case must be highly opaque to 
the radiation that fills it to minimize the rate at which energy is lost to 
the wall (see Section 4.4.3.2 Opacity of Materials in Thermonuclear Design). 
In general the radiation case will either be a lining of the external bomb 
casing, or will be entirely separate from it.

It is inevitable that the wall of the case will ablate away, just as the 
secondary pusher does, and will generate a high pressure shock that blows 
the wall outward. To minimize the rate of case expansion, the casing wall 
should also have a very high mass density. The DOE has reported that 
materials with atomic numbers higher than 71 have been used as radiation 
case linings. Uranium, lead and lead-bismuth alloy are known to have been 
used to line radiation cases. Tungsten, or tungsten-rhenium alloys (such as 
the thin plasma deposited tungsten-rhenium coatings developed at the Kansas 
City Plant) are also good candidates for this purpose. Mercury, thallium, 
and gold have been used in thermonuclear weapons - possibly for this 
purpose.

The radiation temperature around the secondary needs to be maintained until 
the secondary collapse is complete or nearly so, otherwise the outer wall of 
the imploding tamper will decompress and begin expanding, reducing its 
ability to confinement the thermonuclear reaction. This defines the length 
of time that the radiation case must maintain its integrity (at least in the 
part of the weapon where the secondary is located).

The rate of energy loss into the wall probably remains more or less constant 
until the ablation shock arrives at the outer surface of he case. Once this 
occurs, the wave of pressure release will travel backwards to the inner wall 
relatively rapidly. When this release wave reaches the ablation front, the 
rate of energy loss will rapidly increase - ending the useful life of the 
casing. The arrival of the Marshak wave front of the ablation shock at the 
outer surface of the casing was an important diagnostic in early 
thermonuclear weapon tests.

In two compartment weapon designs a separate casing is placed around the 
primary. Since the pressure here is initially much higher (and persists 
longer) than around the secondary, a thick walled sphere of uranium is used 
to provide an especially opaque and dense case.

For weapons that use the soft X-ray kill mechanism (e.g. high altitude ABM 
or space-based interceptors), a radiation case that is transparent to the 
more energetic X-rays produced by the secondary is desirable. Since the 
average photon energy during implosion is only 2 KeV or so, and the bulk of 
the energy emerging from the secondary is carried by photons with energies 
>>20 KeV, this should not be too hard to arrange. In fact with a lining of 
sufficiently low Z, the hot photon flux should be capable of completely 
stripping the nuclei of electrons through photo-ionization, rendering it 
essentially transparent ("bleaching it"). 

4.4.4.2.2   Radiation Channel
The outer wall of the radiation channel is the radiation case. The inner 
wall is generally the pusher of the secondary. The thermal energy released 
by the primary is conducted down the channel by diffusion - a given region 
of the wall is heated by radiation emitted by hotter regions of the wall 
closer to the primary, and in turn re-emits radiation to heat regions of the 
wall that are farther away. 

The rate of energy flow any point in the channel can be modelled by the 
diffusion equation:
     J = -((photon_MFP * c)/3) * (energy_density_gradient)
where J is the energy flux (flow rate), photon_MFP is the mean distance a 
photon travels between emission and capture, c is the speed of light, and 
energy_density_gradient is the rate at which energy density changes with 
distance along the channel. The temperature also changes along the channel 
with energy density, but since temperature is proportional to the fourth 
root of energy density, the gradient here is much smaller.

If the radiation channel is transparent, then the photon mean free path is 
the average distance down the channel a photon will travel between emission 
and absorption. This is determined by channel geometry (plane, cylindrical, 
spherical, etc.), and the width of the channel. Transport is faster along a 
straight channel than a curved one, and faster along a wide channel than a 
narrow one. For an arbitrary small patch of channel wall, the proportion of 
energy emitted at an angle theta from the normal vector is Cos(theta). The 
distance the energy will travel down the channel before absorption is 
Tan(theta)*channel_width. The average of Cos(theta)*Tan(theta)*channel_width 
is simply channel_width. As long as the mean free path in the material 
filling the channel is substantially less than channel_width/Cos(45 
degrees), about 1.4 times the channel width, this will be the effective mean 
free path down the channel.

Since c, the speed of light, is very large the rate of transport tends to be 
extremely fast. The energy density will thus very rapidly come into 
equilibrium, as long as the maximum distance between two points in the 
channel, as measured in photon mean free paths, is not also a very large 
number. Even when energy is flowing into the channel, the energy density 
gradient will remain quite small. If energy is not flowing into the channel, 
any irregularities will rapidly disappear.

The ablation of the channel walls interferes with the need to maintain a 
transparent channel. The high-Z material lining the channel produces a high 
velocity gas as it escapes from the channel wall, and it accelerates further 
as it expands into the channel.  Even at relatively low densities this gas 
is quite opaque, and it has the effect of rapidly collapsing the radiation 
channel until it is completely blocked.

This process can be combated by filling the channel with a transparent gas 
to hold back the ablating walls. It is impossible to hold back the ablating 
material completely, but the highest velocity ablation exhaust is at low 
pressure and is relatively easy to contain. As the gas-filled channel 
closes, its pressure increases as well making it more resistant to further 
collapse.

Radiation channels are typically filled with a dense plastic foam such as 
polystyrene, that has been "blown" (foamed) with a hydrocarbon gas (pentane 
for example). The channel is thus filled only with carbon and hydrogen. The 
ionization energy of the last electron in carbon is 490 eV (hydrogen's 
ionization energy is a mere 13.61 eV), which corresponds to the average 
particle energy at a temperature of 5.7 x 10^6 K. As the radiation channel 
approaches this temperature the foam will become completely ionized and 
nearly transparent to thermal radiation. Polyethylene wall linings have been 
used instead of plastic foam (in Mike for example) although the unless the 
casing is flushed with a low-Z gas, the higher ionization energies of 
nitrogen and oxygen might cause significant absorption. 

Note: that this foam *does not* generate the pressure that causes implosion.

4.4.4.3     Avoiding Fuel Preheating
Compressing fuel efficiently to high densities requires that the fuel have 
relatively low entropy. At the start of the compression process, a 
relatively small amount of heat will increase the entropy significantly and 
reduce the efficiency of the entire compression process, which is why the 
initial shock pressure must be carefully controlled. Fuel preheating can 
also occur from the radiation emitted by the primary. A high-Z radiation 
shield is used to prevent the X-ray flux from directly heating the fuel in 
cylindrical designs, but the neutron flux from the primary can also cause 
significant preheating. This can not only reduce the achievable compression, 
but due to uneven heating in the fuel it could disrupt the symmetry of 
implosion as well (a potentially even more serious problem).

If we assume that 1.5 neutrons escapes from the primary for each fission 
occurring there, then up to 3 MeV (about 1.5% of the total yield since the 
average fission neutron has 2 MeV) could potentially be carried away from 
the primary by neutron kinetic energy. The portion of this that would be 
deposited in the fuel depends on the area of the fuel presented to the flux, 
the distance from the primary, and the effects of materials between the core 
and fuel in absorbing neutron energy. It is difficult to see how any more 
than 5% or so of the flux could be intercepted by the fuel, and is likely to 
be much less than this. The average energy can be expected to be 
significantly less also, due to moderation by the beryllium reflector and 
high explosive.

In a weapon that has a fuel mass/primary yield ratio of one kg per kt, 
intercepting 1% of the neutron kinetic energy emitted by the primary core is 
still some 6x10^12 erg/g. The problem of preheating is especially serious in 
lithium-6 containing fuel, since the Li-6 + n reaction releases 4.8 MeV in 
addition to whatever kinetic energy the incident neutron possesses. 
Spherical secondaries are more likely to be prone to this problem than 
cylindrical ones, since they present a larger surface area. The Morgenstern 
device (designed by Edward Teller) that fizzled in the Castle Koon test 
reportedly had a spherical secondary, and failed due to neutron preheating 
effects.

Neutron preheating can be avoided by attenuating the neutron flux with 
boron-10, the best available fast neutron absorber. Boron carbide (B6C) is 
known to have been incorporated into thermonuclear weapons, possibly for 
this reason. Such a neutron thermal shield would be incapable of stopping 
the neutron flux from reaching the secondary completely, but at most a one 
or two order of magnitude reduction should be sufficient to render 
preheating insignificant. With Z equal to 5, boron is highly transparent to 
thermal X-rays and would not interfere with radiation transport.

4.4.5       Fusion Stage Nuclear Physics and Design
4.4.5.1     Fusionable Isotopes
The important thermonuclear reactions for weapons are given below:
1.  D + T -> He-4 + n + 17.588 MeV (n kinetic energy is 14.070 MeV)
2.  D + D -> He-3 + n + 3.2689 MeV (n kinetic energy is 2.4497 MeV)
3.  D + D -> T + p + 4.0327 MeV
4.  He-3 + D -> He-4 + p + 18.353 MeV

The first fuel ever considered for a thermonuclear weapon was pure deuterium 
(reactions 2 and 3, which are equally likely). This is primarily because 
deuterium is a relatively easy fuel to burn (compared to most other 
candidates), is comparatively abundant in nature, and is cheap to produce. 
In fact, no other fuel has this same combination of desirable properties.

Only one other fusion fuel is easier to ignite - a mixture of deuterium and 
tritium (reaction 1). At moderate thermonuclear temperatures, the T-D 
reaction is 100 times faster than D-D combustion. Unfortunately, tritium 
does not occur in nature in useful amounts, and is very costly to 
manufacture.

The cheapest method of making it industrially is to breed it in reactors, 
where it competes with plutonium production. For each neutron absorbed in 
the reactor for isotope production, either one atom of tritium or one atom 
of plutonium can be produced. Since fusing an atom of tritium produces 17.6 
MeV of energy, compared to 180 MeV from fissioning an atom of plutonium, the 
cost of the energy represented by tritium is ten times that of plutonium. 
Worse still, it decays at a rate of 5.5% annually so simply maintaining an 
inventory of tritium is expensive. Unless the energy output of tritium can 
be magnified greatly, or its effective cost greatly reduced, it is 
uneconomical to use it weapons. 

Tritium can be produced in situ from other reactions in a weapon. Deuterium 
- deuterium combustion, for example, produces tritium naturally through 
reaction 3. In fact far more energy is produced in D-D fusion from fusion of 
the tritium byproduct than from the D-D reaction itself. Since the D-T 
reaction rate is far higher than the D-D rate, and there is always a large 
excess of deuterium, nearly all the tritium produced is burned up.

The helium-3 + D reaction (reaction 4) is even more energetic than the D+T 
reaction, but it is harder to ignite. The cross section is much lower than 
the D+D cross section at temperatures below 200 million degrees K. Helium-3 
is not found in useful amounts on Earth but, like tritium, it is produced as 
a by-product of D-D fusion. Reaction 4 only becomes important with pure 
deuterium fuel when a significant amount of deuterium has burned up (about 
25%). At this point, the temperature has risen to about 250 million degrees 
K, where the cross section for reaction 4 begins to exceed that of 2 and 3 
combined. Also, at this point the concentration of He-3 has built up to be a 
significant proportion of the fuel mass. The conversion of He-3 to tritium 
through neutron capture competes with the build-up of helium-3 however (see 
reaction 10 below).

The net effect of reactions 1-4 together is:
6 D -> 2 He-4 + 2p + 2n + 43.243 MeV
Of the two neutrons produced, one is high energy (14.07 MeV) and one is 
moderate energy (2.450). The ratio of high energy neutrons produced to 
deuterons consumed (or energy produced) is significant for driving fast 
fission reactions. If the He-3 is converted to tritium instead of being 
burned directly, the net reaction is the same with the exception that two 
high energy neutrons are produced.

There are other fusion reactions that occur between these isotopes (T+T and 
He-3+T for example), their reaction products, or with other materials 
commonly mixed with the fusion fuel (like lithium isotopes), but the 
reaction rates are too low to be significant.

4.4.5.2     Neutronic Reactions
The neutrons released by reaction 1 and 2 can be put to use in several ways. 
They can be allowed to escape the weapon to serve as one of the destructive 
weapon effects. They can be used to cause fission (perhaps in cheap non-
fissile material like U-238 or Th-232), thus releasing additional energy. Or 
they can be used to manufacture more fusion fuel to enhance the fusion 
reaction. Both of these last two possibilities are commonly incorporated 
into modern weapons. The use of neutrons as a distinct weapon effect is 
usually only important in special designs (neutron bombs).

The two reactions that have been used to manufacture fusion fuel are:
5.  Li-6 + n -> T + He-4 + 4.7829 MeV
6.  Li-7 + n -> T + He-4 + n - 2.4670 MeV
Both produce tritium which burns rapidly, producing more neutrons.

Lithium-6 is a relatively uncommon isotope in nature (7.42% of natural 
lithium) and must be enriched before reaction 5 can be used to best effect. 
The Li-6 + n reaction has a significant cross section at all neutron 
energies, but it has a large cross section below 1 MeV with a peak of 3.2 
barns at 0.24 MeV. At higher energies endothermic spallation reactions tend 
to occur instead, above 4 MeV the neutron is far more likely to split the 
Li-6 nucleus into He-4 and D.

Lithium-7 constitutes the bulk of natural lithium (92.58%). The endothermic 
Li-7 + n reaction does not occur at all if the neutron energy is less than 
the energy deficit, and is only significant with neutron energies above 4 
MeV. Above 4.5 MeV Li-7 has a much larger cross section from breeding 
tritium than does Li-6.

There are a number of side reactions that can also occur in fusion fuel, 
especially with the very energetic 14.07 MeV fusion neutrons, which can 
cause spallation or fragmentation of target nuclei due to their enormous 
kinetic energy. Among these are:
7.  D + n -> p + 2n - 2.224 MeV
8.  Li-6 + n -> He-4 + D + n - 1.474 MeV
9.  Li-6 + n -> He-4 + p + 2n - 3.698 MeV
10. He-3 + n -> T + p + 0.7638 MeV
11. Li-7 + n -> Li-6 + 2n + -7.250 MeV

In deuterium and Li-6D fuel reactions 7 and 9 are significant in causing a 
modest amount of neutron multiplication (10-15% amplification of 14 MeV 
neutrons), and aiding in the rapid attenuation of highly energetic neutrons. 
Reaction 10 is especially important in pure deuterium fuel where helium-3 
produced by the D-D reaction is the only significant neutron absorber.

With respect to the total energy release, and the composition of the final 
products, the net effect of reactions 10 and 1 together is exactly the same 
effect as reaction 4. That is, converting He-3 to T, then fusing it with D 
is the same as fusing He-3 with D directly. The energy is not distributed 
over the reaction products in exactly the same way however. Reaction 10 
consumes a neutron but this may be a very low energy neutron (in fact it 
most likely will be given the very large cross section below 0.5 MeV - up to 
5 barns). Reaction 1 produces a 14.07 MeV neutron. In effect a very high 
energy neuron is exchanged for a low energy one. This can change the ratio 
of high energy neutrons to deuterons consumed from 1:6 (implied by reaction 
1-4) to as low as 1:3, greatly augmenting fast fission.

Note also that when the above lithium-7 reaction (reaction 11) is combined 
with reaction 5, the net effect is exactly the same as reaction 6. 

Since fusion fuel contains a very high density of very light atoms (like 
deuterium) with good scattering cross sections, we should expect neutrons 
entering the fuel to be rapidly moderated.

In pure deuterium fuel moderation takes only 9 collisions to fully 
thermalize 14.07 MeV neutrons ("thermal" here means on the order of 20 KeV), 
a process essentially complete in 0.25 nanoseconds at a fuel density of 75 
g/cm^3. Deuterium's absorption cross section for neutrons at 20 KeV is only 
about 1 microbarn, given the neutron velocity (2x10^8 cm/sec) and atom 
density (2.25x10^25 atom/cm^3 at 75 g/cm^3) the lifetime of a thermalized 
neutron is about 220 microseconds (for this reaction). The cross section for 
reaction 10 at 20 KeV is 5 barns so when 10% of the fuel has burned 
(creating an He-3 concentration of 2%), the lifetime of a thermalized 
neutron before  He-3 capture will have dropped to 2.2 nanoseconds. Thus the 
formation of tritium through neutron capture by deuterium cannot play any 
significant role, as some have suggested.

Rapid moderation occurs in lithium deuteride fuel as well. Reaction 5, the 
production of tritium from lithium-6 has a very large cross section peak at 
246 KeV (8.15 barns). It averages only 0.77 barn from 0.02 to 0.15 KeV and 
1.1 barns from 1 to 14.1 MeV. Multi-group neutron calculations show that in 
Li-6D fuel at a density of 200 g/cm^3 about half of all tritium production 
occurs with neutrons moderated to the range of 0.15-1.0 MeV. 50% of 14.07 
MeV neutrons are absorbed to form tritium within 0.075 nanoseconds after 
emission, rising to 70% at 0.15 nsec. Most of the rest become thermalized 
with a lifetime of 0.40 nsec before capture.

The above observations for 14.07 MeV neutrons remain valid for the 2.45 MeV 
D-D reaction neutrons, except that fewer collisions are required for the 
moderation. Clearly fusion neutrons give their energy up very quickly to the 
fusion fuel, and relatively few escape the fuel without undergoing 
substantial moderation. We can also conclude that the production of tritium 
from lithium-6 is a rapid, efficient process.

4.4.5.3     Fusion Fuels
These are fuels that produce energy primarily through charged particle 
reactions, driven by thermal kinetic energy. Neutron reactions often play 
important anciliary roles.

4.4.5.3.1   Pure Deuterium
Deuterium is an inexpensive fusion fuel, consisting on the order of $100/kg 
to manufacture, with an effectively unlimited supply. Its major disadvantage 
is that it is a gas at normal conditions, requiring extreme cold to liquefy 
it (to below 23.57 K). It has the additional disadvantage that it is a low 
density liquid - 0.169 (or 0.0845 moles/cm^3). This low density, combined 
with the necessity of extremely efficient insulation implies a large volume 
for any weapon using pure deuterium as a fuel (to say nothing of the cost, 
weight, and complexity of the cryogenic equipment needed for handling it, 
and keeping it cold).

Deuterium has a high energy content however, 82.2 kt/kg with complete 
thermonuclear combustion. It also produces a large excess of neutrons per 
unit of energy released, one neutron for each 21.62 MeV of reaction energy. 
The net reaction is:
6 D -> 2 He-4 + 2 p + 2 n + 43.24 MeV

Pure deuterium has been used in at least one thermonuclear test - Ivy Mike, 
the first radiation implosion design ever tested. The fact of this test 
conveniently demonstrates that thermonuclear energy release in weapons does 
not require tritium breeding neutronic reactions, but can be driven by the 
D+D reactions alone.

4.4.5.3.2   "Dry" Fuels (Lithium Hydrides)
It would be more convenient if deuterium could be incorporated into weapons 
in the form of a stable chemical compound with more convenient physical 
properties than the low boiling point elemental form. A suitable compound 
would be the hydride of a light element, which would give a fairly high 
deuterium content by weight.

While there are several compounds that fit this description, it was realized 
quite early in both the US and Soviet Union that one compound in particular 
was uniquely suited for this role - lithium deuteride. Even more important 
than its high deuterium content (22.4-25% by weight), and high atom density 
(0.103 moles D/cm^3, higher than in liquid deuterium!), is the fact that 
lithium isotopes can also provide additional fusion fuel. By capturing 
neutrons generated as fusion byproducts, reactions 5 and 6 produce highly 
combustible and energetic tritium. Reaction 5 also produces significant 
amounts of energy directly from neutron capture. Probably all fusion devices 
since Mike have used lithium hydrides of varying isotopic composition as 
fusion fuel.

4.4.5.3.2.1 Enriched Lithium Deuteride
The most desirable fuel is pure lithium-6 deuteride since it has the highest 
energy content per kilogram: 64.0 kt/kg. The net reaction is a combination 
of reactions 1 and 5:
Li-6 + D -> 2 He-4 + 22.371 MeV
There are a few considerations that must be addressed before this reaction 
will work. First, the neutrons produced by reaction 1 are too energetic to 
direct drive reaction 5 efficiently - they must undergo a few collisions to 
moderate their energy. Also, there must be an initial source of neutrons or 
tritium to drive reaction 5 before reaction 1 can occur. The overall cycle 
does not breed neutrons.

Some open literature sources assert that reaction 5 is driven by neutrons 
produced by fission reactions in the trigger, the spark plug, or the tamper.

The first of these suggested sources can be easily disposed of as a 
possibility. If neutrons from the primary were to breed a significant amount 
of tritium, severe neutron preheating problems would result.

A number of arguments can be offered against the other possibilities. The 
most obvious is that the net Li-6 + D reaction does not produce spare 
neutrons (although a small excess of 10-15% might be produced though n->2n 
reactions with the fast neutrons). Since only a relatively small proportion 
of the neutron excess can actually cause fast fission in U-238 (due to 
moderation, inelastic scattering, and absorption), for a lithium deuteride 
fueled bomb to produce substantial energy through fast fission some other 
type of fusion reaction must provide the neutron excess.

It can also be observed that it is very difficult to construct a scheme that 
will permit neutrons from the spark plug to play a major role. "Clean" 
weapon tests have been conducted that obtained as much as 98% of their yield 
from fusion reactions. Even if all the fission were due to the spark plug 
(allowing us to neglect the trigger), some 9000 MeV of fusion would have to 
result from the neutrons released by each 180 MeV fission (producing fewer 
than 2 excess neutrons). This implies a process of neutron recycling 
(neutron is absorbed to form tritium, tritium fuses to release neutron) some 
200 reactions long. It is likely that neutron leakage would quench this 
chain long before it got this far.

We can conclude that the source of neutrons to prime the pump for the Li-6 + 
D reaction, and provide the neutron excess for fast fission, is D-D fusion. 
This is natural since D-D is capable of supporting energetic fusion power 
production by itself anyway. Even without tritium breeding, D-D fusion burns 
to effective completion in approximately 20 nanoseconds anyway, producing a 
staggering number of neutrons in the process. The presence of lithium-6 
means that these neutrons are soaked up, producing even faster burning 
tritium and accelerating the combustion process. 

To summarize: D-D initially dominates the fusion process, but as the neutron 
concentration builds up it is quickly superseded by Li-6 bred tritium fusion 
as the prime power producer.

Since lithium-6 constitutes only 7.42% of natural lithium, making use of 
lithium-6 deuteride requires enriched lithium. Varying enrichments can be 
used, but the higher the better. The U.S. has produced and used enriched 
lithium containing 95.5% Li-6, 60% Li-6, and 40% Li-6. It appears that 95.5% 
has made up the bulk of U.S. production (442.2 tonnes total).

4.4.5.3.2.2 Natural Lithium Deuteride
Lithium-7 can serve as a fusion fuel also, either in partially enriched 
lithium or in natural lithium. The unexpected contribution from Li-7 in the 
Shrimp device tested in Castle Bravo (which used 40% Li-6, 60% Li-7 fuel) 
caused it to exceed predictions by a factor of 250% (to 15 Mt, the largest 
U.S. test ever). Natural lithium has also been used successfully as a fusion 
fuel in tests (it was used in the 11 Mt Castle Romeo test for example), and 
fielded weapons.

The contribution from lithium-7 is primarily due to reaction 6, which is 
quite significant above 4.5 MeV. In natural lithium the probability that an 
emitted 14.1 MeV neutron will breed tritium by reacting with Li-7 capture is 
around 50% (failure to appreciate this fact led to the Castle Bravo 
disaster). Since reaction 6 does not actually consume a neutron (a low 
energy neutron is one of the reaction products), in effect the neutron is 
available to also react with any lithium-6 that is present to breed 
additional tritium.

The net reaction for lithium 7 is a combination of reactions 1 and 6:
Li-7 + D -> 2 He-4 + n + 15.121 MeV
for an energy content per kilogram of 38.5 kt/kg. Pure Li-7 is unlikely to 
be used of course. The light isotope in natural lithium will react as well 
yielding 40.3 kt/kg. 

The fact that Li-7 actually does breed additional neutrons may be of 
significance in enhancing energy production through tamper fission.

4.4.5.3.3   Speculative Fuels
Deuterium can be combined with any of the other light elements (except 
helium) to form chemical compounds that could probably be used successfully 
as fusion fuels. Most of these have higher deuterium contents than lithium 
hydride, and all of them are easier to store than liquid hydrogen. Below is 
a list of representative compounds that can be formed with each of the 
elements from Z=4 (beryllium) to Z=8 (oxygen).

Given the convenience of lithium deuteride's physical properties, the 
cheapness of lithium, and the high energy content resulting from the nuclear 
reactions lithium undergoes, there is no reason to prefer any of the fuels 
below to LiD. It is quite unlikely that any of them have ever been used.

Deutero-ammonia (ND3) was seriously considered as a fusion fuel for the 
first radiation implosion device (Mike) in preference to liquid deuterium 
and natural lithium deuteride.

I have not investigated the possible nuclear reactions that the compounding 
agents below might undergo but one of them, boron-10, does have an 
exothermic reaction with neutrons which would add modestly to energy 
production, which produces a usable fusion fuel besides:
B-10 + n -> Li-7 + He-4 + 2.79 MeV

The possibility of using ordinary heavy water as a fusion fuel is 
interesting given its comparative availability and good physical properties.

Formula   Deut.    Properties
          Conc.
B2H6      35.6% Bp -92 C, cryogenic cooling required 
BeD2      30.8% solid, stable to 125 C 
BeD2.B2H6 33.2% solid
CD4       40.0% Bp -164 C, cryogenic cooling req'd (same as LNG)
C2D6      33.3% Bp -88 C, cryogenic cooling or high pressure required
C3D8      30.8% Bp -42 C, storable at room temp under modest pressure
D2O       20.0% Bp 101.5 C, liquid, no special handling
ND3       30.0% Bp -30.9 C, storable at room temp under modest pressure

4.4.5.4     Fusion Tampers
The jacket surrounding the fusion fuel of the secondary is often called upon 
to perform quadruple duty:
1. It provides reaction mass as an ablator to drive the radiation implosion;
2. It acts an inertial mass to confine the fusion fuel during the burn;
3. It acts as a radiation container to prevent loss of heat during the burn; 
and
4. It also acts as an energy producing fuel by reacting with the neutrons 
produced by the fusion reactions. 

The first three functions are essential for successfully releasing energy 
from the secondary. The fourth function is optional (fission energy release 
that is), and it is convenient for weapon designers that materials that meet 
this last requirement also satisfy the first three quite well.

A variety of materials are available that can meet these requirements. 
Functions 1 and 3 basically call for a material with a high opacity at high 
temperatures and pressures - a high Z element. Function 2 ideally calls for 
an material that will be compressed to very high density, which is provided 
by a material that only partially dissociates under high pressure - also a 
high Z element. Function 4 calls for a fissionable isotope (at least with 
fast neutrons) - the only plausible candidates for this (uranium and 
thorium) are the two highest Z natural elements available in substantial 
quantity.

Although the use of a fissionable tamper is optional, fission of the tamper 
provides the majority of the energy released in most thermonuclear weapon 
designs. This is because the energy produced is essentially "free". The 
tamper mass is required in any case, so extracting energy from it increases 
the bomb's yield for the same weight. The cost of the fissionable tamper 
material, in terms of its available energy content, is also generally much 
lower than the other materials used in the bomb, so the cost increase of 
using a fissionable tamper over a cheaper non-fissionable tamper is small.

A high fission yield produces a large amount of radioactive fallout. Weapons 
using fissionable tampers are thus considered "dirty". If this is considered 
undesirable in the weapon, then a non-fissionable tamper may be used. The 
penalty of course is a lower yield to weight ratio, and a more expensive 
arsenal to deliver the same amount of destructive power. 

On the other hand, an increase in fallout relative to yield may be desired, 
perhaps with a custom tailored range of half-lifes. Using a tamper that 
produces highly radioactive byproducts when irradiated by neutrons holds 
this possibility. 

The required mass of the pusher/tamper is set by the several requirements. 
The need to provide sufficient ablation mass (much of the pusher/tamper mass 
is lost during implosion through ablation), sufficient inertia to provide 
the momentum need for fast fuel implosion, sufficient inertia to confine the 
fuel during burnup, and sufficient thickness to capture a high percentage 
neutrons produced (if this is desired). 

If we assume maximally efficient implosion, then 75% of the pusher/tamper 
mass will be lost through ablation. To provide substantial inertial for 
driving implosion and confinement, we would also like the remaining tamper 
mass to significantly exceed the fuel mass. This puts the probable ratio 
between the pusher/tamper and fuel mass in the range of 8-16:1 (the Mike 
device had a ratio of something like 80:1).

The objective of capturing most of the neutrons should not difficult to 
achieve either. At densities of around 500 g/cm^3 for uranium , the 
thickness of tamper required to reduce the flux to 1/e (36.8%) of the 
initial value is no more than 0.5 cm.

The high proportion of the pusher/tamper that should ablate for efficient 
implosion, combined with the difficulties in estimating or measuring the 
high temperature LTE opacities, created a significant problem for early 
designers. If too much of the pusher/tamper ablated, complete failure of the 
secondary could result through insufficient confinement or even burn-through 
before implosion was complete. If not enough ablated, the implosion might be 
too inefficient to give a good yield. This necessitated conservative design, 
and may be the explanation for the apparent failures of the first British 
tests (the Green Granite and Purple Granite devices).

4.4.5.4.1   Fissionable Tampers
The advantage in using a fissionable material as the fusion tamper was 
recognized very early, many years before the first thermonuclear test. The 
highly energetic neutrons produced by fusion are capable of fissioning 
isotopes that are normally considered non-fissile, like U-238 and Th-232.

The early high yield fission weapon designs all used natural or depleted 
uranium as the tamper material. At the time large, inexpensive, high yield 
weapons were the main design objective so a cheap fissionable material was 
necessary. U-238 can only be fissioned by neutrons above about 1.5 MeV 
however. A 14.1 MeV neutron can undergo up to three average collisions with 
deuterium and still have sufficient energy. the 2.45 MeV D-D fusion 
neutrons, up to half the fusion neutrons produced in Mike, cannot be 
scattered even once and still be able to fission the tamper. Most of the 
fusion neutrons produced were thus unable to fission the tamper after they 
escaped the fusion fuel mass.

If all of the excess neutrons had caused fission, then the expected fission 
fraction for Mike (assuming no subcritical multiplication took place in the 
tamper) would be 89.3% (10.4-1 fission-fusion energy production ratio), 
instead of the observed 77% (3.35-1 ratio). Isotopic analysis of Mike 
fallout shows a very high percentage of the tamper material that was not 
fissioned was transmuted to higher isotopes of uranium by these slower 
neutrons (~93% of the U-238 in the inner most layers was transmuted).

If the uranium tamper is significantly enriched in U-235 however, a much 
higher percentage of the neutrons released can be harnessed since this 
isotope is fissioned by neutrons of all energies. The superior fissile 
properties of U-235 boost yield in other ways also. It has a higher fission 
cross section than U-238 even for fast neutrons, so a thinner tamper can be 
equally effective in capturing these as well. U-235 also can achieve much 
higher subcritical multiplication factors in the tamper - making use of the 
fission neutrons to cause more fissions.

Using enriched uranium as the tamper material drives up the cost of the 
weapon, but reduces its weight and size for a given yield. As enriched 
uranium became relatively abundant in the US weapons program, the use of HEU 
(20-80% U-235) instead of natural or depleted uranium became common. A large 
portion of uranium produced by the US for weapons use has been in this 
intermediate range of enrichment. Most or all light weight strategic weapons 
probably use HEU tampers today.

Thorium is an inferior material for producing energy through fission 
compared even to depleted uranium. Its fast fission cross section is lower, 
so a smaller fission yield is obtained. It has a very high atomic number 
(Z=90), second only to uranium among practical tamper materials, and is thus 
a very good tamper. Its lower density may be somewhat of a disadvantage, but 
only because it increases the required tamper thickness - which may be 
undesirable in highly-volume or shape constrained designs.

A nation "breaking out" of the status as a non-weapons state might possibly 
consider salting a U-238 tamper with reactor-grade plutonium to increase 
yield. The neutron background produced could cause predetonation problems in 
the primary, although boron-10 shielding should mitigate it.

4.4.5.4.1   "Clean" Non-Fissile Tampers
The tamper material of choice for clean (MRR or minimum residual radiation 
weapons) seems to have been lead or lead-bismuth alloy. Lead is a readily 
available, inexpensive material, and it has the second highest atomic number 
of any non-fissionable element available in significant quantity (Z=82). It 
has been used in U.S., Soviet, and British weapon designs. The use of lead-
bismuth alloy (known to have been used in British designs at least) is 
interesting. Bismuth may have been added to improve lead's mechanical 
properties, but it should also be noted that bismuth (with Z=83) has *the* 
highest atomic number of any available non-fissionable material. It may have 
thus been used to enhance lead's opacity.

When irradiated with neutrons, neither lead nor bismuth produce isotopes 
that constitute substantial radiological hazards. The major concern is with 
gamma emitters, since neither beta nor alphas are major hazards unless 
ingested. Neither lead nor bismuth produce isotopes that emit gammas in 
significant amounts.

Tungsten has also been seriously considered for use as a tamper material, 
although it has a relatively low atomic number (Z=74). Tungsten carbide, 
which is more convenient to manufacture, has also been considered. Tungsten-
rhenium alloy coatings may have been used as part of tampers in some 
devices. Tungsten is an isotope mixture, and produces a couple isotopes with 
significant gamma emitting properties. Radioactive tungsten isotopes were 
noted in the debris released during the Redwing and Hardtack I test series.

Gold (Z=79) has been used in at least one weapon design as part of the 
tamper (or possibly the radiation case) - the W-71 warhead for the Spartan 
ABM missile. The W-71 used the thermal X-ray flux as its kill mechanism, so 
it was important for them to escape the weapon with as little hindrance as 
possible. The choice of gold may have been to tailor the opacity so that the 
hot X-rays present at the end of the fusion burn could escape without being 
absorbed. Gold is a good tamper material and has been used in ICF target 
designs due to its opacity.

4.4.5.4.1   "Dirty" Non-Fissile Tampers
Tamper materials may also be chosen to maximize residual radiation (relative 
to yield) to create radiological weapons. 

Tantalum was evaluated in the US as a possible tamper material with 
radiological hazard potential. With Z=73, and a density of 16.65, tantalum 
would a very effective tamper. Natural tantalum consists of 99.988% Ta-181, 
which can be converted to Ta-182 with a half-life of 115 days. Ta-182 is a 
beta emitter with decay energy of 1.807 MeV. It emits beta particles with 
energies in the range of 0.25-0.54 MeV, the remaining energy is emitted as 
gammas (mostly in the strong gamma range of 1.19-1.22 MeV).

The most famous radiological material is cobalt. Natural cobalt consists 
100% of Co-59, which becomes the energetic gamma emitter Co-60 with a 5.26 
year half-life when it captures one neutron. Incorporating cobalt into a 
tamper could thus create an effective source of long term contamination. 
Cobalt has an atomic number of only 27, making it a rather poor 
pusher/tamper since it completely ionizes at 9.9 KeV. It could be used 
though if it was combined with a high Z material, and surrounded by a high-Z 
pusher material. No attempts to actually use cobalt in this way are known.

Zinc (Z=30)is a distant runner-up as a long-term radiological contaminant. 
The isotope Zn-64, which makes up 48.9% of natural zinc, would be converted 
to Zn-65 which is a gamma emitter with a 244 day half-life. The advantages 
of Zn-64 is that its faster decay leads to greater initial intensity 
compared to cobalt. Disadvantages are that since it makes up only half of 
natural zinc, it must either be isotopically enriched or the yield will be 
cut in half; and that it is a weaker gamma emitter than Co-60, putting out 
only one-fourth as many gammas for the same molar quantity. Assuming pure 
Zn-64 is used, the radiation intensity of Zn-65 would initially be twice as 
much as Co-60. This would decline to being equal in 8 months, in 5 years Co-
60 would be 110 times as intense.

Gold: I mention gold here because although it was not used in the W-71 for 
this purpose, it does have potential as a tailored radiological hazard. Gold 
consists 100% of Au-197 which breeds Au-198. Au-198 has a half-life of 2.697 
days and emits 0.412 MeV gammas (along with 0.961 MeV betas). The short 
half-life translates into gamma emissions that are initially very intense 
and last for several days, but decay to low levels after several weeks. It 
has been considered for a short-acting battlefield or strategic radiation 
weapon for this reason.