Boosted fission weapon
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Boosted fission weapons are a type of nuclear bomb that uses a small amount of fusion fuel to increase the rate, and thus yield, of a fission reaction.
In a traditional fission design, the fissile fuel is "assembled" quickly with conventional explosives, producing a supercritical mass. In this state the neutrons given out from a fission reaction will induce other atoms in the fuel to undergo fission as well, leading to a chain reaction. The upper limit on a pure-fission weapon is not too much over 500 kilotons, and even this is only possible with highly-developed efficiency systems (the largest pure-fission weapon tested was Ivy King).
Many other nuclear reactions take place much more quickly, and thus much more "explosively". In particular a number of fusion reactions can be triggered by pressure, releasing neutrons. These neutrons can then be used to ignite other fission reactions in the surrounding fuel, increasing the overall rate of the reaction, and thereby allowing the bomb to include much more fuel. Such a design can be scaled up much larger than a pure-fission bomb, but still less than the megaton of a hydrogen bomb. Likewise the system can be used to make a bomb of a smaller size, but use considerably less of the expensive fission fuel. The reduction in fuel alone makes these designs so useful that today almost all modern nuclear devices use some sort of boosting.
There are two general designs for boosted devices. One places a small amount of fusion fuel, typically tritium, inside the core of the fission fuel, which is hollow. Although this makes the assembly somewhat less effective, the burst of neutrons from the fusion fuel in the center more than makes up for this. The other, which was known as the layer cake in the USSR and the alarm clock in the USA, places additional fission fuel in a separate charge, with the fusion fuel, typically lithium deuteride, layered between it and the primary fission device. This design can be stacked in several layers to increase the yield, though even at best it is generally thought to be limited to the sub-megaton range.
The differences between a boosted fission device and a "true" hydrogen bomb are fairly significant. A thermonuclear weapon of the Teller-Ulam configuration functions primarily by using a fission weapon external to the fusion fuel to compress the fusion fuel (rather than placing the fusion fuel in the same part of the weapon as the fission fuel, as in a boosted weapon). The result of this innovation, "staging," means that an arbitrary number of fusion fuel "stages" can be put into any one weapon (and these can themselves induce fission in their uranium casings), allowing for a virtually unlimited upper yield on such a weapon. The most powerful such weapon to ever be developed was the Tsar Bomba of the Soviet Union, which in its full form could have been detonated to a yield of 100 Mt.