The
boosted fission weapon is a
second-generation nuclear weapon. It is based around the idea of making a
fission explosion more efficient (capable of converting more of its
fissile material to
energy) by increasing the number of
neutrons available during the critical stages of
detonation. Ah, I can hear you ask, but how does it do this? Well, there's a couple of ways.
Confinement. One possible method for this is to include a neutron reflector in your weapon design. This is essentially a giant mirror for neutrons. The requirements for the material used are that it reflect neutrons (as opposed to absorbing them like, say, cadmium) and that it be extremely massive so as to retain enough inertia to 'squeeze' the fission reaction in its first few milliseconds of life. The best material for this, actually, is Uranium-238, or U-238. This is also the more plentiful isotope of the stuff produced when raw uranium ore is processed into reactor-grade materials. It is more stable than U-235 or Pu-239. Thus, it's typically available.
It works because it reflects neutrons as required, and because it is very massive. The tensile strength or melting point of a material is irrelevant to how well it will contain a nuclear explosion; such characteristics are pointless at the heart of a sun. What is more important is mass, since it takes more energy to accelerate. As the reflector sits in the way of the detonation, it reflects an enormous number of energetic neutrons back into the critical mass before being vaporized and blown out of the way.
Just as a trivia point, the physical design of a weapon visibly affects the detonation. If you carefully examine high-speed photographs of a nuclear explosion, or even reasonably slow film/video, you will notice that as the initial 'bubble' of the fireball swells outwards from the detonation, there are light and dark areas on its surface. The dark areas are areas where more massive parts of the bomb's construction have 'delayed' energy outrushing into the bubble, making them cooler, or darker.
Neutron Addition. This is the other method of boosting a fission reaction. Rather than retaining larger quantities of neutrons in the initial phases, you take steps to ensure additional neutrons (over and above those liberated from your fission fuel) are present. Since a nuclear detonation is a chain reaction, and chain reactions are exponential (one fissioning atom begets two neutrons, which beget four more, which...), then a few additional neutrons early on can make a huge difference in how much of the available mass is consumed. One popular method of doing this is to add a fusion fuel to the weapon; not enough that the fusion reaction itself adds much to the weapon's output, but enough that the initial detonation creates a flood of fusion-produced neutrons. The most popular material for this is tritium, which is an isotope of hydrogen. Because it has extra neutrons, it is less stable (it's radioactive) and likes to fuse, releasing large quantities of neutrons and energy.
Tritium fusion (referred to sometimes as T-T fusion, for tritium-tritium) is easier to initiate and quite effective. The downside is that tritium needs to be manufactured and retained, and it's radioactive (hazardously so) and has a half-life of only around 12 years, so it needs to be replaced every once in a while, which requires maintenance and/or testing.
One method, referred to in Swords of Armageddon by Chuck Hansen, is called Gas Boosting. Gaseous tritium (and possibly deuterium in order to reduce tritium requirements) is placed inside the fission primary stage of the weapon, ideally inside the core of fissile material of the primary. When the weapon is detonated, the imploding primary causes fusion in the gas, which releases a flood of neutrons. Those neutrons are added to the neutron flux from the fissioning Pu-239 in the core, and the increase results in a much higher 'burn' of the U-235 secondary and an increased yield.
This is one reason that some nuclear weapons require 'refueling.' Apparently the presence of enough plain old hydrogen in the core during detonation can cause chemistry which results in problems and reduced yield, so simply initial overprovisioning isn't an answer. Simply getting to the core of the primary stage is, no doubt, not entirely simple, and is one reason the design of these weapons is so important from angles other than simple power.
Note: the substance used for this is sometimes referred to as 'boost gas.'
It is possible to achieve fusion boosting using 'dry' fuel. A layer of lithium deuteride placed around the fission core will allow early fission neutrons to convert deuterium into tritium. The local conditions during detonation are enough to allow D-T fusion, so a fusion sequence occurs. One advantage of this is that the fusion-produced neutrons that result have around 14 times the energy of the fission neutrons that began the reaction; as a result, those neutrons can initiate fission even in U-238 (depleted uranium). The Soviet weapon design named 'Layer Cake' utilized this method. The US never built a device of this type (to the best of my knowledge).