In a DT plasma at temperatures over about 50 million degrees, random collisions of D and T produce more energy via the fusion reaction than is radiated away by photons. This is the expected initiation temperature for fusion burn—typically the plasma would then heat itself to above 200 million degrees while burning. The reaction rate per particle depends on temperature and density. At 200 million degrees the reaction rate per particle is 5.2 × 107 ρ s-1 ρ where is the DT mixture’s mass density in grams per cubic centimeter. The disassembly time of an isothermal sphere is roughly R/(3Cs) where R is the radius and Cs the sound speed—at 200 million degrees Cs is roughly 108 cm/s. Thus (very approximately) we must have the areal density, ρR, >3-7g/cm2 in order to get a significant proportion of the nuclei to react in the disassembly time. At DT liquid density this would require a sphere of 10-30 centimeters radius and a huge release of energy. To keep the energy to initiate fusion small and the energy released manageable a small sphere (weighing a few milligrams) must be used. This requires compression. The areal density rises during compression (at fixed mass ρR R-2) until it reaches a substantial fraction of fusion-relevant levels (of order 3-7g/cm2). For 3mg of solid/liquid DT an increase of the density of order a thousand is needed.
In most inertial confinement fusion (ICF) schemes, a shell of cryogenic deuterium and tritium fuel is accelerated inward and compressed by the reaction force from an ablating outer shell. The ablating outer shell is heated either by direct laser irradiation (called direct drive) or by the x-rays produced by heating a high Z enclosure (hohlraum) that surrounds the fuel target (called indirect drive). The hohlraum in indirect drive schemes may be driven (heated) by lasers, particle beams, or pulsed power systems. During compression the fuel is kept as cold as possible to minimize the work needed for compression. At stagnation, a central hot spot enclosing a few percent of the total mass is heated and ignited. Ignition occurs when the alpha-particle heating of the hot spot exceeds all the energy losses. Ignition triggers a runaway process (the thermonuclear instability) resulting in a large amplification of the hot spot energy. If the inertia of the surrounding dense DT shell confines the ignited hot spot pressure long enough, the thermonuclear burn will propagate from the central hot spot to the dense shell and the entire fuel mass will burn. The burn is driven by the fusion alpha particles depositing their energy in the cold dense fuel. The burn lasts until the target disassembles, and the fuel burn-up fraction increases with the shell areal density.
Compressing a target to ignition conditions is very challenging and is yet to be fully realized in experiments, although major advances have been made. Drivers must deliver very uniform ablation; otherwise the target is compressed asymmetrically. Asymmetric compression excites strong Rayleigh-Taylor instabilities that spoil compression and mix dense cold plasma with the less dense hot spot. Preheating of the target can also spoil compression. For example, mistimed driver pulses can shock