A generalized scaling law for the ignition energy of inertial confinement fusion capsules

The minimum energy needed to ignite an inertial confinement fusion capsule is of considerable interest in the optimization of an inertial fusion driver. Recent computational work investigating this minimum energy has found that it depends on the capsule implosion history, in particular, on the capsule drive pressure. This dependence is examined using a series of LASNEX simulations to find ignited capsules which have different values of the implosion velocity, fuel adiabat and drive pressure. It is found that the main effect of varying the drive pressure is to alter the stagnation of the capsule, changing its stagnation adiabat, which, in turn; affects the energy required for ignition. To account for this effect a generalized scaling law has been devised for the ignition energy, E-ign proportional to alpha (1.88+/-0.05)(if)v(-5.89+/-0.12)P(-0.77+/-0.03). This generalised scaling law agrees with the results of previous work in the appropriate limits.