Energy scaling of inertial confinement fusion targets for ignition and high gain

The dependence of the ignition threshold on the velocity nu(imp) and compressibility of an imploding fuel mass is central to establishing the driver requirements and implosion strategy for inertial confinement fusion (ICF). Using a series of LASNEX calculations, it is found that ke(imp) proportional to nu(imp)(-alpha)beta(a), where ke(imp) is the kinetic energy in the imploding fuel at the ignition threshold, alpha = 5.5+/-0.5, a = 1.7+/-0.2 and nu(imp) is the implosion velocity. Here, the compressibility parameter beta is related to the pressure P and density rho of the DT fuel by the relation P = beta rho(5/3). These results are obtained by starting at the peak implosion velocity for a fuel shell of a high gain ICF capsule and scaling the isentrope, mass and velocity of the fuel shell. In the presence of a mix of hot and cold material at the edge of the central hot spot, it is also found that the results can be fitted by assuming that the reduced clean fuel radius for a mixed capsule requires a velocity increase of the same magnitude as that which would be required if the entire capsule had been rescaled in size by the same ratio.