Ignition condition and gain prediction for perturbed inertial confinement fusion targets

Abstract

The effect of perturbations on hot spot ignition is studied using full two-dimensional (2D) numerical simulations of the National Ignition Facility [J. D. Lindl, Phys. Plasmas 2, 3933 (1995)] direct drive Laboratory for Laser Energetics target design and newly derived 2D self-similar solutions for a perturbed burn wave propagation. It is shown that the required implosion velocity needed for ignition increases with the perturbation mode number and final amplitude, reaching an asymptotic value for high enough perturbation mode numbers, when the entire mixing zone no longer contributes to the ignition of the hot spot. Using the new self-similar solutions, ignition conditions for various perturbation mode numbers and amplitudes are obtained. These ignition conditions, which correspond to areal densities higher than needed for ignition in the symmetric case, are translated to a required increase in the implosion velocity needed for ignition, using the 1D Levendahl–Lindl scaling, in good agreement with the full 2D numerical simulation results. Finally, using the above results, a model for predicting the gain of a perturbed targets as a function of the perturbation spectra (single-mode and multi-mode) is presented, in good agreement with full numerical simulations.