Non-modal Linear Stability Analysis of Ablation Flows Relative to Inertial Confinement Fusion

Abstract

The first non-modal linear stability analysis of an unsteady ablation waves in the context of inertial confinement fusion is carried out. Optimal initial perturbations are computed using a direct-adjoint method obtained by applying the Lagrange multiplier technique. Particular attention is paid to a proper formulation of a Lagrange functional for compressible flow equations with perturbed dynamical boundaries. Ablation wave perturbations are found to be prone to transient amplification at both short and intermediate final times whether for small or large perturbation wavelengths. Two distinct mechanisms of optimal growth are presently identified. These results contrast with previous results based on normal mode analysis, simulations and dedicated experiments of selected perturbation configurations, for which only large wavelengths are subject to a possible amplification whereas small wavelengths are damped.