Avoided crossings of modes of a finite target with adiabat shaping in inertial fusion implosions

Abstract

In Inertial Confinement Fusion (ICF), a cold target material is accelerated by a hot low density plasma. In this work, the small amplitude disturbances in ablative Rayleigh-Taylor instability in the presence of entropy gradients is studied using a sharp boundary approximation, being the inverse entropy-gradient scale length the quantity Ko = ∝LnSo/∝y. For simplicity, the target considered here is a finite incompressible slab. Due to ablation, the phenomenon of the interactions of two types of modes (Rayleigh mode and entropic mode) is shown. This manifest itself in the occurrence of rapid shifts of rate growth (bumping, avoided crossings). The entire situation is strongly reminiscent of the well-know "avoided crossings" of modes of two coupled oscillators. The growth rate of one mode (Rayleigh mode) approaches that of another one (entropic mode) which is "bumped" to a quite different rate growth, while the "bumping" mode settles at roughly at the original rate growth of the bumped mode.