Instability of spherically imploding shock waves

Abstract

Summary form only given, as follows. The importance of spherically imploding shock waves has increased recently due to their particular applications in inertial confinement fusion (ICF) and the spherical pinch (SP). In particular, the stability of spherically imploding shock waves plays a critical role in the ultimate success of ICF and SP. The instability of spherically imploding shock waves is now systematically investigated. The basic state is Guderley and Landau's unsteady self-similar solution of the implosion of a spherical shock wave. The stability analysis is conducted by combining Chandrasekhar's approach (1961) to the stability of a viscous liquid drops and Zel'dovich's approach (1966) to the stability of spherical flames together. The governing equations for disturbances are derived and we use the condition that perturbed gas flow is potential. The three dimensional perturbation velocity profile and a shock front perturbation are solved by using the kinematic and dynamic boundary conditions in the shock front. The time-dependent amplitudes of the perturbations are obtained by solving the system of ordinary differential equations. This enable us to study the time history of the spherically imploding shock wave subject to perturbations. The relative amplification and decay of the amplitudes of perturbations decides the stability/instability of the spherical imploding shock waves.