Self-similar solutions for implosion and reflection of coalesced shocks in a plasma: spherical and cylindrical geometries

Abstract

Approximate analytic solutions to the self similar equations of gas dynamics for a plasma, treated as an ideal gas with specific heat ratio γ = 5/3, are obtained for the implosion and subsequent reflection of various types of shock sequences in spherical and cylindrical geometries. This is based on the lowest-order polynomial approximation, in the reduced fluid velocity, for a suitable nonlinear function of the sound velocity and the fluid velocity. However, the method developed here is powerful enough to be extended analytically to higher order polynomial approximations, to obtain successive approximations to the exact self-similar solutions. Also obtained, for the first time, are exact asymptotic solutions, in analytic form, for the reflected shocks. Criteria are given that may enable one to make a choice between the two geometries for maximising compression or temperature of the gas. These solutions should be useful in the study of inertial confinement of a plasma.