On the formation of secondary shocks in a self-similar magnetogasdynamic flow

Abstract

The problem of a self-similar flow behind a cylindrical shock wave, produced by the sudden release of a finite amount of energy per unit length along an axis of infinite extent in a plasma permeated by a transverse magnetic field, has been solved exactly for the specific heat ratio γ = 2. This value for the specific heat ratio γ is known to approximate the plasma state in a uniform magnetic field. We used the singular surface theory to study the propagation of a weak discontinuity in this self-similar flow, and calculated the critical time for a shock formation. We find that the appearance of a secondary shock cannot be ignored if the amplitude of the initial discontinuity satisfies appropriate conditions. The condition of the nonimpact between a weak discontinuity and the primary shock has also been discussed.