Emergence of Unstable Modes for Shock Waves in Ideal MHD

Abstract

This note studies classical magnetohydrodynamic shock waves in an inviscid fluidic plasma that is assumed to be a perfect conductor of heat as well as of electricity. For this mathematically prototypical material, it identifies a critical manifold in parameter space, across which slow classical MHD shock waves undergo emergence of a complex conjugate pair of unstable transverse modes. In the reflectionally symmetric case of parallel shocks, this emergence happens at the spectral value 0, and the critical manifold possesses a simple explicit algebraic representation. Results of refined numerical treatment show that for only almost parallel shocks the unstable mode pair emerges from a pair of non-zero imaginary spectral values.