The Riemann problem for equations of a cold plasma

TL;DR

This paper constructs solutions to the Riemann problem for a one-dimensional cold plasma system, revealing complex wave interactions including shocks with delta singularities and proposing an admissibility criterion for non-unique rarefaction waves.

Contribution

It introduces a method to solve the Riemann problem for a nonstrictly hyperbolic plasma system, including handling delta singularities and non-unique rarefaction waves.

Findings

Solutions include rarefaction and shock waves with delta singularities

Admissibility principle for non-unique rarefaction waves proposed

Analysis of wave interactions in cold plasma oscillations

Abstract

A solution of the Riemann problem is constructed for a nonstrictly hyperbolic inhomogeneous system of equations describing one-dimensional cold plasma oscillations. Each oscillation period includes one rarefaction wave and one shock wave containing a delta singularity. The rarefaction wave can be constructed in a non-unique way, the admissibility principle is proposed.