The reflection of an ionized shock wave

TL;DR

This paper applies thermodynamic and kinetic theory to analyze the reflection of ionized shock waves in an electromagnetic shock tube, confirming experimental observations and explaining ionization behavior behind shock fronts.

Contribution

It extends previous one-dimensional models to shock reflection scenarios, proving shock waves satisfy entropy conditions and explaining ionization patterns.

Findings

Both incident and reflected shocks satisfy Lax entropy conditions.

Temperature increases significantly behind the incident shock, but ionization does not.

Ionization increases substantially behind the reflected shock.

Abstract

In a previous paper we studied the thermodynamic and kinetic theory for an ionized gas, in one space dimension; in this paper we provide an application of those results to the reflection of a shock wave in an electromagnetic shock tube. Under some reasonable limitations, which fully agree with experimental data, we prove that both the incident and the reflected shock waves satisfy the Lax entropy conditions; this result holds even outside genuinely nonlinear regions, which are present in the model. We show that the temperature increases in a significant way behind the incident shock front but the degree of ionization does not undergo a similar growth. On the contrary, the degree of ionization increases substantially behind the reflected shock front. We explain these phenomena by means of the concavity of the Hugoniot loci. Therefore, our results not only fit perfectly but explain what was remarked in experiments.