Dispersive shock waves in partially ionised plasmas

TL;DR

This paper studies how weak dispersion caused by Hall currents affects shock waves in partially ionised solar plasmas, revealing that dispersion alters shock characteristics and depends on ionisation degree.

Contribution

It derives a Korteweg-de Vries-Burgers equation for shock waves in partially ionised plasmas considering Hall current effects and analyzes how dispersion influences shock properties.

Findings

Dispersion modifies shock wave characteristics.

Shock fronts widen with more neutrals.

Dispersion can induce short-lived oscillations.

Abstract

Compressional waves propagating in the partially ionised solar lower atmospheric plasmas can easily steepen into nonlinear waves, including shocks. Here we investigate the effect of weak dispersion generated by Hall currents perpendicular to the ambient magnetic field on the characteristics of shock waves. Our study will also focus on the interplay between weak dispersion and partial ionisation of the plasma. Using a multiple scale technique we derive the governing equation in the form of a Korteweg-de Vries-Burgers equation. The effect of weak dispersion on shock waves is obtained using a perturbation technique. The secular behaviour of second order terms is addressed with the help of a renormalisation technique. Our results show that dispersion modifies the characteristics of shock waves and this change is dependent also on the ionisation degree of the plasma. Dispersion can create short lived oscillations in the shocked plasma. The shock fronts become wider with the increase in the number of neutrals in the plasma.