Modelling the Propagation of a Weak Fast-Mode MHD Shock Wave near a 2D Magnetic Null Point Using Nonlinear Geometrical Acoustics

TL;DR

This paper analytically models the behavior of fast-mode MHD waves and weak shocks near a 2D magnetic null point, revealing complex caustic formations, plasma heating distribution, and shock wave dynamics using nonlinear geometrical acoustics.

Contribution

It introduces a nonlinear geometrical acoustics approach to analyze wave and shock propagation near magnetic null points, including caustic formation and plasma heating effects.

Findings

Complex caustic forms around the null point.

Shock wave passes through the null point even in cold plasma.

Plasma heating occurs at caustics and near the null point due to nonlinear damping.

Abstract

We present the results of analytical modelling of fast-mode magnetohydrodynamic wave propagation near a 2D magnetic null point. We consider both a linear wave and a weak shock and analyse their behaviour in cold and warm plasmas. We apply the nonlinear geometrical acoustics method based on the Wentzel-Kramers-Brillouin approximation. We calculate the wave amplitude, using the ray approximation and the laws of solitary shock wave damping. We find that a complex caustic is formed around the null point. Plasma heating is distributed in space and occurs at a caustic as well as near the null point due to substantial nonlinear damping of the shock wave. The shock wave passes through the null point even in a cold plasma. The complex shape of the wave front can be explained by the caustic pattern.