Linear and nonlinear MHD mode coupling of the fast magnetoacoustic wave about a 3D magnetic null point

TL;DR

This study investigates how fast magnetoacoustic waves behave around 3D magnetic null points, finding they remain decoupled from Alfvén modes and focus energy at the null, extending previous 2D results to 3D.

Contribution

It demonstrates that fast magnetoacoustic waves in 3D null points do not couple to Alfvén modes and exhibit focusing behavior, confirming 2D findings in a fully 3D context.

Findings

Fast waves remain decoupled from Alfvén modes in 3D nulls.

Wave energy is focused towards the null point due to refraction.

Pure fast mode generates a nonlinear disturbance along magnetic field lines.

Abstract

Context: Coronal magnetic null points have been implicated as possible locations for localised heating events in 2D models. We investigate this possibility about fully 3D null points. Aims: We investigate the nature of the fast magnetoacoustic wave about a fully 3D magnetic null point, with a specific interest in its propagation, and we look for evidence of MHD mode coupling and/or conversion to the Alfv\'en mode. Methods: A special fieldline and flux-based coordinate system was constructed to permit the introduction of a pure fast magnetoacoustic wave in the vicinity of proper and improper 3D null points. We considered the ideal, {\beta} = 0, MHD equations, which are solved using the LARE3D numerical code. The constituent modes of the resulting wave were isolated and identified using the special coordinate system. Numerical results were supported by analytical work derived from perturbation theory and a linear implementation of the WKB method. Results: An initially pure fast wave is found to be permanently decoupled from the Alfv\'en mode both linearly and nonlinearly for both proper and improper 3D null points. The pure fast mode also generates and sustains a nonlinear disturbance aligned along the equilibrium magnetic field. The resulting pure fast magnetoacoustic pulse has transient behaviour, which is found to be governed by the (equilibrium) Alfv\'en-speed profile, and a refraction effect focuses all the wave energy towards the null point. Conclusions: Thus, the main results from previous 2D work do indeed carry over to the fully 3D magnetic null points and