3D WKB solution for fast magnetoacoustic wave behaviour around an X-line

Abstract

Context. We study the propagation of a fast magnetoacoustic wave in a 3D magnetic field created from two magnetic dipoles. The magnetic topology contains an X-line. Aims. We aim to contribute to the overall understanding of MHD wave propagation within inhomogeneous media, specifically around X-lines. Methods. We investigate the linearised, 3D MHD equations under the assumptions of ideal and cold plasma. We utilise the WKB approximation and Charpit's method during our investigation. Results. It is found that the behaviour of the fast magnetoacoustic wave is entirely dictated by the local, inhomogeneous, equilibrium Alfvén speed profile. All parts of the wave experience refraction during propagation, where the magnitude of the refraction effect depends on the location of an individual wave element within the inhomogeneous magnetic field. The X-line, along which the Alfvén speed is identically zero, acts as a focus for the refraction effect. There are two main types of wave behaviour: part of the wave is either trapped by the X-line or escapes the system, and there exists a critical starting region around the X-line that divides these two types of behaviour. For the set-up investigated, it is found that 15.5% of the fast wave energy is trapped by the X-line. Conclusions. We conclude that linear, β = 0 fast magnetoacoustic waves can accumulate along X-lines and thus these will be specific locations of fast wave energy deposition and thus preferential heating. The work here highlights the importance of understanding the magnetic topology of a system. We also demonstrate how the 3D WKB technique described in this paper can be applied to other magnetic configurations.

Magnetoacoustic Waves in a Stratified Atmosphere with a Magnetic Null Point

“…Other authors have performed ray tracing through magnetic configurations containing nulls (McLaughlin & Hood 2004, 2006aMcLaughlin et al 2008;Longcope & Tarr 2012;Afanasyev & Uralov 2012;McLaughlin et al 2016). Here, the focus is typically quite different compared to the sunspot studies, and addresses whether wave energy is reflected by the null or accumulated at the null, how to determine characteristic damping timescales, etc.…”

3D WKB solution for fast magnetoacoustic wave behaviour within a separatrix dome containing a coronal null point

“…In other words, the 3D WKB technique described in this paper can be both applied to other magnetic configurations and extended further (e.g. by dropping the cold plasma assumption), although there are also limitations of such approaches -see the conclusions of McLaughlin et al (2016). For further information on the WKB method and the wider-family of ray tracing methods, see Tracey et al (2014).…”

“…It is therefore natural to assume that MHD Wave behaviour about null-dome configuration 1391 waves will encounter these magnetic features. This paper follows a series of papers studying the interactions between MHD waves and various magnetic null point topologies (McLaughlin & Hood 2004, 2005, 2006aMcLaughlin, Ferguson & Hood 2008;Thurgood & McLaughlin 2012, 2013aMcLaughlin et al 2016). This series of papers suggest that it is a generic result that fast mode waves will be attracted to the close vicinity of magnetic null points due to a refraction effect, where they subsequently concentrate energy on small scales, experiencing enhanced visco-resistive dissipation and triggering magnetic reconnection (the specific physics of which have been considered by Thurgood, Pontin & McLaughlin 2017, 2018a.…”