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

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 Alfvén 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, β = 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 Alfvén 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) Alfvén-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 so we conclude that 3D null points are locations for preferential heating in the corona by 3D fast magnetoacoustic waves.

Modelling Quasi-Periodic Pulsations in Solar and Stellar Flares

“…fast waves accumulate at null points is entirely general and has been shown to work for double X-type neutral points (McLaughlin and Hood 2005) as well as 3D null points (e.g. McLaughlin 2012, andsee McLaughlin et al 2011 for a review). Crucially, McLaughlin et al (2009) showed that this accumulation of wave energy at the null is enough to induce reconnection, i.e.…”

Three-dimensional Oscillatory Magnetic Reconnection

“…These waves are also manifest in the generation of oppositely signed vorticity tubes in the reconnection region which propagate up along either side of the spine line (Figure 7). Vorticity propagation is a marker of Alfvén waves in 3D MHD, as it corresponds to a rotational disturbances of the magnetic field which allows magnetic tension to act as the predominant restoring force giving rise to the key properties of the wave [Goossens et al, 2011, Thurgood & McLaughlin, 2012, Shelyag et al, 2013. These waves are generated by the swaying of the spine line and neighbouring fieldlines from side to side along the x-axis during each reversal event, which produces two counter rotational vortices in the flow pattern surrounding the spine (somewhat reminiscent of the 'm = 1' kink wave in coronal loops).…”

Magnetoacoustic Waves in a Stratified Atmosphere with a Magnetic Null Point

“…This latter approach has been used to analyze observational data (Tomczyk & McIntosh 2009) but could be applied in three dimensions to simulation output. A third approach is to project the energy density and flux terms onto characteristic directions of the magnetic field as Felipe (2012) has done for the 3D sunspot simulation, Thurgood & McLaughlin (2012) did for a 3D numerical simulation, and McLaughlin et al (2016) did for a 3D null in a WKB ray-tracing investigation. Mumford et al (2015) had some success using this method to determine the energy flux associated with several modes of a 3D expanding flux tube, but the presence of multiple propagation velocities at a given height in their phase diagrams (see, e.g., their Figure 7(a)), suggests that the decomposition is not exact.…”