3D Alfven wave behaviour around proper and improper magnetic null points

Abstract: Context: MHD waves and magnetic null points are both prevalent in many astrophysical plasmas, including the solar atmosphere. Interaction between waves and null points has been implicated as a possible mechanism for localised heating events. Aims: Here we investigate the transient behaviour of the Alfven wave about fully 3D proper and improper 3D magnetic null points. Previously, the behaviour of fast magnetoacoustic waves at null points in 3D, cold MHD was considered by Thurgood & McLaughlin (Astronomy & Astrophysics, 2012, 545, A9). Methods: We introduce an Alfven wave into the vicinity of both proper and improper null points by numerically solving the ideal, $\beta=0$ MHD equations using the LARE3D code. A magnetic fieldline and flux-based coordinate system permits the isolation of resulting wave-modes and the analysis of their interaction. Results: We find that the Alfven wave propagates throughout the region and accumulates near the fan-plane, causing current build up. For different values of null point eccentricity, the qualitative behaviour changes only by the imposition of anisotropic pulse dilation, due to the differing rates at which fieldlines diverge from the spine. For all eccentricities, we find that the fast and Alfven waves are linearly decoupled. During the driving phase, an independently propagating fast wave is nonlinearly generated due to the ponderomotive force. Subsequently, no further excitation of fast waves occurs. Conclusions: We find that the key aspects of the theory of Alfv\'en waves about 2D null points extends intuitively to the fully 3D case; i.e. the wave propagates along fieldlines and thus accumulates at predictable parts of the topology. We also highlight that unlike in the 2D case, in 3D Alfven-wave pulses are always toroidal and thus any aspects of 2D Alfven-wave-null models that are pulse-geometry specific must be reconsidered in 3D.