Phase Mixing of Alfv\'en Waves Near a 2D Magnetic Null Point

The propagation of linear Alfv\'en wave pulses in an inhomogeneous plasma near a 2D coronal null point is investigated. When a uniform plasma density is considered, it is seen that an initially planar Alfv\'en wavefront remains planar, despite the varying equilibrium Alfv\'en speed, and that all the wave collects at the separatrices. Thus, in the non-ideal case, these Alfv\'enic disturbances preferentially dissipate their energy at these locations. For a non-uniform equilibrium density, it is found that the Alfv\'en wavefront is significantly distorted away from the initially planar geometry, inviting the possibility of dissipation due to phase mixing. Despite this however, we conclude that for the Alfv\'en wave, current density accumulation and preferential heating still primarily occur at the separatrices, even when an extremely non-uniform density profile is considered.