Alfven-fast wave coupling in a 3D non-uniform medium

In this paper, we consider the process of Alfv & eacute;n-fast wave mode coupling, through numerical simulation. We model the process using the ideal, linear magnetohydrodynamic equations on a three-dimensional Cartesian grid; assuming the cold plasma limit, beta << 1. We initialize the simulation with a cylindrical Alfv & eacute;n wave pulse (comprising an azimuthal magnetic field and velocity perturbations) propagating along a uniform magnetic field. The wave starts in a region where the density is uniform. As it propagates, part of the Alfv & eacute;n wave encounters a change in density, before emerging into a second uniform region. We introduce the natural Helmholtz Hodge decomposition as a method to identify the properties of the Alfv & eacute;n wave perturbations at the end of the simulation. Our results show that the Alfv & eacute;n wave propagates efficiently through the non-uniform region, with the wave pulse's final structure sharing strong characteristics of the initial wave pulse structure. More than 69 % of the initial energy is carried by the transmitted Alfv & eacute;n wave. Alfv & eacute;n-fast wave coupling has potential applications in planetary magnetospheres, such as in the Io-Jupiter Alfv & eacute;n wave interaction, and the solar corona.