Alfvén wave propagation in a dipole magnetic field

In this paper, we consider the process of Alfvén-fast wave mode coupling due to non-uniform field geometry in a dipole magnetic field through numerical simulation. We model the process using the linear magnetohydrodynamic equations on a 3D grid based on a modified dipole coordinate system in the low plasma β limit. The Alfvén wave is launched along the background field from the equatorial region and is then allowed to bounce between reflecting ionospheres. To focus on the effects of field geometry, we adopt a uniform Alfvén speed in the simulations. Initially, there is some Alfvén wave energy loss through coupling to the fast mode, but this is < 20% of the initial Alfvén wave energy. We find that the Alfvén wave pulse is able to retain most of its initial energy (⁠> 80%) and maintain its identity. Our results further show that this is due to the evolution of the Alfvén wave pulse, through phase mixing, to spatial scales which allow it to asymptotically decouple from the fast mode despite the non-uniform magnetic field. Our results provide an explanation for the observed ability of Alfvén waves to persist in nonuniform space plasmas. A surprising result is that Alfvén waves in a nonuniform medium can have a compressible flow.