Phase Mixing of Nonlinear Visco-resistive Alfv\'en Waves

TL;DR

This paper explores nonlinear Alfvén wave behavior in inhomogeneous plasmas, revealing effects like ponderomotive force, visco-resistive heating, phase mixing, and their impact on plasma temperature and density profiles.

Contribution

It provides the first combined analytical and numerical analysis of nonlinear, nonideal Alfvén waves in 1D and 2D, highlighting new heating and phase mixing phenomena.

Findings

Ponderomotive effect generates a longitudinal wave component.

Visco-resistive heating significantly increases local plasma temperature.

Phase mixing causes drifting of the heating layer and modifies density profiles.

Abstract

We investigate the behaviour of nonlinear, nonideal Alfv\'en wave propagation within an inhomogeneous magnetic environment. The governing MHD equations are solved in 1D and 2D using both analytical techniques and numerical simulations. We find clear evidence for the ponderomotive effect and visco-resistive heating. The ponderomotive effect generates a longitudinal component to the transverse Alfv\'en wave, with a frequency twice that of the driving frequency. Analytical work shows the addition of resistive heating. This leads to a substantial increase in the local temperature and thus gas pressure of the plasma, resulting in material being pushed along the magnetic field. In 2D, our system exhibits phase mixing and we observe an evolution in the location of the maximum heating, i.e. we find a drifting of the heating layer. Considering Alfv\'en wave propagation in 2D with an inhomogeneous density gradient, we find that the equilibrium density profile is significantly modified by both the flow of density due to visco-resistive heating and the nonlinear response to the localised heating through phase mixing.