Mixing of shear Alfven wave packets

TL;DR

This paper models shear Alfven wave packet propagation as a mixing process in inhomogeneous magnetic fields, deriving a kinetic equation and showing a $k^{-1}$ energy spectrum for waves along chaotic magnetic field lines.

Contribution

It introduces a kinetic equation for wave energy based on a mixing process perspective, linking phase mixing to Alfvenic shear and strain flows, and analyzes energy spectra in chaotic magnetic fields.

Findings

Wave packet distortion is described as a mixing process.

A kinetic equation for wave energy is derived from an eikonal approach.

Wave energy spectrum follows a $k^{-1}$ power-law in chaotic magnetic fields.

Abstract

The propagation of shear Alfven wave packets in inhomogeneous magnetic fields, at the origin of their distortion, regardless of the occurrence of non-linear coupling, is considered. It is shown that the distortion mechanism can be regarded as mixing process and hence, standard "phase mixing" corresponds to the effect of an "Alfvenic" shear flow while enhanced dissipation at a magnetic X-point corresponds to mixing by an "Alfvenic" strain flow. The evolution of the global wave field is supposed to result from the dynamics of a superposition of wave packets and a kinetic equation for the wave energy is obtained following this eikonal (WKB) description. Since shear Alfven wave packets experience continuous shearing/straining while transported by an inhomogeneous Alfvenic flow $\mathbf{V}_{A}$, their mixing process, in physical space, is also a cascade of wave energy in k-space. The wave energy spectrum resulting from this linear mechanism of energy transfer is determined for the special case of waves propagating along chaotic magnetic field lines, the analog of a chaotic mixing process. The latter follows a $k^{-1}$ power-law, in the energy conserving range in $k$ space.