Incompressible Extended Magnetohydrodynamics Waves: Implications of Electron Inertia

TL;DR

This paper derives the dispersion relation for incompressible extended magnetohydrodynamics (XMHD), revealing detailed plasma wave behaviors influenced by electron inertia and Hall effects, and demonstrating XMHD's improved accuracy over Hall MHD.

Contribution

It introduces the dispersion relation and eigenvector solutions for incompressible XMHD, highlighting the model's enhanced physical realism compared to Hall MHD.

Findings

XMHD captures ion cyclotron and whistler wave saturation at gyrofrequencies.

XMHD provides a more accurate plasma dynamics model at high wave numbers.

It smooths singularities present in Hall MHD solutions.

Abstract

This paper explores plasma wave modes using the extended magnetohydrodynamics (XMHD) model, incorporating Hall drift and electron inertia effects. We utilize the geometric optics ansatz to study perturbed quantities, with a focus on incompressible systems. Our research concludes with the derivation of the dispersion relation for incompressible XMHD and the associated eigenvector solutions, offering new perspectives on plasma wave behavior under these extended scenarios. The dispersion relation shows distinct ion cyclotron and whistler wave branches, with characteristic saturation at the ion and electron gyrofrequencies, respectively. Comparisons between Hall MHD and XMHD demonstrate that XMHD provides a more accurate representation of plasma dynamics, especially at higher wave numbers, bridging the gap between simplified models and comprehensive two-fluid descriptions and smoothing out singularities present in Hall MHD solutions and capturing more physics of the full two-fluid model.