Limitations of Hall MHD as a model for turbulence in weakly collisional plasmas

TL;DR

This paper assesses the limitations of Hall MHD in modeling turbulence in weakly collisional plasmas, comparing it to kinetic theory and identifying regimes where it accurately describes wave modes relevant to solar wind turbulence.

Contribution

It provides a comprehensive comparison between Hall MHD and kinetic theory, clarifying the conditions under which Hall MHD is valid for plasma turbulence modeling.

Findings

Hall MHD is valid in the cold ion limit.

Spurious wave modes appear at finite ion temperatures.

Key wave modes in turbulence are well described by Hall MHD.

Abstract

The limitations of Hall MHD as a model for turbulence in weakly collisional plasmas are explored using quantitative comparisons to Vlasov-Maxwell kinetic theory over a wide range of parameter space. The validity of Hall MHD in the cold ion limit is shown, but spurious undamped wave modes exist in Hall MHD when the ion temperature is finite. It is argued that turbulence in the dissipation range of the solar wind must be one, or a mixture, of three electromagnetic wave modes: the parallel whistler, oblique whistler, or kinetic Alfven waves. These modes are generally well described by Hall MHD. Determining the applicability of linear kinetic damping rates in turbulent plasmas requires a suite of fluid and kinetic nonlinear numerical simulations. Contrasting fluid and kinetic simulations will also shed light on whether the presence of spurious wave modes alters the nonlinear couplings inherent in turbulence and will illuminate the turbulent dynamics and energy transfer in the regime of the characteristic ion kinetic scales.