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

G G Howes

doi:10.5194/npg-16-219-2009

Abstract

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 Alfvén 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.

Highlights

Understanding the dynamical evolution of the turbulence in the solar wind and its thermodynamic consequences for the energy balance in the heliosphere is a major goal of heliospheric physics
A turbulent plasma inherently involves dynamically significant nonlinear wave-wave interactions which drive the turbulent cascade of energy to small scales, we focus our attention on the ability of compressible Hall MHD to reproduce the properties of the linear wave modes of the VlasovMaxwell kinetic theory
Three key issues are identified regarding the use of Hall MHD to describe turbulence in kinetic plasmas: (1) what are the wave modes comprising the turbulence at scales kdi 1?; (2) are the collisionless damping rates from linear kinetic theory applicable in a nonlinearly turbulent plasma?; and (3) are the nonlinear wave-wave mode couplings inherent in turbulence altered by the presence of spurious, undamped wave modes in Hall MHD? In a weakly collisional plasma, the only three undamped electromagnetic wave modes that exist at scales kdi 1 are the kinetic Alfven wave, the parallel whistler wave, and the oblique whistler wave; each of these waves is generally well-described by Hall MHD for βi 1

Summary

Introduction

Understanding the dynamical evolution of the turbulence in the solar wind and its thermodynamic consequences for the energy balance in the heliosphere is a major goal of heliospheric physics. Understanding the turbulence at these small scales is critical because the kinetic plasma physics at these scales determines the dissipation of the turbulent fluctuations and the inevitable conversion of the fluctuation energy into plasma heat (Schekochihin et al, 2009; Howes, 2008). The simple fluid model of MHD is not sufficient to describe this new regime of kinetic turbulence in the weakly collisional solar wind plasma. The applicability of the Hall MHD model to turbulence in a weakly collisional plasma such as the solar wind, has been called into question (Howes et al, 2008b). We investigate the limitations of the Hall MHD model for the study of turbulence in kinetic plasmas

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Conclusion