On the structure and statistical theory of turbulence of extended magnetohydrodynamics

TL;DR

This paper explores the statistical and structural properties of turbulence in extended magnetohydrodynamics (XMHD), revealing cascade behaviors and spectral characteristics relevant to space and astrophysical plasmas using Hamiltonian methods.

Contribution

It introduces a Hamiltonian framework for XMHD turbulence, analyzes cascade directions, and extends ideal MHD results to include Hall drift and electron inertia effects.

Findings

Inverse cascade of magnetic helicity in Hall MHD range

Direct cascade of spectral quantities in inertial MHD range

Verification of Liouville's theorem for XMHD

Abstract

Recent progress regarding the noncanonical Hamiltonian formulation of extended magnetohydrodynamics (XMHD), a model with Hall drift and electron inertia, is summarized. The advantages of the Hamiltonian approach are invoked to study some general properties of XMHD turbulence, and to compare them against their ideal MHD counterparts. For instance, the helicity flux transfer rates for XMHD are computed, and Liouville's theorem for this model is also verified. The latter is used, in conjunction with the absolute equilibrium states, to arrive at the spectra for the invariants, and to determine the direction of the cascades, e.g., generalizations of the well-known ideal MHD inverse cascade of magnetic helicity. After a similar analysis is conducted for XMHD by inspecting second order structure functions and absolute equilibrium states, a couple of interesting results emerge. When cross helicity is taken to be ignorable, the inverse cascade of injected magnetic helicity also occurs in the Hall MHD range - this is shown to be consistent with previous results in the literature. In contrast, in the inertial MHD range, viz. at scales smaller than the electron skin depth, all spectral quantities are expected to undergo direct cascading. The consequences and relevance of our results in space and astrophysical plasmas are also briefly discussed.