Von Karman-Howarth equation for Hall magnetohydrodynamics: Hybrid simulations

TL;DR

This paper derives a dynamical equation for Hall-MHD turbulence, applies it to hybrid simulation data, and investigates how plasma beta influences cascade behavior across different scales.

Contribution

It rederives the Hall-MHD dynamical law and applies it to simulation data, revealing scale-dependent cascade dynamics influenced by plasma beta.

Findings

Inertial range exhibits classic MHD cascade behavior.

Sub-ion range cascade persists via Hall term, but weakens with higher plasma beta.

Cascade rate decreases in high-beta plasmas at sub-ion scales.

Abstract

A dynamical vectorial equation for homogeneous incompressible Hall-MHD turbulence together with the exact scaling law for third-order correlation tensors, analogous to that for the incompressible MHD, is rederived and applied to the results of two-dimensional hybrid simulations of plasma turbulence. At large (MHD) scales the simulations exhibits a clear inertial range where the MHD dynamic law is valid. In the sub-ion range the cascade continues via the Hall term but the dynamic law derived in the framework of incompressible Hall MHD equations is obtained only in a low plasma beta simulation. For a higher beta plasma the cascade rate decreases in the sub-ion range and the change becomes more pronounced as the plasma beta increases. This break in the cascade flux can be ascribed to non thermal (kinetic) features or to others terms in the dynamical equation that are not included in the Hall-MHD incompressible approximation.