Chiral Exact Relations for Helicities in Hall Magnetohydrodynamic Turbulence

TL;DR

This paper derives new exact relations for helicity invariants in Hall MHD turbulence, linking helicity cascades to polarization states and enabling direct measurement of dissipation rates.

Contribution

It introduces universal laws for Hall MHD turbulence involving mixed structure functions, connecting helicity cascades to polarization and providing tools for experimental analysis.

Findings

Generalized helicity cascade linked to left polarized fluctuations

Magnetic helicity cascade linked to right polarized fluctuations

Universal laws expressed through mixed second-order structure functions

Abstract

Besides total energy, three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses two inviscid invariants which are the magnetic helicity and the generalized helicity. New exact relations are derived for homogeneous (non-isotropic) stationary Hall MHD turbulence (and also for its inertialess electron MHD limit) with non-zero helicities and in the asymptotic limit of large Reynolds numbers. The universal laws are written only in terms of mixed second-order structure functions, i.e. the scalar product of two different increments. It provides, therefore, a direct measurement of the dissipation rates for the corresponding invariant flux. This study shows that the generalized helicity cascade is strongly linked to the left polarized fluctuations while the magnetic helicity cascade is linked to the right polarized fluctuations.