Four-thirds law of energy and magnetic helicity in electron and Hall magnetohydrodynamic fluids

TL;DR

This paper derives new four-thirds laws for energy and magnetic helicity dissipation in electron and Hall magnetohydrodynamic fluids, extending previous theoretical results and highlighting the role of the Hall term.

Contribution

It introduces novel four-thirds laws for magnetic helicity dissipation and generalizes existing energy dissipation laws in Hall MHD systems.

Findings

New four-thirds laws for magnetic helicity dissipation.

Generalization of energy dissipation laws in Hall MHD.

First observation of four-thirds laws for magnetic helicity in these systems.

Abstract

In this paper, by exploiting the feature of the Hall term, we establish some local version four-thirds laws for the dissipation rates of energy and magnetic helicity in both electron and Hall magnetohydrodynamic equations in the sense of Duchon-Robert type. New 4/3 laws for the dissipation rates of magnetic helicity in these systems are first observed and four-thirds law involving the dissipation rates of energy for the Hall magnetohydrodynamic equations generalizes the work of Galtier.