On energy conservation in extended magnetohydrodynamics

TL;DR

This paper investigates energy conservation in extended MHD models with Hall effects and electron inertia, revealing that common models often fail to conserve energy unless specific terms are included.

Contribution

The study identifies missing terms necessary for energy conservation in ideal extended MHD models, providing guidance for more accurate modeling.

Findings

Common models do not conserve energy without additional terms

A specific neglected term in the momentum equation is essential for energy conservation

Guidelines for constructing energy-conserving extended MHD models

Abstract

A systematic study of energy conservation for extended magnetohydrodynamic (MHD) models that include Hall terms and electron inertia is performed. It is observed that commonly used models do not conserve energy in the ideal limit, i.e., when viscosity and resistivity are neglected. In particular, a term in the momentum equation that is often neglected is seen to be needed for conservation of energy.