On energy conservation in extended magnetohydrodynamics

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.

References in corpus (6)

• Hamiltonian formulation and analysis of a collisionless fluid reconnection model
• Hamiltonian magnetohydrodynamics: symmetric formulation, Casimir invariants, and equilibrium variational principles
• Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability - Theory
• Hamiltonian and action formalisms for two-dimensional gyroviscous MHD
• Local thermodynamics of a magnetized, anisotropic plasma
• Nonlinear variational method for predicting fast collisionless magnetic reconnection

Cited by in corpus (32)

• Hamiltonian Formalism of Extended Magnetohydrodynamics
• Action Principles for Extended MHD Models
• Concomitant Hamiltonian and topological structures of extended magnetohydrodynamics
• "Ideal" tearing and the transition to fast reconnection in the weakly collisional MHD and EMHD regimes
• Derivation of the Hall and Extended Magnetohydrodynamics Brackets
• A General Metriplectic Framework with Application to Dissipative Extended Magnetohydrodynamics
• Inertial magnetohydrodynamics
• Hamiltonian and action formalisms for two-dimensional gyroviscous MHD
• Collisionless Magnetic Reconnection in Curved Spacetime and the Effect of Black Hole Rotation
• On the structure and statistical theory of turbulence of extended magnetohydrodynamics
• Nonlinear Alfvén waves in extended magnetohydrodynamics
• The action principle for generalized fluid motion including gyroviscosity
• Helical Fluid and (Hall)-MHD Turbulence: a Brief Review
• Structure and computation of two-dimensional incompressible extended MHD
• Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability -- Examples with Translation Symmetry
• Influence of the Hall effect and electron inertia in collisionless magnetic reconnection
• Nonlinear Resistivity for Magnetohydrodynamical Models
• Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria
• Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria
• Gravitational electromotive force in magnetic reconnection around Schwarzschild black holes
• Modification of magnetohydrodynamic waves by the relativistic Hall effect
• Helically symmetric extended magnetohydrodynamics: Hamiltonian formulation and equilibrium variational principles
• Radiative Back-Reaction on Charged Particle Motion in the Dipole Magnetosphere of Neutron Stars
• Chirality, extended MHD statistics and solar wind turbulence
• Finite-Larmor-radius equilibrium and currents of the Earth's flank magnetopause
• A class of three-dimensional gyroviscous magnetohydrodynamic models
• Hamiltonian formulation of X-point collapse in an extended magnetohydrodynamics framework
• Conservative regularization of compressible dissipationless two-fluid plasmas
• Ellipticity conditions for the extended MHD Grad-Shafranov-Bernoulli equilibrium equations
• Yet Another Modification of Relativistic Magnetohydrodynamic Waves: Electron Thermal Inertia
• Incompressible Extended Magnetohydrodynamics Waves: Implications of Electron Inertia
• Plasma turbulence in the equatorial electrojet: A two-dimensional Hamiltonian fluid model