Action Principles for Extended MHD Models

Abstract

The general, non-dissipative, two-fluid model in plasma physics is Hamiltonian, but this property is sometimes lost or obscured in the process of deriving simplified (or reduced) two-fluid or one-fluid models from the two-fluid equations of motion. To ensure that the reduced models are Hamiltonian, we start with the general two-fluid action functional, and make all the approximations, changes of variables, and expansions directly within the action context. The resulting equations are then mapped to the Eulerian fluid variables using a novel nonlocal Lagrange-Euler map. Using this method, we recover Lüst's general two-fluid model, extended MHD, Hall MHD, and electron MHD from a unified framework. The variational formulation allows us to use Noether's theorem to derive conserved quantities for each symmetry of the action.

13 pages

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Cited by in corpus (30)

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• Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
• Variational approach to low-frequency kinetic-MHD in the current coupling scheme
• A General Metriplectic Framework with Application to Dissipative Extended Magnetohydrodynamics
• Neutral Vlasov kinetic theory of magnetized plasmas
• Variational formulation of relaxed and multi-region relaxed magnetohydrodynamics
• Inertial magnetohydrodynamics
• Action Principles for Relativistic Extended Magnetohydrodynamics: A Unified Theory of Magnetofluid Models
• Magnetohydrodynamic motion of a two-fluid plasma
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• Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability -- Examples with Translation Symmetry
• Multi-region relaxed magnetohydrodynamics with flow
• Translationally symmetric extended MHD via Hamiltonian reduction: Energy-Casimir equilibria
• Energy-Casimir, dynamically accessible, and Lagrangian stability of extended magnetohydrodynamic equilibria
• Differential-geometrical approach to the dynamics of dissipationless incompressible Hall magnetohydrodynamics I: Lagrangian mechanics on semidirect product of two volume preserving diffeomorphisms and conservation laws
• A Maximum Entropy Principle for inferring the Distribution of 3D Plasmoids
• Helicity-based, particle-relabeling operator and normal mode expansion of the dissipationless incompressible Hall magnetohydrodynamics
• Multi-region relaxed Hall magnetohydrodynamics with flow
• Chirality, extended MHD statistics and solar wind turbulence
• A class of three-dimensional gyroviscous magnetohydrodynamic models
• Hall MHD waves: A fundamental departure from their MHD counterparts
• Hamiltonian formulation of X-point collapse in an extended magnetohydrodynamics framework
• Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities
• Symmetries of a reduced fluid-gyrokinetic system
• Yet Another Modification of Relativistic Magnetohydrodynamic Waves: Electron Thermal Inertia
• Incompressible Extended Magnetohydrodynamics Waves: Implications of Electron Inertia