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

References in corpus (4)

• Hamiltonian formulation and analysis of a collisionless fluid reconnection model
• On energy conservation in extended magnetohydrodynamics
• The Hamiltonian structure and Euler-Poincaré formulation of the Vlasov-Maxwell and gyrokinetic systems
• Hamiltonian and action formalisms for two-dimensional gyroviscous MHD

Cited by in corpus (13)

• Hamiltonian Formalism of Extended Magnetohydrodynamics
• Explicit high-order noncanonical symplectic algorithms for ideal two-fluid systems
• Extended MHD turbulence and its applications to the solar wind
• Variational approach to low-frequency kinetic-MHD in the current coupling scheme
• Neutral Vlasov kinetic theory of magnetized plasmas
• Inertial magnetohydrodynamics
• Action Principles for Relativistic Extended Magnetohydrodynamics: A Unified Theory of Magnetofluid Models
• On the structure and statistical theory of turbulence of extended magnetohydrodynamics
• Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability -- Examples with Translation Symmetry
• Multi-region relaxed magnetohydrodynamics with flow
• 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
• Multi-region relaxed Hall magnetohydrodynamics with flow
• Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities