Magnetohydrodynamic motion of a two-fluid plasma

Abstract

The two-fluid Maxwell system couples frictionless electron and ion fluids via Maxwell's equations. When the frequencies of light waves, Langmuir waves, and single-particle cyclotron motion are scaled to be asymptotically large, the two-fluid Maxwell system becomes a fast-slow dynamical system. This fast-slow system admits a formally-exact single-fluid closure that may be computed systematically with any desired order of accuracy through the use of a functional partial differential equation. In the leading order approximation, the closure reproduces magnetohydrodynamics (MHD). Higher order truncations of the closure give an infinite hierarchy of extended MHD models that allow for arbitrary mass ratio, as well as perturbative deviations from charge neutrality. The closure is interpreted geometrically as an invariant slow manifold in the infinite-dimensional two-fluid phase space, on which two-fluid motions are free of high-frequency oscillations. This perspective shows that the full closure inherits a Hamiltonian structure from two-fluid theory. By employing infinite-dimensional Lie transforms, the Poisson bracket for the all-orders closure may be obtained in closed form. Thus, conservative truncations of the single-fluid closure may be obtained by simply truncating the single-fluid Hamiltonian. Moreover, the closed-form expression for the all-orders bracket gives explicit expressions for a number of the full closure's conservation laws. Notably, the full closure, as well as any of its Hamiltonian truncations, admits a pair of independent circulation invariants.

arXiv comment29 pages

References in corpus (4)

• Hamiltonian Formalism of Extended Magnetohydrodynamics
• Action Principles for Extended MHD Models
• Action Principles for Relativistic Extended Magnetohydrodynamics: A Unified Theory of Magnetofluid Models
• Chasing Hamiltonian structure in gyrokinetic theory

Cited by in corpus (13)

• Exact and Locally Implicit Source Term Solvers for Multifluid-Maxwell Systems
• Slow manifold reduction for plasma science
• Normal stability of slow manifolds in nearly-periodic Hamiltonian systems
• General formulas for adiabatic invariants in nearly-periodic Hamiltonian systems
• Variational nonlinear WKB in the Eulerian frame
• Hamiltonian structure of the guiding center plasma model
• Time-dependent relaxed magnetohydrodynamics -- inclusion of cross helicity constraint using phase-space action
• Collisional Gyrokinetics Teases the Existence of Metriplectic Reduction
• A class of three-dimensional gyroviscous magnetohydrodynamic models
• Hamiltonian reduction of Vlasov-Maxwell to a dark slow manifold
• Relaxed Magnetohydrodynamics with Ideal Ohm's Law Constraint
• Hamiltonian formulation of X-point collapse in an extended magnetohydrodynamics framework
• Symmetries of a reduced fluid-gyrokinetic system