Hamiltonian approach to hybrid plasma models

Abstract

The Hamiltonian structures of several hybrid kinetic-fluid models are identified explicitly, upon considering collisionless Vlasov dynamics for the hot particles interacting with a bulk fluid. After presenting different pressure-coupling schemes for an ordinary fluid interacting with a hot gas, the paper extends the treatment to account for a fluid plasma interacting with an energetic ion species. Both current-coupling and pressure-coupling MHD schemes are treated extensively. In particular, pressure-coupling schemes are shown to require a transport-like term in the Vlasov kinetic equation, in order for the Hamiltonian structure to be preserved. The last part of the paper is devoted to studying the more general case of an energetic ion species interacting with a neutralizing electron background (hybrid Hall-MHD). Circulation laws and Casimir functionals are presented explicitly in each case.

27 pages, no figures. To appear in J. Phys. A

References in corpus (5)

• The Navier-Stokes-alpha model of fluid turbulence
• The Maxwell-Vlasov equations in Euler-Poincare form
• The geodesic Vlasov equation and its integrable moment closures
• Geometry of Vlasov kinetic moments: a bosonic Fock space for the symmetric Schouten bracket
• Mini-Conference on Hamiltonian and Lagrangian Methods in Fluid and Plasma Physics

Cited by in corpus (20)

• Hybrid Vlasov-MHD models: Hamiltonian vs. non-Hamiltonian
• Variational approach to low-frequency kinetic-MHD in the current coupling scheme
• Derivation of the Hall and Extended Magnetohydrodynamics Brackets
• Neutral Vlasov kinetic theory of magnetized plasmas
• Stability of compressible reduced magnetohydrodynamic equilibria - analogy with magnetorotational instability
• Hamiltonian Magnetohydrodynamics: Lagrangian, Eulerian, and Dynamically Accessible Stability -- Examples with Translation Symmetry
• Multiscale Turbulence Models Based on Convected Fluid Microstructure
• Energy-Casimir stability of hybrid Vlasov-MHD models
• Stochastic Variational Formulations of Fluid Wave-Current Interaction
• A Lagrangian kinetic model for collisionless magnetic reconnection
• Hamiltonian kinetic-Hall Magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes
• Hamiltonian approach to Ehrenfest expectation values and Gaussian quantum states
• Energy stability analysis for a hybrid fluid-kinetic plasma model
• Existence of Global Weak Solutions to a Hybrid Vlasov-MHD Model for Magnetized Plasmas
• Chaotic and integrable magnetic fields in one-dimensional hybrid Vlasov-Maxwell equilibria
• A low-frequency variational model for energetic particle effects in the pressure-coupling scheme
• Variational mean-fluctuation splitting and drift-fluid models
• From liquid crystal models to the guiding-center theory of magnetized plasmas
• The initial value problem in Lagrangian drift kinetic theory
• Global well-posedness and decay rates of strong solutions to the incompressible Vlasov-MHD system