Variational approach to low-frequency kinetic-MHD in the current coupling scheme

Abstract

Hybrid kinetic-MHD models describe the interaction of an MHD bulk fluid with an ensemble of hot particles, which is described by a kinetic equation. When the Vlasov description is adopted for the energetic particles, different Vlasov-MHD models have been shown to lack an exact energy balance, which was recently recovered by the introduction of non-inertial force terms in the kinetic equation. These force terms arise from fundamental approaches based on Hamiltonian and variational methods. In this work we apply Hamilton's variational principle to formulate new current-coupling kinetic-MHD models in the low-frequency approximation (i.e. large Larmor frequency limit). More particularly, we formulate current-coupling hybrid schemes, in which energetic particle dynamics are expressed in either guiding-center or gyrocenter coordinates.

arXiv commentv3.0. 30 pages

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• Field theory and structure-preserving geometric particle-in-cell algorithm for drift wave instability and turbulence
• Local Energy Conservation Law for Spatially-Discretized Hamiltonian Vlasov-Maxwell System
• Hamiltonian kinetic-Hall Magnetohydrodynamics with fluid and kinetic ions in the current and pressure coupling schemes
• Energetic-particle-modified global Alfvén eigenmodes
• Existence of Global Weak Solutions to a Hybrid Vlasov-MHD Model for Magnetized Plasmas
• Testing the conservative character of particle simulations: II. Spurious heating of guiding centers and full orbits subject to fluctuations expressed in terms of $\mathbf{E}$ and $\mathbf{B}$
• A class of three-dimensional gyroviscous magnetohydrodynamic models
• A fluid-kinetic framework for self-consistent runaway-electron simulations
• Hamiltonian structure of the gauge-free gyrokinetic Vlasov-Maxwell equations
• A low-frequency variational model for energetic particle effects in the pressure-coupling scheme
• Variational mean-fluctuation splitting and drift-fluid models
• Variational Integration for Ideal Magnetohydrodynamics and Formation of Current Singularities
• Entropy functionals and equilibrium states in mixed quantum-classical dynamics
• Hamiltonian structure of the guiding-center Vlasov-Maxwell equations