Hamiltonian structure of the guiding center plasma model

Abstract

The guiding center plasma model (also known as kinetic MHD) is a rigorous sub-cyclotron-frequency closure of the Vlasov-Maxwell system. While the model has been known for decades, and it plays a fundamental role in describing the physics of strongly-magnetized collisionless plasmas, its Hamiltonian structure has never been found. We provide explicit expressions for the model's Poisson bracket and Hamiltonian, and thereby prove that the model is an infinite-dimensional Hamiltonian system. The bracket is derived in a manner that ensures it satisfies the Jacobi identity. We also report on several previously-unknown circulation theorems satisfied by the guiding center plasma model. Without knowledge of the Hamiltonian structure, these circulation theorems would be difficult to guess.

5 pages with references, v. 2.0

References in corpus (7)

• GEMPIC: Geometric ElectroMagnetic Particle-In-Cell Methods
• Variational integration for ideal magnetohydrodynamics with built-in advection equations
• Hamiltonian particle-in-cell methods for Vlasov-Maxwell equations
• Finite-dimensional collisionless kinetic theory
• Variational principles for the guiding-center Vlasov-Maxwell equations
• Magnetohydrodynamic motion of a two-fluid plasma
• Application of the phase space action principle to finite-size particle plasma simulations in the drift-kinetic approximation

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• A low-frequency variational model for energetic particle effects in the pressure-coupling scheme
• Variational mean-fluctuation splitting and drift-fluid models