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.