Hamiltonian structure of the guiding center plasma model

TL;DR

This paper uncovers the Hamiltonian structure of the guiding center plasma model, providing explicit Poisson brackets and Hamiltonian, and revealing new circulation theorems that deepen understanding of strongly-magnetized collisionless plasmas.

Contribution

The paper explicitly derives the Hamiltonian structure of the guiding center plasma model, a fundamental step previously missing in plasma physics literature.

Findings

Derived explicit Poisson bracket satisfying Jacobi identity

Proved the model is an infinite-dimensional Hamiltonian system

Discovered new circulation theorems for 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.