Hamiltonian approach to hybrid plasma models

TL;DR

This paper explicitly identifies Hamiltonian structures in various hybrid plasma models, including fluid and kinetic interactions, and extends the framework to complex plasma systems like hybrid Hall-MHD.

Contribution

It provides a comprehensive Hamiltonian formulation for hybrid plasma models, including pressure-coupling and current-coupling schemes, with explicit structures and conservation laws.

Findings

Hamiltonian structures are explicitly identified for several hybrid plasma models.

Pressure-coupling schemes require a transport term in the Vlasov equation to preserve Hamiltonian structure.

Circulation laws and Casimir functionals are derived for hybrid Hall-MHD.

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.