Euler-Poincar\'e formulation of hybrid plasma models

TL;DR

This paper derives and compares three hybrid plasma models using Euler-Poincaré and Hamiltonian reduction, highlighting their invariants, symmetries, and extensions of classical fluid relations.

Contribution

It provides a unified Euler-Poincaré framework for three major hybrid MHD models, including new invariants and extensions of classical relations.

Findings

Explicit Kelvin-Noether theorems for each scheme

New expressions for cross helicity invariants

Extensions of Ertel's potential vorticity relation

Abstract

Three different hybrid Vlasov-fluid systems are derived by applying reduction by symmetry to Hamilton's variational principle. In particular, the discussion focuses on the Euler-Poincar\'e formulation of three major hybrid MHD models, which are compared in the same framework. These are the current-coupling scheme and two different variants of the pressure-coupling scheme. The Kelvin-Noether theorem is presented explicitly for each scheme, together with the Poincar\'e invariants for its hot particle trajectories. Extensions of Ertel's relation for the potential vorticity and for its gradient are also found in each case, as well as new expressions of cross helicity invariants.