A compressible Hamiltonian electromagnetic gyrofluid model

A Lie–Poisson bracket is presented for a four-field gyrofluid model with magnetic field curvature and compressible ions, thereby showing the model to be Hamiltonian. The corresponding Casimir invariants are presented, and shown to be associated to four Lagrangian invariants advected by distinct velocity fields. This differs from a cold ion limit, in which the Lie–Poisson bracket transforms into the sum of direct and semidirect products, leading to only three Lagrangian invariants.

► We present a Lie–Poisson bracket for a gyrofluid model.
► Our model includes magnetic field curvature and compressible ions.
► We present the four Casimir invariants.
► We show that all four Casimir invariants are Lagrangian in nature.