A Hamiltonian Five-Field Gyrofluid Model

Abstract

A Lie-Poisson bracket is presented for a five-field gyrofluid model, thereby showing the model to be Hamiltonian. The model includes the effects of magnetic field curvature and describes the evolution of the electron and ion gyro-center densities, the parallel component of the ion and electron velocities, and the ion temperature. The quasineutrality property and Ampere's law determine respectively the electrostatic potential and magnetic flux. The Casimir invariants are presented, and shown to be associated to five Lagrangian invariants advected by distinct velocity fields. A linear, local study of the model is conducted both with and without Landau and diamagnetic resonant damping terms. Stability criteria and dispersion relations for the electrostatic and the electromagnetic cases are derived and compared with their analogs for fluid and kinetic models.

arXiv comment11 pages, 9 figures

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• Structure and computation of two-dimensional incompressible extended MHD
• Weakly nonlinear dynamics in noncanonical Hamiltonian systems with applications to fluids and plasmas
• A Hamiltonian gyrofluid model based on a quasi-static closure
• A class of three-dimensional gyroviscous magnetohydrodynamic models