Beltrami States for Plasma Dynamics Models

TL;DR

This paper explores the Beltrami states across various plasma physics models, revealing common features and deriving these states through energy minimization and Hamiltonian methods.

Contribution

It introduces a unified approach to derive Beltrami states for multiple plasma models using variational principles within a Hamiltonian framework.

Findings

Beltrami states exhibit robustness against plasma compressibility effects.

Beltrami states are derived by energy minimization with helicity constraints.

Common features are identified across diverse plasma models.

Abstract

The various plasma models - incompressible magnetohydrodynamic (MHD) model, compressible MHD model, incompressible Hall MHD model, compressible Hall MHD model, electron MHD model, compressible Hall MHD with electron inertia model - notwithstanding the diversity of the underlying physics, are shown to exhibit some common features in the Beltrami states like certain robustness with respect to the plasma compressibility effects (albeit in the barotropy assumption) and the {\it Bernoulli} condition. The Beltrami states for these models are deduced by minimizing the appropriate total energy while keeping the appropriate total helicity constant. A Hamiltonian formulation framework is used to carry out these variational problems.