Derivation of reduced two-dimensional fluid models via Dirac's theory of constrained Hamiltonian systems

TL;DR

This paper derives reduced two-dimensional plasma fluid models, including the Charney-Hasegawa-Mima equation, from a parent Hamiltonian system using Dirac's theory of constrained Hamiltonian systems, highlighting their underlying Hamiltonian structure.

Contribution

It introduces a Hamiltonian derivation method for reduced plasma fluid models using Dirac brackets, unifying their structure from a common parent model.

Findings

Reduced models retain Hamiltonian structure via Dirac brackets

Derivation applies to models like Charney-Hasegawa-Mima

Unified framework for plasma fluid model reduction

Abstract

We present a Hamiltonian derivation of a class of reduced plasma two-dimensional fluid models, an example being the Charney-Hasegawa-Mima equation. These models are obtained from the same parent Hamiltonian model, which consists of the ion momentum equation coupled to the continuity equation, by imposing dynamical constraints. It is shown that the Poisson bracket associated with these reduced models is the Dirac bracket obtained from the Poisson bracket of the parent model.