Hamiltonian derivation of the Charney-Hasegawa-Mima equation

TL;DR

This paper presents a fundamental Hamiltonian derivation of the Charney-Hasegawa-Mima equation starting from ion fluid dynamics, emphasizing its Hamiltonian structure and noncanonical Poisson bracket.

Contribution

It provides the first principle derivation of the equation from ion fluid dynamics, highlighting its Hamiltonian formulation and underlying geometric structure.

Findings

Derivation from ion fluid dynamics confirms the Hamiltonian nature.

Clarifies the role of the noncanonical Poisson bracket.

Establishes a foundational link between fluid dynamics and plasma physics.

Abstract

The Charney-Hasegawa-Mima equation is an infinite-dimensional Hamiltonian system with dynamics generated by a noncanonical Poisson bracket. Here a first principle Hamiltonian derivation of this system, beginning with the ion fluid dynamics and its known Hamiltonian form, is given.