Hamiltonian closures for fluid models with four moments by dimensional analysis

TL;DR

This paper develops Hamiltonian fluid models with four moments derived from the Vlasov-Ampère equations, ensuring the preservation of the Hamiltonian structure through dimensional analysis and explicit closure relations.

Contribution

It introduces all Hamiltonian closures for four moments obtained via dimensional analysis, providing explicit models, Poisson brackets, and Casimir invariants.

Findings

Two explicit Hamiltonian models with closures are derived.

All closures satisfying the Jacobi identity are identified.

The models preserve the Hamiltonian structure of the kinetic equations.

Abstract

Fluid reductions of the Vlasov-Amp{\`e}re equations that preserve the Hamiltonian structure of the parent kinetic model are investigated. Hamiltonian closures using the first four moments of the Vlasov distribution are obtained, and all closures provided by a dimensional analysis procedure for satisfying the Jacobi identity are identified. Two Hamiltonian models emerge, for which the explicit closures are given, along with their Poisson brackets and Casimir invariants.