Hamiltonian fluid reductions of drift-kinetic equations and the correspondence with water-bag distribution functions

TL;DR

This paper derives Hamiltonian fluid models for the first three moments of the drift-kinetic distribution, linking them to water-bag solutions and highlighting their unique Hamiltonian structure compared to Vlasov equations.

Contribution

It introduces Hamiltonian models for drift-kinetic moments and establishes their exclusive connection with water-bag closures, emphasizing their Hamiltonian properties.

Findings

Water-bag solutions are the only Hamiltonian fluid reductions for the drift-kinetic equation.

Derived models include equations of motion and Casimir invariants.

Clarified the link between water-bag closures and Hamiltonian structure.

Abstract

Hamiltonian models for the first three moments of the drift-kinetic distribution function, namely the density, the fluid velocity and the parallel pressure, are derived from the Hamiltonian structure of the drift-kinetic equations. The link with the water-bag closure is established, showing that, unlike the one-dimensional Vlasov equations, these solutions are the only Hamiltonian fluid reductions for the drift-kinetic equation. These models are discussed through their equations of motion and their Casimir invariants.