Hamiltonian structure of reduced fluid models for plasmas obtained from a kinetic description

TL;DR

This paper explores the Hamiltonian structure of reduced fluid plasma models derived from kinetic Vlasov-Maxwell equations, identifying the limitations of existing Poisson brackets and emphasizing the fundamental role of density and velocity moments.

Contribution

It demonstrates that only the zeroth and first moments form a valid Poisson subalgebra, clarifying the Hamiltonian structure of fluid models from kinetic plasma descriptions.

Findings

Only density and velocity moments form a Poisson subalgebra.

The bracket involving second moments does not satisfy Jacobi identity.

Clarifies the Hamiltonian structure of reduced plasma fluid models.

Abstract

We consider the Hamiltonian structure of reduced fluid models obtained from a kinetic description of collisionless plasmas by Vlasov-Maxwell equations. We investigate the possibility of finding Poisson subalgebras associated with fluid models starting from the Vlasov-Maxwell Poisson algebra. In this way, we show that the only possible Poisson subalgebra involves the moments of zeroth and first order of the Vlasov distribution, meaning the fluid density and the fluid velocity. We find that the bracket derived in [Phys. Rev. Lett. 93, 175002 (2004)] which involves moments of order 2 is not a Poisson bracket since it does not satisfy the Jacobi identity.