Hamiltonian fluid reduction of the 1.5D Vlasov-Maxwell equations

TL;DR

This paper derives reduced Hamiltonian fluid models from the 1.5D Vlasov-Maxwell equations, capturing key kinetic features like the Weibel instability through a Hamiltonian framework.

Contribution

It introduces a Hamiltonian reduction method for the 1.5D Vlasov-Maxwell system, including Casimir invariants and stability analysis.

Findings

Reproduction of the Weibel instability in the linearized model

Derivation of reduced Poisson brackets and Casimir invariants

Validation of the fluid model capturing essential kinetic physics

Abstract

We consider the Vlasov-Maxwell equations with one spatial direction and two momenta, one in the longitudinal direction and one in the transverse direction. By solving the Jacobi identity, we derive reduced Hamiltonian fluid models for the density, the fluid momenta and the second order moments, related to the pressure tensor. We also provide the Casimir invariants of the reduced Poisson bracket. We show that the linearization of the equations of motion around homogeneous equilibria reproduces some essential feature of the kinetic model, the Weibel instability.