Four-field Hamiltonian fluid closures of the one-dimensional Vlasov-Poisson equation

TL;DR

This paper derives a Hamiltonian closure for a four-moment fluid model of the 1D Vlasov-Poisson system, ensuring stability of equilibria and providing a consistent reduced dynamics framework.

Contribution

It introduces a novel Hamiltonian closure for the four-field fluid moments of the Vlasov-Poisson equation, derived via Jacobi identity solutions.

Findings

The closure ensures Hamiltonian structure of the reduced model.

Symmetric homogeneous equilibria are shown to be stable.

The model links higher-order moments to the first four through a specific equation of state.

Abstract

We consider a reduced dynamics for the first four fluid moments of the onedimensional Vlasov-Poisson equation, namely, the fluid density, fluid velocity, pressure and heat flux. This dynamics depends on an equation of state to close the system. This equation of state (closure) connects the fifth order moment-related to the kurtosis in velocity of the Vlasov distribution-with the first four moments. By solving the Jacobi identity, we derive an equation of state which ensures that the resulting reduced fluid model is Hamiltonian. We show that this Hamiltonian closure allows symmetric homogeneous equilibria of the reduced fluid model to be stable.