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

Authors

C. Chandre, Aix Marseille UniversityFollow
Bradley Allan Shadwick, University of Nebraska - LincolnFollow

Date of this Version

6-14-2022

Citation

arXiv:2206.06850v1 [ nlin.CD] 14 Jun 2022

Published (2022) Physics of Plasmas, 29 (10), art. no. 102101 . DOI: 10.1063/5.0102418

Abstract

We consider a reduced dynamics for the first four fluid moments of the one-dimensional 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.