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

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.

References in corpus (5)

• Universal Probability Distribution Function for Bursty Transport in Plasma Turbulence
• Higher order Hamiltonian fluid reduction of Vlasov equation
• On the effect of intermittency of turbulence on the parabolic relation between skewness and kurtosis in magnetized plasmas
• Hamiltonian structure of reduced fluid models for plasmas obtained from a kinetic description
• Hamiltonian fluid closures of the Vlasov-Amp{è}re equations: from water-bags to N moment models