Vlasov multi-dimensional model dispersion relation

Abstract

A hybrid model of the Vlasov equation in multiple spatial dimension $D>1$ [H. A. Rose and W. Daughton, Physics of Plasmas v. 18, 122109 (2011)], the Vlasov multi dimensional model (VMD), consists of standard Vlasov dynamics along a preferred direction, the $z$ direction, and $N$ flows. At each $z$ these flows are in the plane perpendicular to the $z$ axis. They satisfy Eulerian-type hydrodynamics with coupling by self-consistent electric and magnetic fields. Every solution of the VMD is an exact solution of the original Vlasov equation. We show convergence of the VMD Langmuir wave dispersion relation in thermal plasma to that of Vlasov-Landau as $N$ increases. Rotational symmetry about the $z$ axis in $3D$ of small perpendicular wavenumber Langmuir fluctuations is demonstrated for $N\ge 6$, with flows arranged uniformly over the azimuthal angle.

6 pages, 9 figures

References in corpus (3)

• Langmuir wave self-focusing versus decay instability
• Langmuir wave filamentation instability
• Vlasov simulation in multiple spatial dimensions

Cited by in corpus (2)

• Langmuir wave filamentation in the kinetic regime. I. Filamentation instability of Bernstein-Greene-Kruskal modes in multidimensional Vlasov simulations
• Langmuir wave filamentation in the kinetic regime. II. Weak and Strong Pumping of Nonlinear Electron Plasma Waves as the Route to Filamentation