Collisionless fluid equations: Lagrangian, Eulerian, and local forms

Abstract

A recent paper [N. Mattor, Phys. Plasmas 5, 1822 (1998)] derived closed fluid moment equations from a collisionless kinetic equation. These fluid equations retain the effects of linear and nonlinear wave-particle resonances, traditionally thought to require kinetic equations. This paper gives three methods to calculate this term. In the Lagrangian form, the components making up the closure term are constant along phase rays, and so can be traced from the initial time. The Eulerian form evolves the components on a constant spatial grid and so does not require explicit calculation of phase rays. The local approximation is a heuristic method of approximating global integrals based on local gradients, and offers significant simplification over the other two methods.