Unified fluid/kinetic description of plasma microinstabilities. Part I: Basic equations in a sheared slab geometry

Abstract

Unified fluid/kinetic equations for the plasma perturbed density (ñ), parallel flow velocity (ũ∥) and temperature (T̃) are developed in a sheared slab geometry by calculating the fluid moment closure relations kinetically. At first, a set of (unclosed) nonlinear perturbed fluid equations for ñ, ũ∥ and T̃ is developed using a drift ordering analysis and a new gyroviscous force (△⋅Πg). Thereafter, to develop linear closure relations for b⋅∇⋅Π̃∥ and q̃∥, a drift-kinetic version of a new Chapman–Enskog-like (CEL) equation is developed and solved by using a moment approach and a physically realistic collision operator (Lorentz scattering operator plus the momentum restoring terms). The resultant closure relations for b⋅△⋅Π̃∥ and q̃∥ unify the fluid and kinetic approaches. In the collisional fluid limit the equations reduce to the well-known Braginskii equations. In the adiabatic limit they reproduce the usual kinetic results, including Landau damping. It is shown that this new CEL approach is more compatible with a fluidlike description of plasmas than the usual drift/gyrokinetic approach. Remarkably simplified forms of the closure relations are presented. The results are compared with other Landau damping models and shown to be more accurate, complete, and physically realistic. Applications of this set of equations to various microinstabilities in tokamak plasmas are presented in a separate paper (Part II) [Phys. Fluids B 4, 1182 (1992)].