Nonlinear gyroviscous force in a collisionless plasma

Nonlinear gyroviscous forces in a collisionless plasma with temperature variations are calculated from the gyrofluid moments of the gyrokinetic Vlasov equation. The low-frequency gyrokinetic ordering and electrostatic perturbations are assumed, and an additional finite Larmor radius (FLR) expansion in a parameter ε⊥≡(k⊥ρ)2<1 is performed. This approach leads naturally to an expression for the gyroviscous force, (∇⋅πg), in terms of the gyrocenter distribution function, thus including all resonant effects, and represents a systematic FLR expansion in a general form (no assumption of any closure is made). The expression of (∇⋅πg) is also calculated in terms of the particle-fluid moments by making the transformation from the gyrocenter to particle coordinates. The calculated (∇⋅πg) represents a modification of the Braginskii gyroviscosity for a collisionless plasma with ∇T≠0. It is compared with previous calculations based on the traditional fluid approach. As a byproduct of the gyroviscosity calculations, we derive a set of nonlinear reduced gyrofluid (and a corresponding set of particle-fluid) moment equations with FLR corrections, which exhibit a generalized form of the “gyroviscous cancellation.”