On higher order corrections to gyrokinetic Vlasov–Poisson equations in the long wavelength limit

In this paper, a simple iterative procedure is presented for obtaining the higher order E × B and d E / d t (polarization) drifts associated with the gyrokinetic Vlasov–Poisson equations in the long wavelength limit of k ⊥ ρ i ∼ o ( ϵ ) and k ⊥ L ∼ o ( 1 ) , where ρ i is the ion gyroradius, L is the scale length of the background inhomogeneity, and ϵ is a smallness parameter. It can be shown that these new higher order k ⊥ ρ i terms, which are also related to the higher order perturbations of the electrostatic potential ϕ , should have negligible effects on turbulent and neoclassical transport in tokamaks regardless of the form of the background distribution and the amplitude of the perturbation. To address further the issue of a non-Maxwellian plasma, higher order finite Larmor radius terms in the gyrokinetic Poisson’s equation have been studied and shown to be unimportant as well. On the other hand, the terms of o ( k ⊥ 2 ρ i 2 ) and k ⊥ L ∼ o ( 1 ) can, indeed, have an impact on microturbulence, especially in the linear stage, such as those arising from the difference between the guiding center and the gyrocenter densities due to the presence of the background gradients. These results will be compared to a recent study questioning the validity of the commonly used gyrokinetic equations for long time simulations.