Parallel magnetic field perturbations in gyrokinetic simulations

Abstract

At low β it is common to neglect parallel magnetic field perturbations on the basis that they are of order β2. This is only true if effects of order β are canceled by a term in the ∇B drift also of order β [H. L. Berk and R. R. Dominguez, J. Plasma Phys. 18, 31 (1977)]. To our knowledge this has not been rigorously tested with modern gyrokinetic codes. In this work we use the gyrokinetic code GS2 [Kotschenreuther et al., Comput. Phys. Commun. 88, 128 (1995)] to investigate whether the compressional magnetic field perturbation B∥ is required for accurate gyrokinetic simulations at low β for microinstabilities commonly found in tokamaks. The kinetic ballooning mode (KBM) demonstrates the principle described by Berk and Dominguez strongly, as does the trapped electron mode, in a less dramatic way. The ion and electron temperature gradient (ETG) driven modes do not typically exhibit this behavior; the effects of B∥ are found to depend on the pressure gradients. The terms which are seen to cancel at long wavelength in KBM calculations can be cumulative in the ion temperature gradient case and increase with ηe. The effect of B∥ on the ETG instability is shown to depend on the normalized pressure gradient β′ at constant β.