Comparison of kinetic and extended magnetohydrodynamics computational models for the linear ion temperature gradient instability in slab geometry

We perform linear stability studies of the ion temperature gradient (ITG) instability in unsheared slab geometry using kinetic and extended magnetohydrodynamics (MHD) models, in the regime k∥/k⊥≪1. The ITG is a parallel (to B) sound wave that may be destabilized by finite ion Larmor radius (FLR) effects in the presence of a gradient in the equilibrium ion temperature. The ITG is stable in both ideal and resistive MHD; for a given temperature scale length LTi0, instability requires that either k⊥ρi or ρi/LTi0 be sufficiently large. Kinetic models capture FLR effects to all orders in either parameter. In the extended MHD model, these effects are captured only to lowest order by means of the Braginskii ion gyro-viscous stress tensor and the ion diamagnetic heat flux. We present the linear electrostatic dispersion relations for the ITG for both kinetic Vlasov and extended MHD (two-fluid) models in the local approximation. In the low frequency fluid regime, these reduce to the same cubic equation for the compl...