Comparison of Kinetic and Extended MHD 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 MHD models, in the regime k‖/k⊥ << 1. The ITG is a parallel (to B) sound wave that may be destabilized by 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 LT i0, instability requires that either k⊥ρi or ρi/LT i0 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 complex eigenvalue ω = ωr + iγ. An explicit solution is derived for the growth rate and real frequency in this regime. These are found to depend on a single non-dimensional parameter. We also compute the eigenvalues and the eigenfunctions with the extended MHD code NIMROD, and a hybrid Department of Physics, University of Wisconsin, Madison Department of Physics, University of Colorado, Boulder TriAlpha Energy, Inc. Department of Physics, University of Colorado, Boulder