Gyrokinetic theory of slab universal modes and the non-existence of the gradient drift coupling (GDC) instability

A gyrokinetic linear stability analysis of a collisionless slab geometry in the local approximation is presented. We focus on k∥=0 universal (or entropy) modes driven by plasma gradients at small and large plasma β. These are small scale non-MHD instabilities with growth rates that typically peak near k⊥ρi∼1 and vanish in the long wavelength k⊥→0 limit. This work also discusses a mode known as the Gradient Drift Coupling (GDC) instability previously reported in the gyrokinetic literature, which has a finite growth rate γ=β/[2(1+β)]Cs/|Lp| with Cs2=p0/ρ0 for k⊥→0 and is universally unstable for 1/Lp≠0. We show that the GDC instability is a spurious, unphysical artifact that erroneously arises due to the failure to respect the total equilibrium pressure balance p0+B02/(8π)=constant, which renders the assumption B0′=0 inconsistent if p0′≠0.