Gyrokinetic theory of slab universal modes and the non-existence of the Gradient Drift Coupling (GDC) instability

Abstract

A gyrokinetic linear stability analysis of a collisionless slab geometry in the local approximation is presented. We focus on $k_{\parallel }=0$ universal (or entropy) modes driven by plasma gradients at small and large plasma $\beta$. These are small scale non-MHD instabilities with growth rates that typically peak near $k_{\perp }{\rho }_i\sim 1$ and vanish in the long wavelength $k_{\perp }\to 0$ 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 $\gamma =\sqrt{\beta /[2(1+\beta )]}{C}_s/|L_p|$ with $C_s^2=p_0/{\rho }_0$ for $k_{\perp }\to 0$ and is universally unstable for $1/L_p\ne 0$. We show the GDC instability is a spurious, unphysical artifact that erroneously arises due to the failure to respect the total equilibrium pressure balance $p_0+B_0^2/(8\pi )=\text{constant}$, which renders the assumption $B_0^{\prime }=0$ inconsistent if $p_0^{\prime }\ne 0$.