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

TL;DR

This paper presents a gyrokinetic linear stability analysis of slab universal modes, demonstrating that the previously reported Gradient Drift Coupling (GDC) instability is unphysical and results from inconsistent equilibrium assumptions.

Contribution

The work clarifies the nature of universal modes and debunks the GDC instability as a spurious artifact caused by neglecting pressure balance constraints.

Findings

Universal modes are small-scale, non-MHD instabilities peaking near $k_ot ho_i \,\sim\, 1$.

The GDC instability is shown to be an unphysical artifact due to inconsistent equilibrium assumptions.

The analysis emphasizes the importance of proper pressure balance in gyrokinetic stability studies.

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 $1/L_p\neq 0$. 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 $B_0'=0$ inconsistent if $p_0'\neq 0$.