Oscillations and instabilities in E\!\!B plasma discharges play a major role in driving turbulence and anomalous transport. The presence of gradients and applied fields that result in a relative drift between the charged species causes the onset of drift-gradient instabilities. This work puts forward a kinetic approach to the low-frequency stability of E\!\!B, two-species, partially magnetised plasmas. It presents a local linear analysis of electrostatic modes in the long-wavelength limit, assuming wave propagation perpendicular to the magnetic field. Magnetised electrons are described by a drift-kinetic equation, while unmagnetised ions are described as a cold fluid. This allows for a consistent treatment of electron temperature perturbations in an inhomogeneous plasma that takes into account kinetic resonance effects, changing the threshold conditions for drift instabilities previously found in fluid descriptions. The well-known fluid dispersion relation for the collisionless Simon–Hoh instability is recovered by considering the weak magnetic inhomogeneity limit of our kinetic model and, in addition, a perturbative extension of the instability criterion that includes the gradients of the magnetic field and the electron temperature is obtained.
Ramos et al. (Sun,) studied this question.