The lower-hybrid drift instability in a slab geometry

Abstract

The lower-hybrid drift instability is studied within a model problem with some of the features that characterize the anode plasma in the magnetic insulated diode experiment at the Weizmann Institute (Phys. Rev. A, in press). The spatial dependence of the amplitude of the linear electrostatic perturbations is calculated. First the equilibrium is determined by selecting distribution functions that depend on the constants of motion in a collisionless plasma and by imposing quasineutrality. In the particular equilibrium studied, the electric field, temperature, and drift velocities are uniform and the density decreases exponentially. The Vlasov–Poisson equations are then linearized assuming magnetized electrons and unmagnetized ions. The governing equation is a second-order ordinary differential equation for the perturbed electrostatic potential. A dispersion relation is derived and analytical solutions are written for the eigenfunctions. The growth rate of each mode is determined by the plasma parameters at its respective turning point. Since the only plasma parameter that is not uniform is the density, the growth rates of the different eigenmodes are similar when the roots of the local dispersion relation depend only weakly on the density. Since the distance between successive turning points is usually very small, it is concluded that for the chosen equilibrium the perturbations will grow uniformly across the plasma.