Finite amplitude E × B oscillations in bounded plasmas

A semi-infinite plasma slab with a density gradient and an externally applied electric field normal to an applied magnetic field is considered. Stable finite amplitude density and potential oscillations are investigated for parameters favourable for the E × B instability. Explicit expressions for the oscillation amplitudes, frequency, and wavelength are derived in the limit of a weak density gradient. The calculations are performed with a closed set of zero and first harmonic equations. It is shown that second harmonic contributions are small in the case considered.