The influence of a non-uniform electrical field, perpendicular magnetic on drift instability was studied by Sanuki et al.1,2 They have shown, that the drift instability is stabilized at a rather large gradient of an electrical field. This result was received by means of the analysis of an integral wave equation, which describes the plasma oscillations with Gaussian profile of density and linear profile of an electrical field at arbitrary Larmour radius of charged particles.

We describe the drift oscillation by the differential wave equation. This equation can be used at any profiles of plasma density and electrical field, if Larmour radius of the charged particles is rather small. In case of linear profile of an electrical field, our results confirm those received in 1,2. We have also shown, that the drift instability is transformed to Kelvin-Helmholtz instability in case of an electrical field profile with an inflexion point (smooth step profile).