Electron oscillations of a collisionless plasma in a static electric field

The influence of a static electric field on electron oscillations of (i) a cold beam of electrons and (ii) a hot non-drifting plasma is investigated. The importance of the relative strength of the field is emphasized. In the weak field limit the oscillations are adiabatic, manifested by the existence of adiabatic invariants, preservation of eigenmodes and absence of reflexion. If the field is strong, however, interesting new features, such as mutual coupling of eigenmodes and wave reflexion, appear. Possible stability properties of a monotonic electrostatic transition (shock, double layer) are also discussed. (author)