OSCILLATIONS OF LOW-CURRENT ELECTRICAL DISCHARGES BETWEEN PARALLEL-PLANE ELECTRODES .3. MODELS

Simple models are developed to describe the results of measurements of the oscillatory and negative differential resistance properties of lo w- to moderate-current discharges in parallel-plane geometry. The time -dependent model assumes that the ion transit time is fixed and is sho rt compared to the times of interest, that electrons are produced at t he cathode only by ions, and that space-charge distortion of the elect ric field is small but not negligible. Illustrative numerical solution s are given for large voltage and current changes and analytic solutio ns for the time dependence of current and voltage are obtained in the small-signal limit. The small-signal results include the frequency and damping constants for decaying oscillations following a voltage chang e or following the injection of photoelectrons. The conditions for und erdamped, overdamped, and self-sustained or growing oscillations are o btained. A previously developed steady-state, nonequilibrium model for low-pressure hydrogen discharges that includes the effects of space-c harge distortion of the electric field on the yield of electrons at th e cathode is used to obtain the negative differential resistance. Anal ytic expressions for the differential resistance and capacitance are d eveloped using the steady-state, local-equilibrium model for electron and ion motion and a first-order perturbation treatment of space-charg e electric fields. These models generally show good agreement with dat a from dc and pulsed discharge experiments presented in the accompanyi ng papers.