Av. Phelps et al., OSCILLATIONS OF LOW-CURRENT ELECTRICAL DISCHARGES BETWEEN PARALLEL-PLANE ELECTRODES .3. MODELS, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 47(4), 1993, pp. 2825-2838
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.