Dynamics of a hollow cathode discharge in the frequency range of 1–500 kHz

Abstract

We present results from 2D axisymmetric fluid simulations of the partially-ionized Xe gas in a 25-A cathode discharge, for a range of flow rates (5–20 sccm) in which transition between the so-called spot and plume modes has been observed in laboratory experiments. The simulations for the first time capture very well the characteristic rise of the peak-to-peak amplitude in the keeper voltage oscillations with decreasing flow rate—the so-called ‘plume margin’—thereby allowing for a closer interrogation of the processes that drive them. The oscillations are found to be due to plasma dynamics in the near-plume region that increase in amplitude as the flow rate is reduced. The cathode interior remains largely quiescent and changes in the emitter peak temperature do not exceed 2% across the entire range of flow rates examined. Along the cathode centerline the amplitude of the electron density oscillations peak at a location where the number density of the Xe atoms has diminished to its minimum value and the degree of ionization is close to one. The computed spectra reveal that most of the oscillation power resides in the frequency range of 100–300 kHz. These frequencies are much greater than the local ionization collision frequency ( < 10 kHz), and are associated with wavelengths of several centimeters. Such wavelengths are many orders of magnitude greater than λD. The waves are largely longitudinal with wave vector in the axial direction, and phase velocity ω/k > 10 km s−1, which is more than 6× greater than the ion acoustic speed. Though the computed and measured plume margins are in good agreement the measured spectra show that most of the power resides between ∼60 and 90 kHz, lower than the computed range (100–300 kHz), and exhibits a sharper distribution. It is argued this is due to the presence of a rotational mode in the experiment that is coupled with the longitudinal mode, yielding a complex 3D plasma motion that cannot be captured by the simulations due to the assumption of azimuthal axisymmetry, but that it is indeed the longitudinal plasma motion that drives the transition from spot to plume modes. An anomalous resistivity has been invoked in the simulations that is based on the formulations of Sagdeev and Galeev for the saturation of IAT which is long known to exist in these discharges. Though the simulations do not account for possible anomalous heating of the ions, the idealized model for the electrons is found to be sufficient in capturing the abovementioned dynamics, yielding a multiplication coefficient α of the anomalous collision frequency να = αωpe(Te/Ti)(ue/uTe) that is within a factor of two of the estimated theoretical value.