Rarefied xenon flow in orificed hollow cathodes

Abstract

A parametric study is conducted to quantify the effect of the keeper electrode geometry on the neutral flow quantities within orificed hollow cathodes, prior to cathode ignition. The keeper impinges directly on the flow out of the cathode orifice and its geometry strongly influences the product between the pressure in the orifice-keeper region and the distance between cathode and keeper, $P_{ko}\cdot D_{ko}$, a key parameter for successful cathode ignition. A representative cathode equipped with a keeper is simulated using the Direct Simulation Monte Carlo method. The numerical model is first validated with computational results from the literature, and a parametric study is then conducted. Parameters include the cathode pressure-diameter in the range of 1-5 Torr-cm and the following geometric ratios: cathode orifice-to-cathode inner radii in the range of 0.1-0.7, keeper orifice-to-cathode orifice radii in the range of 1-5, and keeper distance-to-cathode-orifice diameter, in the range of 0.5-10. If both keeper and cathode have identical orifice radii, the flow remains subsonic in the cathode orifice-to-keeper region. In most cases, however, the flow becomes underexpanded and supersonic, and the static pressure within the cathode orifice-keeper region is, on average, 4% that of the upstream pressure value. The orifice-keeper region pressure increases with either a decrease in the keeper orifice diameter or an increase in the distance between the cathode orifice plate and the keeper plate, in agreement with literature data. Trends are explained through control-volume-based conservation laws. The ratio of ignition-to-nominal mass flow rates is found to be in the range of 9-120, with a most probable value of 40, in agreement with literature data. This suggests that heater-less cathode ignition at a minimum DC voltage may be achieved by increasing the input mass flow rate by a factor of 40.