Physics of thermionic orificed hollow cathodes: II. Scaling laws and design rules

Abstract

Abstract Scaling laws for the total pressure, electron temperature, and attachment length within orificed hollow cathodes are derived from a theoretical zero-dimensional model combined with a charge-exchange-limited ambipolar diffusion model. These quantities are critical as they control the operational life of thermionic hollow cathode inserts. The underlying models were delineated and evaluated experimentally in a companion paper (Part 1). In the present paper, scaling laws are derived from first principles for the total pressure, and from a semi-analytical approach for the electron temperature and attachment length. The total pressure is found to scale with the sum of the square of the mass flow rate multiplied by a weak function of discharge current, and with the square of the discharge current. This scaling can be physically interpreted as due to the relative importance of the Lorentz force density and the gasdynamic pressure. Both electron temperature and attachment length are found to vary inversely with the neutral gas pressure-cathode diameter product. The predicted emission length is found to be between 0.6–1.4 times the insert radius for the experimental data considered, to scale weakly with the pressure-diameter product for Pd ⩾ 2 Torr-cm, and to be nearly independent of the orifice diameter. The analysis suggests that the diffusion-dominated nature of the insert plasma can account for the scaling of the emission length. A general cathode design rule is formulated based on the results of the analysis: the insert diameter should be chosen such that the attachment length is similar to the insert length to minimize the emission current density.