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

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 P d ≥ 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: insert diameter should be chosen such that the attachment length is similar to the insert length to minimize the emission current density.

The attachment length in orificed hollow cathodes

“…For the linear fit of ln n e with parameters β0 and β1 , we have Example of the derivation of the attachment length from an experimentally measured electron density profile. Experimental data from [9] for the NSTAR discharge cathode operating at 15 A. Reproduced with permission from [33].…”

“…Cathodes operating at lower current have undergone life tests of up to 50 kh [26]. Higher-current cathodes capable of providing up to 300 A of discharge current have been developed [28,33], with estimated lifetimes of 10 to 20 kh for those developed by Goebel and Chu [28]. Because life tests are both time-consuming and costly, there is a clear need for the development of methods that can accurately predict the operational life of hollow cathodes.…”

Physics of thermionic, orificed hollow cathodes: I. Theory and experimental validation

“…Gray areas on the model indicate the minimum and maximum values obtained for the indicated cathodes, with sheath voltage and gas temperature with values between 1-10 V and 2000-4000 K, respectively. Adapted with permission from [67] Copyright 2020, Pierre-Yves C. R. Taunay. electron fluxes is likely captured within the range of sheath potentials considered. Although the scaling is likely captured, we caution that, because of the exponential dependence of the random electron flux (i.e.…”

“…(e) PLHC. Adapted with permission from [67] Copyright 2020, Pierre-Yves C. R. Taunay. higher than the typical application range of barium-based emitters.…”

“…None of the cathodes for which lifetime testing was conducted reached end-of-life. Reproduced with permission from [67] Copyright 2020, Pierre-Yves C R Taunay. 800 A of discharge current for a typical Hall-effect thruster (assuming an efficiency of 100%, a specific impulse of 2000 s, and xenon gas).…”