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

Abstract

A model aimed at illuminating the physics of thermionic, orificed hollow cathodes is developed and validated with experimental data. The model is intended to describe the variation of total (neutrals, ions, and electrons) static pressure with controllable parameters. That pressure must be properly evaluated because it influences important plasma parameters in the cathode such as the attachment length and the electron temperature, which directly impact the lifetime of thermionic inserts. The model, which combines a zero-dimensional approach to the conservation of energy and momentum for the combined plasma-neutral fluid and a charge-exchange-limited ambipolar diffusion model, allows for the computation of all plasma quantities, including the total fluid pressure. The model depends on the operating conditions (discharge current and mass flow rate), cathode geometry, and the gas species, along with two non-controllable parameters: the neutral gas temperature and the sheath potential. Total pressure data at up to 307 A of cathode discharge current were obtained experimentally and were used, along with data from the literature, to validate the model. Good agreement is obtained for all quantities. The model is used in a companion paper to clarify the role of magnetic and gasdynamic pressure in the scaling of total pressure, to derive scaling laws applicable to thermionic, orificed hollow cathodes, and to propose novel cathode design rules.

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

“…We show in figure 1 the statistical distribution of the total pressure-diameter product for Siegfried and Wilbur's mercury and noble gas cathodes [10-13], Friedly's cathode [14], Salhi's cathode [3] operating on both argon and xenon, the T6 1 To correctly obtain the potential distribution from the plasma density in a collisional and weakly-ionized plasma the current continuity may be used [8].…”

“…[17]). However, the viscous losses in the feed system are likely small (on average 3% for the NSTAR, NEXIS, JPL 1.5 cm, PLHC, and Salhi's cathodes) [1]. The distribution is shown both as a histogram with 40 bins and as a density function obtained using the kernel density estimation (KDE) technique.…”

“…The origin of each term is shown in figure 3. For a complete and detailed explanation of each term and where the associated forces act, the reader is referred to the companion paper (section 3.2 and figure 10 in [1]). These quantities are defined as…”

“…In the preceding paper [1], we developed and evaluated a theoretical model for thermionic orificed hollow cathodes. The model is based on a 0D approach to the conservation of energy and momentum for the combined plasma-neutral fluid and on a 2D charge-exchange-limited ambipolar diffusion model.…”

“…The use of the Laplace equation to solve the potential distribution within a plasma is not justified because the assumption of quasineutrality does not imply that the charge density in Poisson's equation must vanish [7]. 1 The fact that Salhi et al obtain the correct scaling for the attachment length is likely due to the exponential nature of the potential distribution decay in the axial direction. We have found that our cathode, the experimental setup of which was presented in the previous paper, can operate above the maximum current suggested by Salhi et al, which implies that including only resistive heating and convection losses limits the domain of applicability of the relationship for the maximum discharge current that can be drawn by a cathode.…”