Theoretical Model of a Lanthanum Hexaboride Hollow Cathode

Abstract

A model to predict the plasma properties inside a thermionic hollow cathode as a function of operational conditions and geometry is presented. The hollow cathode features a lanthanum hexaboride (LaB6) insert, which is capable of emitting current densities as high as 10(5) Am-2 at temperatures of similar to 1900 K, along with a tantalum orifice plate located at the downstream end of the cathode tube. The model self-consistently computes the plasma parameters in both the emitter and orifice regions. A simple semiempirical relation is suggested to evaluate the plasma penetration depth in the cathode interior, which is of primary importance to establish the plasma conditions. The heat transfer mechanisms and the related temperature gradients along the cathode are evaluated with the aid of a dedicated thermal model, which is coupled to the plasma model and accounts for temperature-dependent material properties. A parametric study of the cathode performance was conducted to assess the dependence of the power consumption and operational lifetime on discharge current and mass flow rate, as well as on the geometry. The results are in good agreement with both theoretical and experimental trends found in the literature as well as with experimental data collected by Alta. Further developments will include a deeper investigation into the cathode erosion phenomena, along with a broader comparison with empirical data

Development of Hollow Cathodes for Space Electric Propulsion at Sitael

“…The cathode geometry was selected on the basis of a theoretical model previously developed at Sitael, which describes the operation of a hollow cathode [7]. A global (volume-averaged) model Concerning the emitter material, LaB 6 has been selected for the high robustness in handling and processing, capability to deliver high current densities in the order of 10 5 A/m 2 [4], and long life, with respect to the traditional dispenser cathodes.…”

“…The cathode geometry was selected on the basis of a theoretical model previously developed at Sitael, which describes the operation of a hollow cathode [7]. A global (volume-averaged) model appeared to be the most practical compromise between including details and keeping the model flexible and time-saving.…”

“…A global (volume-averaged) model appeared to be the most practical compromise between including details and keeping the model flexible and time-saving. The model is self-consistent: once defined the cathode geometry and the operating conditions in terms of discharge current and mass flow rate, the plasma parameters, surface temperatures, and total discharge power are estimated by solving a system of particle and energy balance equations [7]. The dependence of the results on the geometry can thus be assessed to target the definition of the main dimensions of the cathode, i.e., emitter inner and outer diameters, emitter length, orifice diameter, and orifice length.…”

“…However, in these models, experimental data are used as input or assumptions are made to set the plasma density, the electron temperature, or the coupling voltage to the keeper [5]. A reduced-order model was thus proposed to overcome these limitations through the development of a self-consistent code, encompassing all the relevant components of an orificed hollow-cathode assembly [7]. The theoretical study paved the way to the development of several hollow cathodes, for Hall effect thrusters belonging to different power classes [8].…”

2-D Modeling of Orificed Hollow Cathodes of Stationary Plasma Thrusters SPT-100

“…It is noteworthy that pressure inside the tube increases proportionally with anode current. This is due to gas temperature growth and addition of volume source (13), which prevents xenon from passing through the small orifice.…”