Thermal Model of the Hollow Cathode Using Numerically Simulated Plasma Fluxes

Abstract

The first results from a hollow cathode thermal model are presented. The thermal model uses the spatially distributed plasma fluxes, calculated by a two-dimensional axisymmetric model of the plasma inside the emitter region, as the heat source to predict the hollow cathode and insert temperatures. The computed insert temperature profiles are compared with measured values for a cathode similar to the 0.635-cm diameter discharge cathode used in the NASA solar electric propulsion technology applications readiness ion engine. The insert temperatures can be used to predict cathode life from barium depletion. The present results and related experimental studies yield three important conclusions. First, the emitter in the NASA solar electric propulsion technology applications readiness hollow cathode does not operate in the emission-limited regime. The thermionic electron current is about 20 A higher than the discharge current and requires significant reverse electron flux from the plasma to satisfy current continuity. Second, the high-plasma density near the centerline of the cathode results in power deposition on the orifice plate that is more than twice the emitter power deposition. Third, despite a higher heat load to the orifice plate, the operating temperature where it would be measured by a thermocouple is approximately 100 C lower than the emitter. The lower orifice plate temperature is due to poor thermal contact between the emitter and the cathode tube and higher than anticipated radiative losses from the external surface of the heater. Nomenclature F = geometrical configuration factor IP = ionization potential, V j emission = emission current density, A=m 2 j the e = plasma thermal current density, A=m 2 j i = plasma ion current density, A=m 2 _ q rad = heat loss by radiation, W=m 2 _ q emission = heat loss by electron emission, W=m 2 _ q e = heating by plasma electrons, W=m 2 _ q i = heating by plasma ion flux, W=m 2 T = material temperature, K T e = plasma electron temperature, eV WF = emitter work function, eV ij = Kronecker delta " = material emissivity = material thermal conductivity, W=m K = Stephan-Boltzman constant, W=m 2 K 4 sheath = sheath potential, V Introduction H IGH-POWER, long-life electric thrusters were considered necessary as NASA planned many of the challenging missions under the Prometheus program. These missions might have required an increase in both life and emission current compared with hollow cathodes used on NASA's Deep Space 1 spacecraft. Although both the discharge and neutralizer hollow cathodes were operating at the end of the NASA solar electric propulsion technology applications readiness (NSTAR) thruster 30,000-h extended life test [1], the future missions may be even more challenging. A previous life test of the International Space Station plasma contactor hollow cathode [2] ended after 28,000 h, when the cathode would no longer ignite. One scenario for end of life is when the insert can no longer provide free barium to lower the work function and the remaining barium in th...

Hollow cathode modeling: I. A coupled plasma thermal two-dimensional model

“…We found that this value provides the best agreement between the simulated emitter temperature profile and measurements. Assuming that the heat transfer between these two surfaces is purely radiative and that the radiative flux is close to that of a black body at 1400 (a rough estimation of the emitter temperature [2]), we obtain that should be on the order of 600 . .…”

“…All information given here about the thermal design of the cathode have been either obtained from the literature on general hollow cathode design [29] or from articles which did specifically focus on the NASA NSTAR cathode [2]. Missing dimensions and parameters were deduced through fitting of numerical simulation results to experimental data obtained for the same NASA NSTAR cathode.…”

“…3). We also account for an imperfect thermal contact between the insert and the cathode tube through an interfacial surface conductivity [2], which we set to = 800 . .…”

“…Plasma sheath and most importantly emissive sheaths are accounted for through a new first principles based emissive sheath model which is valid in Page 4 of 48 AUTHOR SUBMITTED MANUSCRIPT -PSST-101445.R2 both space charge limited and thermionic emission limited regimes. Unlike most of earlier models published in the literature (with one noteworthy exception in [2]), we couple here the plasma model to a thermal model which allows us to compute self-consistently the emitter temperature. Therefore this model could be applied in principle to any cathode geometry or operating point without requiring any input from experimental measurements.…”

Hybrid-PIC Simulation of LaB₆ Hollow Cathode Self-Heating Characteristics

“…[7][8][9][10][11][12] This can estimate energy fluxes on the walls, and then those are utilized as boundary conditions for thermal analysis. 13) Another fluid simulation code has also been developed at University of Toulouse, where a thermal model is self-consistently coupled with plasma simulation. 14) In this study, the hollow cathode plasma was simulated by using a hybrid particle-in-cell (PIC) model that treats the heavy species (neutrals and ions) and electrons as particles and fluid, respectively.…”