Collisionless cathode sheath models to predict power distribution in 1 kW hydrazine arcjets

Abstract

This paper presents two different approaches to predict the cathode sheath potential necessary to account for the total voltage in a 1 kW hydrazine arcjet operating at 10 A. The first approach is a modification of the sheath model first developed by K. Fujita, and the second approach is the cathode sheath model developed by K. D. Goodfellow. The Fujita cathode sheath model is modified here to calculate the cathode sheath potential, electron temperature and number density at the cathode sheath edge of a 1 kW hydrazine arcjet, using near-cathode bulk plasma properties from a nonequilibrium numerical model developed by Megli, Krier, and Burton. The sheath potential is sensitive to current attachment area, cathode tip temperature, and the properties of the near-cathode bulk plasma. For a 1 kW hydrazine arcjet operating at 10 A and 50 mg/s, the sheath potential from the modified Fujita model is approximately -30 volts for a pure tungsten cathode with 2 x 108 m2 attachment area, and 3680 K cathode tip temperature. The Goodfellow model consists of a near-cathode plasma model and a thermal model of the cathode. The plasma model contains models for the surface, sheath, presheath and ionization regions. The input parameters for the combined model are the total pressure, the arcjet current, and one of the following: cathode temperature, sheath voltage, or attachment area/current density. The cathode temperature is the best understood of these three parameters and is used here. Comparisons between the two cathode models have shown good agreement for the determinations of the sheath voltage, electron temperature and the electron number density.