A 0-D model for orificed hollow cathodes with application to the scaling of total pressure
A scaling relationship for the total pressure inside orificed hollow cathodes is derived from a theoretical zero-dimensional model from which plasma quantities are computed, including the total pressure. The variation of total pressure with controllable parameters must be properly evaluated because it is critical for determining the lifetime of thermionic inserts. The model is based on the conservation of energy and momentum for the combined plasma-neutral fluid and on the assumption of charge-exchange-dominated ambipolar diffusion in the insert region plasma. The controllable inputs of the model are the cathode geometry, the gas species used, and the operating conditions (discharge current and mass flow rate). The neutral gas temperature and sheath potential are two non-controllable parameters. Good agreement is obtained with pressure data from the literature and new experimental total pressure data measured at up to 300 A of discharge current in a large hollow cathode. A scaling relationship for the total pressure is derived from the plasma fluid momentum balance and the numerical results of the theoretical model. The total pressure is found to scale with the square of the mass flow rate multiplied by a weak function of discharge current, and with the square of the discharge current. The nature of the scaling is interpreted physically to be due to the relative importance of the magnetic pressure and the gasdynamic pressure modified to take into account the plasma contribution to the orifice speed of sound.