Total pressure in thermionic orificed hollow cathodes: Controlling mechanisms and their relative importance
A statistical analysis is conducted to identify which physically relevant non-dimensional parameters influence the total (neutral, ion, and electron) static pressure inside thermionic orificed hollow cathodes. It is critical to uncover and order the importance of the physical mechanisms that affect the pressure inside hollow cathodes because it influences the plasma attachment length, the electron temperature, and the sheath potential. These plasma parameters, in turn, affect the emitter lifetime. A principal component analysis of total pressure data obtained from the literature reveals that four non-dimensional variables can account for most of the variation in the total-to-magnetic pressure ratio over five orders of magnitude. The relevant variables are identified with a backward stepwise selection process and an exhaustive grid search and include, by order of importance: the gasdynamic-to-magnetic pressure ratio, the ratio of the mass flow rate to the discharge current, the orifice-to-insert diameter ratio, and the orifice Reynolds number. It is also shown, using various models and regression analyses, that empirical, Poiseuille, or isentropic flow models should not be used for predictive cathode design work. The data-driven study suggests that, while viscous effects may be important, the variation in those effects between cathodes is negligible compared to the effects of the modification of the gas constant due to the plasma, the transitional flow, the flux of heavy species on the orifice plate, and the Lorentz force.