An empirical scaling relationship for the total pressure in hollow cathodes
A non-dimensional scaling relationship for the total pressure inside thermionic, orificed hollow cathodes is derived empirically from a large database of experimental measurements and is analyzed statistically. The relationship allows calculating the total pressure inside hollow cathodes, which is necessary for self-consistent analytical models of the insert region and for insert lifetime calculations. The scaling relationship is a function of cathode operational parameters and is expressed as a non-dimensional power law. It is compared to experimental data for self-consistency and to theoretical modeling efforts. It is found that the empirical correlation agrees with experimental data with an R-squared value of 0.98 and average error of 24.5%, allows calculating the pressure over a range of three orders of magnitude or five orders of magnitude in the non-dimensional space, and is able to capture the dependency of the total pressure on the discharge current where theoretical models can not. For the dataset considered the scaling is shown to be insensitive to variations in the cathode orifice length, propellant ionization energy, and viscosity.