Computational Validation of a Two-Dimensional Semi-Empirical Model for Inductive Coupling in a Conical Pulsed Inductive Plasma Thruster

A two-dimensional semi-empirical model of pulsed inductive thrust efficiency is developed to predict the effect of such a geometry on thrust efficiency. The model includes electromagnetic and gas-dynamic forces but excludes energy conversion from radial motion to axial motion, with the intention of characterizing thrust efficiency loss mechanisms that result from a conical versus a at inductive coil geometry. The range of conical pulsed inductive thruster geometries to which this model can be applied is explored with the use of finite element analysis. A semi-empirical relation for inductance as a function of current sheet radial and axial position is the limiting feature of the model, restricting the applicability as a function of half cone angle to a range from ten degrees to about 60 degrees. The model is nondimensionalized, yielding a set of dimensionless performance scaling parameters. Results of the model indicate that radial current sheet motion changes the axial dynamic impedance parameter at which thrust efficiency is maximized. This shift indicates that when radial current sheet motion is permitted in the model longer characteristic circuit timescales are more efficient, which can be attributed to a lower current sheet axial velocity as the plasma more rapidly decouples from the coil through radial motion. Thrust efficiency is shown to increase monotonically for decreasing values of the radial dynamic impedance parameter. This trend indicates that to maximize the radial decoupling timescale should be long compared to the characteristic circuit timescale.