## Effect of Inductive Coil Geometry on the Operating Characteristics of a Pulsed Inductive Plasma Accelerator

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### Abstract

The effect of inductive coil geometry on the operating characteristics of a pulsed inductive plasma thruster is investigated analytically and experimentally. Coil inductance is measured as a function of the position of a simulated current sheet and modeled using finite element analysis to develop a two-dimensional semi-empirical inductance relation that is used to expand a circuit-based acceleration model from one to two dimensions. The model includes electromagnetic and gas-dynamic forces but excludes any process to translate radial plasma motion into axial motion. Furthermore a magnetically-impermeable current sheet encompassing all the propellant for a pulse is assumed to form immediately at the start of the pulse and at the surface of the inductive coil. The two-dimensional acceleration model is nondimensionalized, yielding a set of dimensionless performance scaling parameters. Model results indicate that the introduction of radial current sheet motion caused by a conical inductive coil geometry (versus a flat circular plate) increases the axial dynamic impedance parameter at which thrust efficiency is maximized and generally decreases the overall achievable thrust efficiency. Operational characteristics of two thrusters with inductive coils of different cone angles are explored through thrust stand measurements and time-integrated, unfiltered photography. Trends in impulse bit measurements indicate that, in the present configuration, the thruster with the inductive coil possessing a smaller cone angle produced larger values of thrust, in apparent contradiction to results of the model. Areas of increased light intensity in photographs of thruster operation are assumed to qualitatively represent locations of increased current density. Light intensity is generally greater in images of the thruster with the smaller cone angle when compared to those of the thruster with the larger half cone angle for the same operating conditions, and generally decreases in both thrusters for decreasing mass flow rate and capacitor voltage. The location of brightest light intensity shifts upstream for decreasing mass flow rate of propellant and downstream for decreasing applied voltage. Recognizing that there exists an optimum ratio of applied electric field to pressure with respect to breakdown efficiency, this result may indicate that the optimum ratio was not achieved uniformly over the coil face, leading to non-uniform, weak current sheet formation in violation of the model assumption of immediate formation from all injected propellant of a magnetically-impermeable current sheet.