Electromagnetic Acceleration of a Plasma Slug

Abstract

The slug model of a plasma accelerator is formulated and analyzed. The coupled nonlinear system equations involving seven parameters are transformed into a three-parameter set. The formulation includes as special cases Artsimovich's treatment, which neglects all system resistances, and Schock's treatment, which assumes negligible resistance of the accelerator electrodes. Small coupling, as well as small and large time asymptotic, solutions, which include the effect of variable rail resistance, are derived and compared with exact analog computations. In cases of practical concern, the small time solutions are valid well past the first maximum of the current discharge, bridging the gap left by Schock's approximate solution whose applicability is restricted to cases where the acceleration takes place over a number of cycles. Finally, it is shown how to optimize the efficiency of an accelerator through suitable adjustment of the system parameters.

Current Speed in a Magnetic Annular Shock Tube

“…It was motivated by evidence obtained in a previous investigation3 of the shape of the current sheet that serious discrepancies betwe-en the measured and predicted 4 ', 5 sheet speeds were occurring. Since the sheet speed is one of the most important and, in principle, easiest parameters to predict, this was considered quite serious.…”

Gas-Fed Pulsed Plasma Thrusters: Fundamentals, Characteristics and Scaling Laws

“…[30] is interesting in that it provides a resistance that varies as the current sh^et moves down the electrodes, however, they found this to be a minimal efTact. Their "short time" solutions do not include the effective resistance generated by the current sheet motion.…”

“…The first simple scaling relation came from the asymptotic solutions of a slug-model studied at Republic Aviation [30]. In that model, the efficiency was seen to scale as:…”

“…In one of the first papers on an acceleration model for plasma thrusters, Republic Aviation used a non-dimensional slug-model for the propellant eliminating any dynamic efficiency effects [30]. They also did not include any effects of plasma resistance, wall effects or radiation, although they did include a linearly distributed resistance for the electrodes.…”

“…Research at Republic Aviation (more commonly know later as FairchildRepublic for their later ablative pulsed plasma thruster work) began with a theoretical paper on the acceleration of a plasma slug [30]. They used a non-dimensional, constant mass model for the propellant eliminating any dynamic efficiency effects.…”