Theoretical analysis of performance parameters in oscillating plasma thrusters

Conventional expressions and definitions describing performance of plasma thrusters, including the thrust, specific impulse, and the thruster efficiency, assume a steady-state plasma flow with a constant flow velocity. However, it is very common for these thrusters that the plasma exhibits unstable behavior resulting in time variations of the thrust and the exhaust velocity. For example, in Hall thrusters, the ionization instability leads to strong oscillations of the discharge current (so-called breathing oscillations), plasma density, ion energy, and as a result the ion flow. This paper revisits the formulation of the thrust and the thrust efficiency to account for time variations of the ion parameters, including the phase shift between the ion energy and the ion flow. For sinusoidal oscillations it was found that thrust can potentially change more than 20%. It is shown that, by modulating ion energy at specific amplitudes, thrust can be maximized in such regimes. Finally, an expression for the thruster efficiency of the modulating thruster is derived to show a mechanism for inefficiencies in such thrusters.