Inductive pulsed plasma thruster model with time-evolution of energy and state properties

A model for pulsed inductive plasma acceleration is presented that consists of a set of circuit equations coupled to both a one-dimensional (1D) equation of motion and an equation governing the partitioning of energy. The latter two equations are obtained for the plasma current sheet by treating it as a single element of finite volume and integrating the governing equations over that volume. The integrated terms are replaced where necessary by physically equivalent approximations that are calculated through the solution of other parts of the governing equation set. The model improves upon previous 1D performance models by permitting the time-evolution of the temperature consistent with the time-varying energy flux into the plasma. The plasma state properties are also more realistically modelled and evolved in time, allowing for the tailoring of the model to different gases that may be chosen as propellants. Computational results for argon propellant are presented to demonstrate the efficacy of the model. The model produces a result where efficiency is maximized at a given value of the electrodynamic scaling term known as the dynamic impedance parameter. The scaling of different energy sinks as a function of the dynamic impedance parameter provides insight into the global energy partitioning in these types of accelerators. Results from the present model deviate from the previous version where temperature is selected as an input without regard for the energy that would be deposited to heat the gas to that temperature. Qualitatively and quantitatively, the model predicts specific impulse values that compare favourably with those measured for two separate inductive pulsed plasma thrusters. Efficiency is underpredicted in the regime where data are available, but the trends in the data and simulations follow similar trajectories that appear to be converging towards a predicted peak efficiency as the dynamic impedance parameter is increased.