The primary electro-mechanical model is developed for the acceleration kinetics of electromagnetic railguns. Pulsed plasma thrusters (PPT), whose operation principle is something like that of electromagnetic railguns, generate thrust via electromagnetic acceleration of plasmas. Therefore, the electro-mechanical model serves as a valuable analytical tool to explore the mechanisms of energy conversion and thrust generation of PPTs. In fact, a PPT initiates discharge at its propellant surface and then ejects the discharged channel away to form accelerated plume. During the acceleration, the plasma channel assumes curved shapes, which differ from a flat sheet shape. The curved geometry of PPT discharge channels makes the flat current sheet model used in the present electro-mechanical model be of inherent shortcomings. This paper proposes an 2D curved current sheet model to improve the PPT electro-mechanical model, by referring to the curved morphology of PPT discharge plasma channels. Fig.I shows the schematic of a typical PPT discharge circuit and the curved PPT discharge plasma channel that is indicated as the pink curve $\mathop {ab}\limits^ \wedge $ according to the curved thin current sheet model. Also in Fig.I a current element of the discharge channel is taken arbitrarily to display its instant velocity and the Ampere force element <b><i>df</i></b> exerted by the magnetic field induced by the PPT current circuit. The pink dashed curve cdsymbolizes the position of the current sheet at the moment <i>dt</i> later. From the 2D curved current sheet model on, according to the detail shown in Fig.I, the Ampere force on discharge plasma channels and corresponding kinetics can be deduced aiming final kinetic energy of discharge plasma channels. As a result, the relation between the kinetic energy and the inductance of PPT discharge circuit is obtained as expression: ${E_k} = {\int {_0^{{t_{end}}}i(t)} ^2}\frac{{d{L_{eq}}(t)}}{{dt}}dt$. To determine the inductance as a temporal function, an algorithm for the inductance is proposed that employs time-segment fitting of PPT discharge waveforms. Moreover, based on the temporal function of the inductance, PPT discharge waveforms can be simulated using the ODE45 solver of MATLAB with high fitting goodness. So far, a calculation scheme for the kinetic energy of PPT plumes and simulation code for PPT discharge waveforms are setup based on the improved electro-mechanical model. To verify the improved model and the corresponding calculation scheme, a PPT prototype is used via assessing its energy conversion efficiency. The results show that the model enables elucidating the low PPT electro-mechanical efficiency, which is attributed to the partition limitation of PPT energy to electromagnetic acceleration process. Accordingly, a possible exploration routine for elevating PPT electro-mechanical efficiency is suggested.
