The primary electro-mechanical model is developed for the acceleration kinetics of electromagnetic railguns. Pulsed plasma thrusters (PPTs), whose operation principle is similar to that of electromagnetic railguns, generate thrust via electromagnetic acceleration of plasma. 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 a curved shape, which is different from the flat sheet shape. The curved geometric shape of PPT discharge channel makes the flat current sheet model currently used in the electro-mechanical models inherently flawed. In this paper, a two-dimensional (2D) curved current sheet model is proposed to improve the PPT electro-mechanical model, by referring to the curved morphology of PPT discharge plasma channels. No matter what is the real geometry of the 2D current sheet, the Ampere force on discharge plasma channels and corresponding kinetics can be derived to obtain 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 and expressed as $ {E}_{{\mathrm{k}}}=\displaystyle\int _{0}^{{t}_{{\mathrm{e}}{\mathrm{n}}{\mathrm{d}}}}{i\left(t\right)}^{2}\frac{{\mathrm{d}}{L}_{{\mathrm{e}}{\mathrm{q}}}\left(t\right)}{{\mathrm{d}}t}{\mathrm{d}}t $. To determine the inductance as a temporal function, an algorithm for the inductance is proposed in which time-segment fitting of PPT discharge waveforms is adopted. Moreover, based on the temporal function of the inductance, PPT discharge waveforms can be simulated by 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 have set up based on the improved electro-mechanical model. To verify the improved model and the corresponding calculation scheme, the PPT prototype is used to evaluate 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.
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