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.

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