Analytical model of high-speed flows has been developed for the channel of quasi-stationary plasma accelerator used to create powerful electric jet plasma engine of new generation. The model of two-dimensional axisymmetric flows is based on the stationary equations of two-fluid magnetohydrodynamics for the ideal plasma and the smoothly varying channel approximation. The new approach to organizing flows using non-equipotential electrodes is associated with the electron current-transport regime, which ensures slipping of the heavy ion component of the plasma along anode and cathode. As a result of studying transonic flows in the profiled channel, the potential distributions along non-equipotential electrodes, as well as the integral characteristics of the flow, including mass flux and thrust, were determined.