Processes in a vicinity of electrodes and the stability of the plasma streams in the channel of the quasi-steady high-current plasma accelerator are studied. Mathematical modeling is done on the basis of the two-fluid MHD model. The computational results are compared to the experimental data defining the presence of the critical modes. The area of parameters is found, and a criterion adequate to the laminar plasma flows in the absence of instability in the vicinity of the electrodes is formulated. The effect of changing the ways of the plasma inflow on the channel input and of an additional longitudinal magnetic field on the development of the processes in the vicinity of the electrodes and formation of the current crisis are investigated.
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