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This paper analyzes some physical effects that occur on the electrode surface in plasma-armature rail launchers when the linear current density is higher than the critical value. The melt on the electrode surface is found to be unstable. An analysis of the possible development of a number of instabilities showed that under experimental conditions, Rayleigh-Taylor and Kelvin-Helmholtz instabilities and magnetohydrodynamic instabilities due to the interaction of the current with the self-magnetic field can develop over times much smaller than the discharge time. As a result, the electrode material can enter the plasma armature, thus limiting projectile velocity. X-ray recording of the electrode surface confirmed the presence of small-scale inhomogeneity and ejection of the electrode material from the surface. Under certain conditions, the emergence of conducting metal jets from the electrode surface was detected.