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Erosion of the copper cathode in Trichel-pulse negative corona discharge was investigated in the atmospheric pressure air in point-to-plane electrode configuration. Nanometer-size craters were found on the cathode surface as a result of discharge treatment. Therefore, the current density on the cathode surface was estimated to be around 108 A/cm2. The value of the integral of specific current action of Trichel pulse argues in favor of electroexplosive mechanism of cathode erosion in Trichel-pulse negative corona.