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The potential barrier model considering an additional current that can lead to the high-gradient breakdowns in accelerating structures is proposed. An oscillatory resonance feature of the field emission current from a double-layer metal system with a nanoscale coating is shown. The double potential barrier was used for calculations of the field emission current density value. The presence of resonant properties of the field emission current density of a double-layer metal system with a nanometric coating is revealed. The field emission current increasing more than 5 times (for the constant value of an electric field strength E = 5 G V / m ) when considering not ideal copper surface with the presence of nanoclusters on the surface of or nanoscale voids in the near-surface layer is observed. [ABSTRACT FROM AUTHOR]