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Experimental diagnostics in a hollow-anode vacuum arc device have shown that the repetitive growth and collapse of an anode sheath is responsible for observed tens-of-kV voltage spikes. A dynamic model of device operation based on circuit effects and a time varying quasi-Child-Langmuir sheath is presented. The scaling of the repetition rate with respect to cathode material is discussed. The device is being investigated for use as a current limiter for ~10-MW pulses.