A mechanism for nanosecond cathode spot operation in vacuum arcs

A model for nonstationary cathode spot operation in vacuum arcs is proposed. The model takes into account increasing spot current during the spot life time. Calculations for a copper cathode indicate that the spot current density increases when the rate of rise of the spot current dI/dt increases and can exceed 10⁸ A/cm² for dI/dt about 10¹¹ A/s. The plasma density is 10²⁰-10²¹ cm^-3. The plasma electron temperature T_e is about 3-4 eV when the cathode potential drop U_c=15-20 V and T_e reaches 7-8 eV when the U _c fluctuates and increases up to 40-50 V. The calculated spot parameters are in the range measured in recent experiments with nanosecond time resolution. The effect of different mechanisms of electron emission (thermo-and thermo-field emission) was investigated. The self-sustained solution shows that the spot current density changes by factor 2 by using different emission mechanism in the system of equation