Thermal Runaway Prevention in Arc Spots

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Abstract
After recapitulation of the energy balance equation of cathode arc spots, the condition of thermal runaway is derived, i.e., of the unlimited increase of the temperature at a finite critical current density, because of temperature dependent resistive heat generation. It is shown that in arc spots such a thermal runaway is not possible for two reasons. First, the temperature dependent electron emission cooling forces a limitation of the stationarily achievable temperature (negative feedback). The current density remains limited, however. Second, the short time scale of arc spot development (crater formation time, ~10 ns) is not sufficient for thermal runaway that needs ~100 ns (order-of-magnitude values), besides the case of very small protrusions, where the time scale drops to less than 0.1 ns.