Thermal Runaway Prevention in Arc Spots

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.