Cathode potential drop at a transient cathode spot on a microprotrusion

Phenomena in the space charge layer at the cathode surface were considered to determine the cathode potential drop (CPD), taking into account the electron momentum and energy. The approach was based on the heavy particle kinetics in the Knudsen layer developed previously for a bulk cathode with a smooth surface. The modified kinetic model was considered in order to obtain the CPD dependence on time for a transient spot on a cathode protrusion, taking into account heat transfer. The erosion of the protrusion, and hence its size decrease, during cyclic plasma action with life time τ was included in the model. The calculation showed that the CPD decreased with time t, e.g. for a 5 μm Cu protrusion from about 90 to 13 V, when t increased from 50 ns to 1 μs. During this period the spot temperature decreased from 4500 to 3600 K and the calculated spot current was about 3-5 A (which agrees with that observed for spot fragments). These results facilitate understanding the relatively large voltage needed for arc ignition compared to the low voltage appearing during steady arc operation.