Two-dimensional thermal model of a refractory anode in a vacuum arc

A two-dimensional (2-D) thermal model for cylindrical graphite and molybdenum anodes in vacuum arcs is presented. The model includes heat flux from the plasma to anode surface, radiation from surfaces of the whole anode, and temperature-dependent thermophysical coefficients of the anode material. Arcs equipped with 3.2-cm in diameter and 1-3-cm-long anodes, with 175- and 340-A currents, and duration up to 250 s are analyzed. The results of the 2-D calculations indicate that the temperature of the active anode surface is distributed relatively uniformly, and the rate of anode temperature rise is larger for short (1 cm) anodes than for long (3 cm) anodes. Maximum active surface temperature depends weakly on anode length. The rear surface temperature for a 3-cm anode length is lower for graphite anodes (1600 K) than for molybdenum (2100 K) when I=175A. The active surface temperature of both graphite (for 175-340 A) and molybdenum (for 175 A) and shorter (1 cm) anodes varies from 2000 to 2400 K, indicating that the vacuum arc can operate as a hot-refractory anode vacuum arc.