Temperature distribution dependence on refractory anode thickness in a vacuum arc: Theory

Anode heating by plasma heat flux in a vacuum arc was modeled. The model included the nonlinear 2-D heat conduction equation with temperature-dependent thermophysical material properties and heat losses by StefanBoltzmann radiation from the anode surfaces. The heat conduction equation was solved numerically for 32-mm-diameter tungsten cylindrical anodes with different anode thicknesses and arc currents. The time-dependent heat flux to the tungsten anode was determined using measured anode temperatures. The time-dependent effective anode voltage U_ef was found to decrease from an initial to a steady-state value, e.g., from 11.4 to 7.05 V, for 175 A, anode thickness d=30 mm, and electrode gap h=10 mm. It was shown that U_ef increases with d at t = 0 and in the transient period, while at steady state, U_ef slightly decreases with d and h.