Numerical modelling of arc attachment to cathodes of high-intensity discharge lamps

The axisymmetric energy fluxes in an arc cathode are calculated by a commercial finite-element analysis code. The model decouples the sheath from the arc. Exclusively a spot mode exists at small integral loads by heat flux in the steady state for a cathode in 1 MPa xenon and direct currents below 10 A. The diffuse mode occurs at high loads by heat flux or current. In-between multiple solutions are possible. A spot mode is favoured by lower thermal conductivity, higher emissivity, lower support temperature, greater diameter and a smaller length of the cathode. This conforms with experiments. The method provides a design tool for cathodes.