Numerical modelling of a dynamic mode change of arc attachment to cathodes of high-intensity discharge lamps

A commercial finite-element analysis code is used to calculate axisymmetric transient temperature fields, current density distributions and energy fluxes in the cathode of a high-intensity discharge lamp powered by a unipolar current I(t). The calculation is based on a sheath model of the near-cathode layer and the assumption that the resulting cathode fall voltage U(t) is spatially constant. So a calculation of the fields in the are region is not necessary. Depending on the electrode dimensions and the frequency of I(t) hysteresis-like periodic transitions between the diffuse and spot modes of are attachment are observed in the numerical solutions for 0.62 MPa mercury discharges with pure, as well as thoriated, tungsten cathodes. These findings are compared with measurements from the literature. The simulation shows that the latent heal has negligible influence on spot formation and that the average cathode power loss can be smaller for a time-varying current than for the direct current with equal mean value. The presented method can be used as a guide to better electrode geometries and current forms.