Cathodic arc attachment in a HID model lamp during a current step

Changes in the cathodic arc attachment mode during a current step are studied both experimentally under well-defined and reproducible conditions, and by finite element calculations. A transition from diffuse to spot and back to diffuse attachment is observed as the response to the step. Spot formation is identified experimentally by a sharp peak in the light intensity in front of the cathode and a steep decrease in the lamp voltage. Numerical three-dimensional solutions of the thermal-conduction equation in the cathode body exposed to nonlinear surface heating give good quantitative agreement of the time course of the observed changes in attachment modes. The model that describes the heating by the near cathode layer uses a simpler equation for the ion current density than other models in the recent literature. The model describes how an excess energy flux is created in the layer in front of a spot, which cannot be transported back to the cathode by the ion current and must, therefore, be supplied to the arc. The calculated integral excess power shows a time course similar to the observed light intensity.