Breakdown characteristics of high intensity discharge lamps filled with xenon

A comparison between measured and modelled breakdown voltages of HID lamps filled with xenon at pressures of $0.1$--$5$ bar is presented. Measurements of current and voltage characteristics and high speed photography were done on specially prepared lamps at voltage rise times of $1$ MV/s to $2\times 10^5$ MV/s. The model consists of the Poisson equation and continuity equations for electrons and ions using the drift-diffusion approximation for the particle fluxes. Transport parameters for the electrons as functions of E/N have been determined by solving the 0-D Boltzmann equation. Appropriate boundary conditions couple the plasma to the outer circuit. The model is solved on a 1-D, inhomogeneous grid using an adaptive time step. Following the cubic interpolated propagation scheme each time step is divided into advective and non-advective parts. The latter is solved by applying the Crank-Nicholson scheme. The model gives a cathode-directed ionization front which turns into a cathode sheath. The model breakdown voltages increase with filling pressure and voltage rise time and are in good agreement with experiments.