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Pulsed high pressure arc lamps are often operated with a small sustaining current during the interpulse period in order to minimize the arc expansion time, to increase the lamps' operating lifetime and to enable operation at higher repetition frequencies. It is common to select a sustaining current level associated with an arc voltage which lies between the maximum DC source voltage and the minimum sustaining voltage. This paper shows that the radius of the arc tube, the amount of convection and radiation and the assumptions regarding the nature of the radiation model strongly influence the current value associated with the minimum sustaining voltage. Pressure and boundary temperature have only a slight effect on the current associated with the minimum sustaining voltage but affect the minimum sustaining voltage. Heat conduction plays the primary role in tubes with a small radius while optically thin radiation plays the primary role in tubes with a large radius. The simulation results were obtained using Patankar's control volume algorithm along with boundary conditions. The extended Ellenbass-Heller equation in cylindrical coordinates was solved. The numerical results for the electric field as a function of current are somewhat smaller than the experimentally derived results. Convection appears to be the reason for this difference.