Rare gas–halogen excimer lasers excited by electron‐beam‐sustained discharges (EBSD) will operate stably for only a limited length of time (hundreds of nanoseconds to a few microseconds). In this paper, results from a multidimensional model for an EBSD KrF laser are used to study various aspects of discharge ionization and geometric stability, and the relationship between the two. We examine the effects of photodetachment of electrons from the halogen negative ion, of circuit response, and of nonuniforme‐beam power deposition upon the onset of discharge instabilities. We find that both spontaneous emission from KrF* and laser oscillation resulting in photodetachment of electrons from F−can initiate an ionization instability. By operating with high impedance electrical circuits, the tendency towards instabilities by this effect can be reduced. We also find that the spatial uniformity of thee‐beam power deposition is directly correlated with both the rate of discharge constriction and the time at which the discharge suffers an ionization instability.