We have augmented the code POSINST to include solenoid fields, and used it to simulate the build up of electron cloud due to electron multipacting in the PEP-II positron ring. We find that the distribution of electrons is strongly affected by the resonances associated with the cyclotron period and bunch spacing. In addition, we discover a threshold beyond which the electron density grows exponentially until it reaches the space charge limit. The threshold does not depend on the bunch spacing but does depend on the positron bunch population.
