[en] Two recent failures of the positron source solenoid have led to a design study of more conservative coils. A Monte Carlo program has been used to calculate the distribution in phase space of the electromagnetic shower from the target of the SLAC positron source. Positron and electron yields were calculated for copper and tungsten targets. A ray tracing program was used to calculate the acceptance of the focusing system. The existing source makes use of an adiabatically tapered solenoid. The yield of this system has been compared with 3 alternatives: two possible modifications of the tapered solenoid, and a focusing system using a short solenoid as a quarter wave transformer. The calculated yield for the existing system is in reasonable agreement with experimental observation