The current generation of multiple beam klystrons (MBKs) uses singly convergent electron guns where the center of the cathode is coincident with the axis of the individual beam tunnels through the circuit. Any increase in power requires a corresponding increase in cathode emission current density or an RF circuit with overmoded cavities. Current density increases reduce klystron lifetime, and overmoded cavities are subject to parasitic modes and instabilities. These can be avoided using doubly convergent electron guns where the center of the cathodes is at a larger radius than the beam tunnels. Design of doubly convergent electron guns requires 3D simulation tools with advanced optimization capabilities. This presentation will describe the development of these simulation tools and design of a doubly convergent multiple beam gun.