On the Choice of Positron-Producing Energy in Linac-Injected e± Colliders

The optimum positron-producing energy in linac injected e± colliders is investigated from the averge luminosity point of view. It has been found that with a fixed injector energy, Et, there exists a minimum injection time at E+/Et=1/4, where E+ is the positron-producing energy. This corresponds to the maximum of average luminosity when no single beam instability occurs. On the other hand, when the storable currents are limited by fast head-tail instability, the minimum injection time takes place at E+/Et=1/3 while the maximum of average luminosity shifts to lower value. These results can be understood because, besides the two competing physical processes, i.e. the number of positrons produced favors higher E+ and the damping time favors lower E+, now lower E+ gives higher instability threshold. For numerical calculations, the parameters of Beijing Electron Positron Collider (BEPC) are used.