Effect of the induced voltage on the bunch motion at the transition energy

Analysis of the induced 160 MHz rf voltage on the bunch distribution indicates that the tolerable remnant 160 MHz rf voltage is V2<25KV at the transition energy region. The phase space growth is found proportional to V2/V1, where V1 is the accelerating voltage. These remnant field are not important outside the transition energy region due to synchrotron mixing. Since the bunch length in the accelerating rf system is approximately 2π radians in the high frequency rf phase, the error in the high frequency rf stable phase plays little role to the phase space area growth. 5 refs., 3 figs