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

The requirement of the two RF systems in the RHIC (Relativistic Heavy Ion Collider), 26.7 MHz for the particle acceleration and 160 MHz for storage collision mode, raises the difficult problem of the induced high-frequency RF voltage during the bunch acceleration through 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<25 kV at the transition energy region. The phase space growth is found to be proportional to V ₂/V₁, where V₁ is the accelerating voltage. These remnant fields 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 in the phase space area growth