Contribution of synchrotron oscillation to spill ripple in RF-knockout slow-extraction

We have studied the effect of synchrotron oscillations on the spill ripple in RF-knockout extraction, in order to investigate the ripple component of the synchrotron-oscillation frequency and to suppress this component. By using a simplified model of RF-knockout extraction and the simulation, it was found that the following conditions are essential for suppressing the spill ripple including the component of the synchrotron-oscillation frequency: (1) sufficient amplitude of the synchrotron oscillation and (2) uniform distribution in longitudinal phase-space. In the experiment at the Heavy Ion Medical Accelerator in Chiba (HIMAC) synchrotron, the debunch-recapture was carried out before the extraction to obtain the larger oscillation amplitude and the uniform distribution in the longitudinal phase-space. In this article, the contribution of the synchrotron oscillation to the spill ripple is described in detail.