Dependence of a frequency bandwidth on a spill structure in the RF-knockout extraction

A spill structure in the RF-knockout extraction was studied on colored noise of the RF-knockout, in order to investigate the diffusion process of particles inside the separatrix. It is found that frequency bands solely around the resonances (n+1/3 and n+2/3) contribute to the diffusion and the uniform spill, or equivalently uniform diffusion requires to include many bands around the resonances. A particle density distribution inside the separatrix would be modulated in the process of diffusion even if a frequency band covers the single betatron tune spread. With a spectrum of RF knockout including many bands around the resonances, the superposition of modulations by each band would make the unevenness of distribution small. The colored noise with multi-bands is proposed to reduce the power of amplifier, since frequency bands outside around the resonances do not contribute to the extraction. The simulation using the multi-bands spectrum shows the same uniform spill with a wide bandwidth.