Reducing the coupled-bunch oscillation in the Fermilab Booster by optimizing RF voltage

In the Fermilab Booster, the coupled bunch oscillation is excited between transition and extraction by parasitic high order modes (HOM) in 17 RF cavities. the growth rate is determined by the coherent frequency shift and natural Landau damping due to nonlinearity of RF waveform. The passive damping and active feedback are normally used to reduce coherent frequency shift. Here we report that Landau damping can be enhanced through careful programming of RF voltage through the acceleration cycle. It is very effective during ramping where synchronous phase is big and bucket area is very sensitive to the RF voltage. In the case of a stationary bucket, the Landau damping is not sensitive to RF voltage