Adaptive RF Transient Reduction for HIGH Intensity Beams with Gaps

When a high-intensity beam with bunch-trains and gaps passes a cavity with a high-gain vector feedback enforcing a constant voltage, large transients appear, stressing the RF high power hardware and increasing the trip rate. By modulating the cavity voltage with a varying periodic waveform (set-function), the RF power can be made constant while still preserving the high feedback gain. The average cavity voltage is conserved but bunches have to settle at slightly shifted positions. A method is derived to obtain this set-function in practice while making no assumptions or measurements of the beam or RF parameters. Adiabatic iterations are made including the whole machine as an analog computing device, using all parameters as they are. A computer simulation shows the success of the method.