Cancellation of klystron-induced energy and arrival-time variations in linear accelerators with arc-type bunch compressors

We explain how the accelerating field amplitude and phase vary with modulator voltage in pulsed radio frequency high-power amplifiers based on klystron tubes. Changes in modulator voltage give rise to correlated changes of amplitude and phase, affecting the properties of the accelerated beam, in particular energy, arrival time, and bunch duration. We show, both theoretically and experimentally, that there exists a postcrest acceleration phase (the magic angle) where the changes of beam energy due to phase and amplitude shifts caused by modulator-voltage variations cancel out. When accelerating at the magic angle, the klystron modulator voltage jitter no longer contributes to energy and arrival-time jitter in the accelerator. Off-crest operation at the magic angle can be implemented for bunch compression schemes in accelerators with arc-type bunch compressors, which have positive momentum compaction. The experimental results, obtained at the MAX IV laboratory, show the benefit of operating close to the magic angle in arc-type bunch compressors. In a direct measurement of normalized electron-energy jitter, the energy jitter was reduced by a factor of 1.8 down to $8.2\times {10}^{-5}$ when operating at the magic angle.