Accelerator waveform synthesis and longitudinal beam dynamics in a small induction recirculator

A recirculating induction accelerator requires accelerating waveforms that produce current amplification and provide bunch length control throughout the acceleration process. Current amplification occurs because of both an increase in the beam velocity and a shortening of the length of the beam bunch. The pulsed acceleration and control waveforms seen by the beam change as the pulse duration shortens. For one acceleration cycle of the small recirculator, each accelerating gap is driven by a burst of 15 pulses. As the beam gains velocity, the time interval between pulses shortens from approximately 20 to 10 μsec. A zero-dimensional design code REC is used to develop the accelerator waveforms. An envelope/fluid code CIRCE and a 3-D particle code WARP3d are used to confirm the REC design and study the effects of errors. We find that acceleration errors can lead to space-charge waves launched at the bunch ends that strongly affect or even destroy the current pulse shape. The relation between the rate of longitudinal compression and the velocity of space charge waves is studied