Matching Bunched Beams to Alternating Gradient Focusing Systems

A numerical procedure for generating phase-space distributions matched to alternating gradient focusing systems has been tested. For a smooth-focusing system a matched distribution can be calculated. With a particle tracing simulation code such a distribution can be followed while adiabatically deforming the focusing forces until an alternating gradient configuration is reached. The distribution remains matched; the final distribution is periodic with the structure period. External nonlinearities, including nonlinear couplings, were included in our examples but space charge was not. This procedure is expected to work with space charge but will require a 3-D space-charge calculation in the simulation code.