Beam dynamics of alternating-phase-focused linac

A simple method to find an array of synchronous phases for alternating-phase-focused (APF) linacs is presented. The phase array is described with a smooth function having free parameters. With a set of the parameters, a simulation on the beam dynamics was made and distributions of the six-dimensional phase spaces were calculated for each set of the parameters. The parameters were varied, and numbers of the simulations have been performed. An optimum set of the parameters were determined so that the simulations of the beam dynamics yield large acceptances and small emittances of the extracted beams. Since the APF linac can provide both axial and radial stability of beams just with the rf acceleration-field, no additional focusing element inside of drift tubes are necessary. Comparing with conventional linacs having focusing elements, it has advantage in construction and operation costs as well as its acceleration rate. Therefore, the APF linacs would be suited for an injector of medical synchrotrons. A practical design of the APF linac for an injector of a medical accelerator is presented.