Longitudinal Beam Dynamics of a Rapid Cycling Synchrotron Demonstrator

A Muon collider is an innovative idea for a lepton accelerator not constrained by synchrotron radiation. The fast decay of the muons necessitates quick acceleration, and hence fast ramp rates of the bending magnets. For this purpose a new synchrotron design has been proposed dubbed the hybrid rapid cycling synchrotron, which would combine super conducting and normal conducting magnets. This new design is quite different from a regular synchrotron as the path of the synchronous particle would vary during the acceleration. For this reason it has been suggested to build a demonstrator facility which would test the hybrid magnet layout. In the demonstrator the super conducting magnets would be replaced with normal conducting ones so that after its original purpose, the facility could be changed to a regular synchrotron and become a user facility or be used as an injector for a storage ring. In this report we simulate the longitudinal beam dynamics of the demonstrator and the effects of beam loading in its user mode using a set of assumed parameters. It is found that the Tesla cavities planned to be used in the actual muon collider would experience strong beam loading, and other cavities may be better suited. Additionally the bunch length may be limited due to the effect of quantum excitations.