Simulation of space-charge dominated beam dynamics in an isochronous AVF cyclotron

This paper describes a beam dynamics code `PICN´ for simulation of high current proton beams in an isochronous azimuthally-varying-field cyclotron. It is assumed that the median plane and vertical motions are decoupled, so that the internal space-charge forces can be calculated by a particle-in-cell method applied to the median plane charge distribution. We assume operation in a regime where vertical focusing is not weak. This paper details the simulation method and approximations including a summary of the equations of motion. Results of the code, when applied to the PSI Injector II cyclotron are presented and compared with results from an earlier code that treated the beam composed of a distribution of rigid spheres