The cyclotron-like storage ring dedicated to Rare-RI Ring project consists of 6 magnetic sectors and 6 straight sections, having a circumference of 56.13 m. The magnetic sector works for both bending and focusing. The total circulation is assumed to be 1,000 turns. Over the momentum range from -1% to +1% in ∆p/p, the required isochronisity is 10-6 while the beam emittance is sevaral tens of π mm-mrad. To examine the design of cyclotron-like storage ring and fix its parameters, we have developed a high precision beam optics simulation. To achieve the precision as high as possible within a feasible computational time, we have adopted a geometrical tracking assuming a circular orbit for a small spatial segment. For that purpose, it is enough that the magnetic sector is divided into 150 sub-sectors in calculation. In each sub-sector, the magnetic field is given as a function of radial position but uniform around the vicinity of beam trajectory. The beam trajectory is evaluated in 4th order Runge-Kutta algorithm. Finally, we have achieved a precision of 10-9 in ∆T/T and a computational time of 1.8 sec on a typical PC server for ray tracing of single particle undergoing a circulation of 1,000 turns.
Effect of Numerical Noise on Beam Emittance Growth in PIC Code