Evaluation of Nonlinear Effects in the 3-GeV Rapid Cycling Synchrotron of J-PARC

The 3-GeV Rapid Cycling Synchrotron (RCS) of J-PARC is designed to accelerate 8.3 × 10
¹³
protons per pulse up to 3 GeV at a repetition rate of 25 Hz. In order to implement the painting injection which is effective to defuse the space-charge force and to gain an excellent collimation efficiency, the RCS has a large acceptance in comparison with ordinary rings, which leads to a large aspect ration of the magnets (inner diameter over magnet length). In such a case, intrinsic field nonlinearities play a significant role, and the nonlinear behavior of particles at large amplitude and large momentum deviation is a essential issue. In this paper, we discuss influences of the intrinsic field nonlinearity of the main dipole magnet and combined effects with the sextupole field utilized for the chromatic correction. In addition, a possible correction scheme for the induced betatron resonances is discussed.