Nonlinear field effects in the collector ring due to large-amplitude particle oscillations

Abstract

In the frame of the FAIR project, the Collector Ring (CR) is planned to be built for efficient cooling of antiprotons and rare isotope beams [1]. In order to accept hot beam from separators large acceptances are required. This paper examines the effects which can influence the beam dynamics due to large betatron oscillation amplitude and momentum spread. Using analytic expressions, the amplitude-dependent tune shifts driven by sextupole magnets, the fringe field of quadrupole magnets, and kinematics effects have been calculated. The obtained results have been compared with numerical simulations by means of precise multi-turn particle tracing. The tracking analysis for the CR has been performed considering the real shape of the magnetic field of the wide aperture quadrupole. We report on quantitative studies of the effects on the dynamic aperture of the rings.