Excitation of half-integer resonances by random quadrupole field errors in the BETA-BEAM RCS

The Rapid Cycling Synchrotron of the Beta-Beam facility has been designed to operatewith horizontal and vertical tunes between 6 and 7 in order to avoid systematicresonances up to the fourth order. Nevertheless, unavoidable magnet imperfections mayexcite non systematic second order resonances which may pertub particle motion.In this paper an Hamiltonian treatment based on a well established formalism [1-3] is used to analyze the resonance excitation and to suggest correction schemes minimizing their effects.[1] A. Schoch. Theory of linear and non linear perturbations of betatron oscillations inalternating gradient synchrotrons. CERN 52-21, 1958.[2] G. Guignard. A general treatment of resonances in accelerators. CERN 78-11, 1978.[3] J-L. Laclare, G. Leleux, and A. Tkatchenko. Resonnances quadrupolaires- aleatoiresquadrupolaires et corrections. DSS-GERS- 74-91/TP-06, 1974