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 operate
with horizontal and vertical tunes between 6 and 7 in order to avoid systematic
resonances up to the fourth order. Nevertheless, unavoidable magnet imperfections may
excite 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 in
alternating 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- aleatoires
quadrupolaires et corrections. DSS-GERS- 74-91/TP-06, 1974.