Tune splitting in the presence of linear coupling

For RHIC (Relativistic Heavy Ion Collider), a tune splitting as large as 0.2 was found in one case. A correction system has been developed for correcting this large tune splitting which uses two families of skew quadrupole correctors. It has been found that this correction system corrects most of the large tune splitting, but a residual tune splitting that is still appreciable remains. The residual tune splitting appears to be due to higher-order effects of the random a/sub 1/ multipole. Loosely speaking, one may say that the residual tune splitting is associated with the nearby linear sum resonance, nu /sub x/+ nu /sub y/=integer. A skew quadrupole correction system that appears capable of correcting a large part of the residual tune splitting has been developed.<>