Tkeatment of Weak Coupling Using Smooth Approximation

This paper describes a study of controlling the coupling between the horizontal and the vertical betatron oscillations in the APS storage ring. Firit, we investigate the strengthening of coupling using two families of skew quadrupoles. Using smooth approximation, we obtained the formulae to estimate the coupling ratio defined as the ratio of the vertical and horizontal emittances or, for a single particle, the ratio of the maximum values of the CourantSnyder invariants. Since we knew that the coupling is mostly enhanced by the 21St harmonic content of skew quadrupole distribution, we carried out the harmonic analysis in order to find the optimum arrangement of the skew quadrupoles. The numerical results from tracking a single particle are presented for the various configurations of skew quadrupoles. Second, we describe the global decoupling procedure to minimize the unwanted coupling effects. These are mainly due to the random roll errors of normal quadrupoles. It is shown that even with the rather large rms roll error of 2 mrad we can reduce the coupling from 70 percent to 10 percent with a skew quadrupole strength which is one order of magnitude lower than the typical normal quadrupole strength.