Effects of correction sextupoles in synchrotrons

In order to have a usable acceptance of the beam momentum spread (Δp/p), synchrotrons must have at least two families of correction sextupoles which are generally placed at locations where the momentum dispersion function is large. These sextupoles are often called chromaticity correction sextupoles since their function is to eliminate (or to change in the most desirable manner) the dependence of the tunes of betatron oscillation on (Δp/p) caused by the chromatic aberration of quadrupoles. This report describes various harmful effects arising from these sextupoles and suggests possible cures. In particular, it is emphasized here that the second-order effects be minimized in order to prevent a potentially disastrous reduction in the transverse acceptance of the ring even when the tunes are considered to be safely away from the lowest-order (i.e., third-integer) resonances. The terms responsible for the dependence of tunes on the betatron oscillation amplitudes are explicitly given as a function of the five integrals representing the resonance-driving terms of the lowest-order Hamiltonian. The expression involves sums of infinite number of Fourier components but they can all be computed analytically