Second order effects in the sextupole-corrected SPS lattice

Chromaticity correction is essential in the SPS accelerator both for normal operation and for high density single bunch acceleration and storage, required for the CERN proton-antiproton collider project. Linear correction is presently achieved with one set of 36 F sextupoles and another set of 36 D sextupoles, regularly placed around the machine circumference. This lumped sextupole distribution induces non-linear variations of the machine tune with Delta p/p. These higher order effects which are also encountered in large electron machines cannot actually be corrected in the SPS, where they are well observable at least up to second order. Analytic calculation of the non-linear chromaticity, using Fourier expansions of the lattice functions, as well as computer simulation with the AGS program closely agree with the measurements performed at various energies. For the same reason, the transition energy depends upon the momentum deviation Delta p/p of the beam, which can lead to losses when beams with large Delta p/p are accelerated through transition, since no correct phase- jump timing can be found for all particles. Measurements of this effect in the presence of different chromatic corrections are presented and also compared with the predictions of the analytic calculations and of the computer evaluations with the AGS program. (9 refs).