Dynamic aperture and long term particle stability in the presence of strong sextupoles in the CERN SPS

The reduction of dynamic aperture produced by strong sextupoles has been measured in the SPS (Super Proton Synchrotron). The short-term aperture, inside which particles survive for at least one second, is well predicted by computer simulations based on the early detection of chaotic motion. Inside this aperture particles diffuse slowly to larger amplitudes, so that long-term stability is only assured in a smaller region of the phase space, the long-term aperture. Slow tune modulations increase the chaotic regions and could explain the observed diffusion phenomena. The criteria based on tune shift and smear which are used in the design of large hadron colliders are discussed