Beam-beam interaction and high order resonances

There is experimental evidence from the SPS (Super Proton Synchrotron) that very high order resonance (an order>10) can cause particle loss during the beam-beam interaction. These results can be simulated by tracking a single particle against a round beam. If the round beam has an RMS size of sigma and the particle's initial amplitude is 2 sigma then no effects are observed due to high-order resonances. However, if the particle's initial amplitude is 5 sigma the beam-beam 16th-order resonances are strong. Furthermore, if tune modulation is added (i.e. power supply ripple) then the 5 sigma particle's motion becomes chaotic (when it is near a 16th-order resonance) and can result in particle loss.<>