Beam-Beam Synchrobetatron Resonances

Electron storage rings see dangerous beam-beam synchrobetatron sidebands which are almost invisible to single beams, for example the diagonal resonances Qz-Qx = mQs. Colliding protons and antiprotons in the SPS do not see diagonal sidebands, despite the absence of stabilisation by radiation damping. One SPS feature, proton loss or emittance blow-up at vertical tunes of less than Qz = (0).674, could be a beam-beam synchrobetatron effect off the 4/6 resonance. This report uses a strong-weak numerical simulation to show that an apparent tune modulation, induced by longitudinal collision point oscillations, can cause synchrobetatron sidebands, to a distance of about 2Qs from a beam-beam resonance. The concurrent analytic description illustrates several reasons why flat beams * <<* * 1) 1 << z x z x behave quite differently from round beams 2) %*= S* , a* = a and why the SPS is so resonance free. Transverse electron trajectories can become stochastic beyond a critical longitudinal amplitude limit, making microbeta optics unstable. Round beam-beam sidebands are found to be stronger near Qz = 2/3 than near the diagonal. Chromaticity is more dangerous to the SPS as a source of (real) tune modulation, than the modulation due to collision point oscillations.