Influence of vertical dispersion and crossing angle on the performance of the LHC

Misalignments, magnetic field deviations and the beam crossing angle induce closed orbit deviations and residual dispersions at the interaction points (IPs) of the LHC. At IP1 and IP5, the horizontal and vertical dispersion functions are approximately ±2 cm while at IP2 and IP8 they can reach values up to 50 cm. A numerical study of the excitation of synchro-betatron resonances by crossing angles and dispersions shows that the beam size changes by less than 5% and has corresponding effects on the luminosity. Since the effects of bunch length are important in this context we have used the numerical code BBC for the study. When the betatron tunes are close to a synchro-betatron resonance excited by the crossing angle the amplitude of particle oscillations increases. The superposition of vertical dispersion modifies the strength of the resonance. For example, sidebands of the resonance 13Qx = 4 yield an increase of the amplitude of the betatron oscillation by less than 10 % at an initial amplitude of 5s. Including residual dispersion of 10 cm results in a further increase of amplitude by at most 7.5 %. Correction of the dispersion at the IP is possible with closed orbit bumps in the arcs.