Excitation of Coherent Beam-Beam resonances for beams with unequal tunes in the LHC.

In the Large Hadron Collider (LHC) two proton beams of equalstrength will collide at several interaction points. It is known that thehead-on collision of two equally strong beams excites coherent modes ofoscillation. If Landau damping does not act on these modes the beams canbe unstable, in particular when excited by the proximity of a resonance.Colliding the beams with unequal tunes Landau damping is restored.The transverse motion of two colliding beams operated with equal orunequal working points is studied by multi-particle tracking. Oursimulation shows that, for the presently proposed LHC working points, allthe combinations of working points are inside or too close to the stopbandof coherent resonances. Landau damping acts on the coherent modes and theinstability is suppressed but at the expense of a significant emittancegrowth.