Beam-Beam Effect with an External Noise in LHC

In absence of synchrotron radiation, proton beams do not have any damping mechanism for incoherent betatron motion. A noise, which kicks beam particles in the transverse plane, gives a coherent betatron amplitude. If the system is linear, the coherent motion is maintained in amplitude. Nonlinear force, beam-beam and beam-electron cloud interactions, cause a decoherence of the betatron motion keeping the amplitude of each beam particle, with the result that an emittance growth arises. We focus only on fast noise with a correlation time of 1-100 turns. Slower noise is less serious, because it is regarded as an adiabatic change like a closed orbit change. As sources of the noise, we consider the bunch by bunch feedback system and phase jitter of cavities which turns to transverse noise via a crab cavity.