Emittance Growth of the LHC Beam due to the Effect of Head-on Beam-Beam Interaction and Ground Motion

The influence of ground motion on the LHC beam is estimated by applying the existing theories of particle diffusion due to a weak-strong beam-beam collision with random offset at the interaction point. Noise at odd harmonics of the betatron frequency contributes significantly to particle diffusion. Extrapolating the characteristics of the random offset from the ground motion spectrum at the LHC site shows a fast fall-off with frequency and the amplitude is very small even at the first harmonic. We find that the head-on beam-beam force in the weak-strong approximation and ground motion by themselves do not induce significant diffusion over the lifetime of the beam.