Emittance growth for the LHC beams due to head-on beam-beam interaction and ground motion

The influence of ground motion on the LHC beam is estimated 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. The spectrum of the random offset, as obtained 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. They 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