Diffusive Aperture Due to Long-Range Beam-Beam Interaction

Weak-strong tracking simulations for the Large Hadron Collider (LHC) show that long-range beam-beam collisions give rise to a well-defined diffusive aperture beyond which particles are lost quickly. We calculate the tune shift with amplitude and single-resonance driving terms for beam-beam collisions with an arbitrary transverse off-set, and then apply Chirikov resonance overlap criterion to construct an analytical estimate of the diffusive aperture induced by long-range collisions. The analytical results are compared with tracking data for the LHC.