Stability diagrams of colliding beams in the Large Hadron Collider

Most hadron synchrotrons rely on lattice nonlinearities for Landau damping of impedance driven coherent modes of oscillation. However, in a collider, the presence of beam-beam interactions strongly modifies the transverse amplitude detuning and therefore the resulting stability diagram. A numerical tool to evaluate the effect of beam-beam on the stability diagram has been developed and is used to discuss observations during different phases of the operational cycle of the Large Hadron Collider during the 2012 proton run. In particular, we show the evolution of the stability diagram when the strength of long range beam-beam interactions is increased, during the betatron squeeze. Also, we investigate the stability of beams colliding with a small transverse offset and compare to observations of instabilities when bringing the beams into collision and while leveling the luminosity.