Prediction of Long-Term Stability in Large Hadron Colliders

Short-term tracking data are used to compute early indicators of long-term stability in large hadron colliders. A phenomenological picture of the mechanisms that lead to long-term particle loss is outlined, using numerical simulations. The Lyapunov exponent and the variation of the nonlinear tunes with time are computed with an automated procedure and compared to model-independent thresholds. In addition, a law is proposed to interpolate the dynamic aperture as a function of the number of turns. The law can be explained in terms of the Nekhoroshev theorem. The motion of particles is considered stable for ever when the early indicators are below the threshold whilst the dynamic aperture at large number of turns can be computed by extrapolating our empiric law à la Nekhoroshev. Comparisons of our predictions with the results of standard element-by-element tracking are carried out for a realistic model of the CERN-LHC.