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 o f the mechanisms that lead to long-term particle loss is outlined, usi ng numerical simulations. The Lyapunov exponent and the variation of t he nonlinear tunes with time are computed with an automated procedure and compared to model-independent thresholds: the motion of particles is considered stable when the early indicators are below the threshold . in addition, a law is proposed to interpolate the dynamic aperture a s a function of the number of turns, and its extrapolation allows one to predict the dynamic aperture at large number of turns. The law has some analogies with the estimate given by the Nekhoroshev theorem. Com parisons of our predictions with the results of standard element-by-el ement tracking are carried out for a realistic model of the CERN-LHC.