Early Indicators Of Long Term Stability In Hadron Colliders

Abstract

Early indicators of long-term stability, based on short-term tracking data, are considered in hadron colliders, such as the CERN-LHC. Two early indicators are analysed: the Lyapunov coefficient and the variation of the instantaneous nonlinear tunes. A threshold is associated to each indicator, by which a simple and automated procedure can be defined to select chaotic from regular trajectories. The methods are checked against long-term tracking for a linear lattice with a sextupole (Henon map). The results show that rather precise long-term dynamic aperture estimates can be worked out using short-term tracking data. The method is successfully applied to identify the dynamic aperture of the CERNLHC in realistic situations. 1 INTRODUCTION Fast indicators of long-term stability are very useful to speed up the numerical simulations of the dynamic aperture in hadron colliders, that for a large machine such as the planned LHC should be carried out for more than 10 7 turns. One approach is ..