Fast indicators of long-term stability

The problem of finding effective fast indicators of long-term stability for single particle betatronic motion in hadron accelerators is considered. Two indicators are analysed: the maximal Lyapunov exponent and the variation of the instantaneous tune. An automatic procedure to select stable from unstable particles is proposed. The guess of the dynamic aperture provided by these fast indicators is checked against long-term tracking for the 4D Henon map and for a simplified version of the SPS lattice used for experiments. Both indicators prove to be very effective to determine long-term stability with a limited number of turns.