Estimates for Long-term stability for the LHC

Since about 10 years survival plots have been used to evaluate single-particle long-term stability. In a recent paper (M. Giovannozzi et al.) this concept has been reviewed, using a dynamic aperture (Dyn.Aper.) definition based on the average over different ratios of emittances. It has been shown that the survival times evaluated according to this procedure decay with the inverse of the logarithm of the number of turns in several different systems. In this paper the validity of this conjecture is tested in the case of the latest LHC lattice which has been studied extensively. The inverse log conjecture also predicts a non-zero Dyn.Aper. at infinite times called $D_{\infty}$. The tracking data are analysed for the LHC lattice to determine the relation between $D_{\infty}$ and the onset of chaos determined through Lyapunov exponents. Two different methods to automate the prediction of the Lyapunov exponent are tested and are compared with $D_{\infty}$ƒ.