Numerical optimization of collimator jaw orientations and locations in the LHC

The collimation system of LHC will consist of flat collimator jaws distributed along the IR7 lattice with the aim of limiting the maximum combined amplitudes of secondary halo particles (born along the edges of the primary collimators). The code DJ (Distribution of Jaws) computes this amplitude using a quasi-analytic algorithm (no tracking), by which the maximum initial angles are found, corresponding to trajectories escaping all secondary jaws. We report the latest version of DJ, which contains the following enhancements: (1) the orientation of each pair of jaws is a free variable (instead of using only vertical, horizontal, or 45/spl deg/ skew jaws); (2) the minimizing method used is "simulated annealing", which, for our case of a discontinuous function of up to 32 variables, always finds a global minimum. Different initial jaw distributions lead to different final ones, but they all give essentially the same maximum halo amplitude; this seems to depend only on the number of jaws and the lattice parameters, particularly the tune-split. We discuss lattice characteristics found favorable for collimation.