Sorting strategies for non-local compensation of non-linear errors in large hadron colliders

The problem of sorting the random non-linear errors to improve the dynamic aperture of a magnetic lattice is considered. The paper analyses the CERN Super-Proton-Synchroton whose eight strong extraction sextupoles can be independently powered to simulate random errors. The sorting strategy based on analytical quality factors derived through one-turn maps and normal forms is applies. This approach is proven to be well suited for non-local compensation. The analysis of the whole configuration space of the possible permutations shows that the analytical solution is very close to be optimal. Good configurations are shown to be rather abundant and simulated annealing techniques do not significantly improve the solution. The effectiveness of the ordering procedure is verified for long-term six-dimensional motion and different working points