Sorting strategies for the LHC dipoles

Two techniques are proposed for sorting the LHC dipoles. The first one uses the perturbative analysis of the nonlinear betatron motion to find dynamical quantities which allow to evaluate rapidly the dynamical aperture (DA). These quantities are called quality factors. The search for a satisfactory rearrangement is performed by generating random permutations of the magnetic elements, selecting the permutation which optimises the QF and hence the DA. The effectiveness of this method depends on the degree of correlation of the QF with the numerical estimate of the dynamic aperture. The second approach is based on the local cancellation of random errors by pairing the magnets with similar errors in magnitude and sign and placing the pairs in strategic positions along the azimuth of the accelerator. We refer to these methods as deterministic algorithms