Sorting Strategies for the Lhc Dipoles

Unavoidable field-shape imperfections are present in the superconducting magnets of modern hadron colliders, due to mechanical tolerances, persistent currents, design imperfections, coil deformations and iron saturation. The residual multipolar errors, typically of the order of a few units in 10 4 at the usual reference radius of 1 cm, have a detrimental effect on the stability of the particle orbits. A sound design of the machine layout, with well focused orbit functions and a suited set of multipolar correctors, may help in improving the beam stability. However, quite often, the dynamic aperture (hereafter DA), is strongly dependent on the random part of the multipolar imperfections and on the specific distribution of the errors along the machine azimuth. Sorting strategies can be applied to provide the mutual compensation of the residual errors. This procedure is quite demanding, therefore it is crucial to evaluate in detail the expected beneficial effects on beam dynamics. In fact, all the magnets have to be carefully measured as they are manufactured and qualified in terms of the random imperfections. In addition, a sizeable number of magnets must be available for sorting before the final installation. 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 DA. These quantities are called Quality Factors (hereafter QF) [1; 2]: the search of 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 the 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 alghoritms[3; 4]. In Section 2 we present in detail the sorting strategies. In Section 3 we apply them to a realistic LHC model. Conclusions are drawn in Section 4.