Study of self-compensation of random field errors in low-β insertion triplets of hadron colliders

The presence of unavoidable field errors in superconducting low-β insertion triplets is one of the major causes for limiting the dynamic aperture of colliders during collisions. Sorting of quadrupoles of the triplets, in which the quadrupoles are installed in the ring according to a certain sequence based on the measured multipole errors, is a way to reduce the adverse effects of random field errors without an increase in the cost. Because of a very small phase advance within each triplet, significant self-compensation of random field errors of the triplet can be achieved even with sorting of a small number of quadrupoles. A study on low-β insertion triplets of the LHC interaction regions show that sorting of the quadrupoles with the vector sorting scheme is quite effective in enlargement of the dynamic aperture and improvement of the linearity of the phase-space region occupied by beams. Since the sorting scheme is based entirely on the local compensation of random errors, the effectiveness of the sorting is independent of the operational condition of the collider.