Scaling laws for Beta* in the LHC interaction regions

Abstract

A lay-out for the triplet in the low-beta interaction regions of the Large Hadron Collider based on the present baseline is studied. A parametric analysis of the dependence of the beta function in the interaction point and in the triplet on the magnet length and technology (Nb-Ti or Nb3Sn) is carried out. Solutions with large aperture quadrupoles and low beta functions in the interaction point are presented. A final comparison of the triplet lay-outs using different technologies and distance to the interaction point are discussed. INTRODUCTION The Large Hadron Collider (LHC) features two lowbeta interaction regions (IR) where triplets of quadrupoles strongly focus the beams to get a beta function β in the interaction point (IP) of 55 cm [1]. In the present baseline, the geometric luminosity reduction factor due to the crossing angle in the IP prevents from obtaining significantly higher peak luminosities by a reduction of β below its nominal value [2]. This bottleneck could be bypassed by introducing an early separation dipole D0 in the detectors [3] and/or using crab cavities [4]: in this case, a further reduction of β would directly increase the peak luminosity. An upgrade relying on the reduction of β would be easier and faster to implement than a scenario based on the increase of the beam current: for this reason, studies on optics even smaller than 25 cm are ongoing [5]. In this paper we present a parametric analysis based on the approach outlined in [5] and [6] to evaluate the possible options for the triplet lay-out, namely its length, aperture and distance to the IP. Matching the aperture requirements with the gradient-aperture relation induced by the type of superconducting technology, we find a family of solutions for the lay-outs. We point out that large aperture quadrupoles allow reaching β down to 7 cm. The field quality that can be achieved in large aperture quadrupoles is estimated on the ground of the experience acquired during the LHC and Relativistic Heavy Ion Collider [7] magnet productions [8]. Issues arising from the optics and beam dynamics associated to very large β functions in the triplet can be critical: here, we sketch some scaling laws for the geometric aberrations. We finally show that a comparison of the different options strongly depends on the underlying hypothesis. Results relative to lay-outs with the same triplet length or with the same linear chromaticity are presented. BETA FUNCTIONS IN A BASELINE-LIKE TRIPLET LAY-OUT Triplet structure We consider a triplet whose structure is similar to the LHC baseline [1], i.e., is made up of two focusing quadrupoles Q1, Q3 of equal length l1, and with two defocusing quadrupoles Q2, each of length l2, in between. Let l be the distance of the beginning of the triplet from the IP (see Fig. 1). 0 25 50 Distance from IP (m) Q1