Here we analyze the measurements relative to the field quality of the RHIC and LHC superconducting quadrupoles to find out the dependence of field errors on the size of the magnet aperture. Finally, we show that the uncertainty in the mean of the magnetic field errors is for most of the harmonics related to statistical errors due to the limited number of magnets in the series, and not because of systematic defects in the coilĪ possible scenario for the luminosity upgrade of the Large Hadron Collider is based on large aperture quadrupoles to lower β* in the interaction regions. It makes possible to explain some phenomenon observed on the dispersion of the magnetic measurement in a quadrupole series. Following this, an analytical method based on statistics is developed. A comparison with values obtained for Nb-Ti magnets is also presented. The estimate has been obtained by using an existing method and from tow recently built Nb3Sn magnet series. Subsequently, for the first time, an estimate of the reproducibility in the coil-blocks positioning in Nb3Sn magnets is given. Secondly, the magnetic design of the quadrupole coil cross-section is realized using a novel optimization method based on analytical equations of the magnetic field. It allows estimating the energy with a precision of 10 %. First, to rapidly estimate the magnetic energy stored in a cos2-type quadrupole, an analytical formula based on the Fourier transform of the current is developed. This new quadrupole features an unprecedented large aperture (120 mm) and opens the way toward large aperture quadrupoles. It aims at replacing the current insertion quadrupoles used in the Large Hadron Collider (LHC) at CERN by 2014. The main objective of the work presented in this thesis is the design of a quadrupole magnet based on Nb-Ti. A single coupling-loss-induced quench unit ensures a safe magnet operation with a 300 K hotspot temperature. The design is mechanically constrained with a conventional collar structure leading to collaring peak stress of 115 MPa. A discussion on cable windability allows for the selection of one design generating 367 T/m. An exploration of the strand diameter (0.7–0.9 mm), the cable size (40–60 strands), as well as the protection delay (30–40 ms) is performed on two-dimensional (2-D) magnetic designs of the FCC main quadrupole. Indeed, the idea is to only challenge the ∼5000 FCC main dipoles and stay at a relatively low complexity for the ∼700 FCC main quadrupoles so they have a limiting impact on the machine operation and reliability. Therefore, the number of coil layers has been reduced from four to two and the load-line margin has been increased from 14% to 20% compared to previous investigations (“Design of a Nb3Sn 400 T/m quadrupole for the future circular collider,” The goal of this study is to propose an alternative FCC quadrupole design where the risk from both their fabrication and their operation in the machine is reduced compared to previous analysis.
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