Scaling Laws for Magnetic Energy in Superconducting Quadrupoles

The stored energy in superconducting magnets is one of the main ingredients needed for the quench calculation and for designing quench protections. Here we propose an analytical formula based on the Fourier transformation of the current density flowing within the winding to determine the magnetic energy stored in superconducting quadrupoles made of sector coils. Two corrective coefficients allowing to estimate the energy enhancement produced either by current grading or by the presence of an unsaturated iron yoke are respectively derived from a numerical and an analytical study. This approach is applied to a set of real quadrupoles to test the validity limits of the scaling law, which are shown to be of ~10%

130 mm Aperture Quadrupoles for the LHC Luminosity Upgrade

Several studies for the LHC luminosity upgrade pointed out the need for low-beta quadrupoles with apertures larger than the present baseline (70 mm). In this paper we focus on the design issues of a 130 mm aperture quadrupole. We first consider the Nb-Ti option, presenting a magnetic design with the LHC dipole and quadrupole cables. We study the electromagnetic forces and we discuss the field quality constraints. For the Nb$_{3}$Sn option, we sketch three designs, two based on the LARP 10 mm width cable, and one on a larger cable with the same strand. The issue of the stress induced by the e.m. forces, which is critical for the Nb$_{3}$Sn, is discussed using both scaling laws and finite element models

Energy Deposition Studies for the LHC Insertion Region Upgrade Phase-I

While the Large Hadron Collider (LHC) at CERN is starting operation with beam, aiming to achieve nominal performance in the shortest term, the upgrade of the LHC interaction regions is actively pursued in order to enhance the physics reach of the machine. Its first phase, with the target of increasing the LHC luminosity to 2-3 1034cm-2s-1, relies on the mature Nb-Ti superconducting magnet technology and is intended to maximize the use of the existing infrastructure. The impact of the increased power of the collision debris has been investigated through detailed energy deposition studies, considering the new aperture requirements for the low-ß quadrupoles and a number of other elements in the insertions. Effective solutions in terms of shielding options and design/layout optimization have been envisaged and the crucial factors have been pointed out

Parametric Study of Energy Deposition in the LHC Inner Triplet for the Phase 1 Upgrade

To be able to make a global parametric analysis and to have some basic understanding of the influence of critical parameters, scaling laws may be of help. For the design of the LHC insertion regions triplets, among the critical parameters the energy deposited in the superconducting triplet plays a fundamental role in avoiding magnet quench, too heavy load on the cryogenic system, and degradation of the materials due to radiation. The influence on energy deposition of the lay-out key parameters, such as the magnet apertures, the magnet lengths and positions, has been studied for beta* = 0.25

AC Loss in the Superconducting Cables of the CERN Fast Cycled Magnet Prototype

Fast Cycled Superconducting Magnets (FCM's) are an option of interest for the long-term consolidation and upgrade plan of the LHC accelerator complex. The economical advantage of FCM's in the range of 2 T bore field, continuously cycled at 0.5 Hz repetition rate, depends critically on the AC loss property of strand and cable. In this paper we report the results of the AC loss measurements that we have performed both on strands and cables manufactured for the CERN FCM prototype program

Analysis of Optical Layouts for the Phase 1 upgrade of the CERN Large Hadron Collider Insertion Regions

In the framework of the studies for the upgrade of the insertions of the CERN Large Hadron Collider, four optical layouts were proposed with the aim of reducing the beta-function at the collision point down to 25 cm. The different candidate layouts are presented. Results from the studies performed on mechanical and dynamic aperture are summarized, together with the evaluation of beam-beam effects. Particular emphasis is given to the comparison of the optics performance, which led to retain the most promising layouts for further development

Canted-cosine-theta magnet (CCT)-A concept for high field accelerator magnets

Canted-Cosine-Theta (CCT) magnet is an accelerator magnet that superposes fields of nested and tilted solenoids that are oppositely canted. The current distribution of any canted layer generates a pure harmonic field as well as a solenoid field that can be cancelled with a similar but oppositely canted layer. The concept places windings within mandrel's ribs and spars that simultaneously intercept and guide Lorentz forces of each turn to prevent stress accumulation. With respect to other designs, the need for pre-stress in this concept is reduced by an order of magnitude making it highly compatible with the use of strain sensitive superconductors such as Nb3Sn or HTS. Intercepting large Lorentz forces is of particular interest in magnets with large bores and high field accelerator magnets like the one foreseen in the future high energy upgrade of the LHC. This paper describes the CCT concept and reports on the construction of CCT1 a "proof of principle" dipole

Multipoles Induced by Inter-Strand Coupling Currents in LARP Nb3Sn Quadrupoles

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Analytic Estimates of Magnetic Energy in Superconducting Quadrupoles

In this paper, we propose analytical formulae to determine the magnetic energy stored in superconducting quadrupoles made of sector coils. The study is based on the Fourier transformation of the current density flowing within the coils. The case of real magnets (i.e., magnets which are not made of pure sector coils) is treated and a heuristic corrective coefficient allowing taking into account the energy enhancement due to current grading is derived from a numerical study. We also introduce the effect of an unsaturated iron yoke on the stored energy and we discuss the issue of the yoke saturation