Alain Mailfert

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 Nb3Sn 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 Nb3Sn, is discussed using both scaling laws and finite element models.

Magnetic compensation of the gravity by using superconducting axisymmetric coils: spherical harmonics method

It is important for space research to study the behavior of fluids such as liquid oxygen and liquid hydrogen under weightless conditions (microgravity). In addition, since 1991 some magnetic ground-based stations have allowed compensating gravity and meeting space conditions. Magnetic devices allow low-cost microgravity experiments with unlimited time. The goal of these techniques is to reach the same or better conditions (residual acceleration of the studied fluid) than those during parabolic flights. In this paper, several specific distributions of the magnetic field are determined. These distributions allow compensating gravity by means of axisymmetric coils (solenoids). This paper introduces several distributions of the residual forces useful for different kinds of microgravity experiments.

A Method for Coil Design of Superconducting Quadrupoles Based on Sector Coils and Fourier Series

In this paper we present a novel method to optimize quadrupole coil cross-sections based on the cos 2¿-type. We first approximate real coil blocks made of cables with concentric sectors powered with a constant current density to make use of analytical expressions of the magnetic field based on the Fourier series development. This allows a rapid evaluation of the field harmonics which permits an almost exhaustive scan on sectors position and dimensions for coil layouts made of up to five sectors. The coil layouts having a larger short-sample gradient can be further explored, approximating them with blocks of Rutherford cables. This second step requires a second fine tuning of the cross-section around the previously found optimum. The method has been used to design a proposed coil cross-section for the new inner triplet quadrupole for the LHC.

Magnetic and Mechanical Design of a 130 mm Aperture

For the next generation of dipoles for accelerators, two main challenges come into play. In one hand, high dipolar fields in the range of 13 to 15 T are targeted. In the other hand, large apertures (above 80 mm) are required in the interaction regions. These two requirements lead to two issues. First, a new superconductor has to replace the NbTi as its limits have been reached around 10 T with the LHC. The superconducting material liable to be its successor is the Nb3Sn. However, it is a very mechanical stress sensitive material. Up to now, a mechanical stress of 150 MPa is supposed to degrade its critical properties. Second, large aperture dipole can not be considered with the well-known cosine theta design. Indeed, above 88 mm, azimuthal Lorentz forces in this magnetic configuration produces mechanical stresses on the coil mid- plane higher than the acceptable limit. In this paper, an alternative coil arrangement based on intersecting ellipses and limiting the mechanical stresses is proposed for a 130 mm aperture dipole. The first part of this paper is dedicated to the magnetic study of this magnet. We can underline the fact that the field quality required in particle accelerators can be reached with a bore field of about 13 T. The second part deals with the mechanical structure of the magnet which is necessary to withstand the Lorentz forces involved and to apply pre-stress.

{\hbox{Nb}}_{3}{\hbox{Sn}}

The capabilities of copper coil electromagnet are dealt in this paper. The poles of this device must generate into the air gap a magnetic flux density invariant in one direction. This electromagnet is used in order to perform magnetic levitation of paramagnetic or diamagnetic substances. The poles shape are specific and allow to obtain a magnetic flux density and a gradient of the squared magnetic flux density, which have the same direction as the axis of symmetry of the poles

Dipole Magnet

Magnetic compensation of gravity allows for ground-based experiments to be carried out under weightless conditions at reasonable cost and without the time limitation of systems such as zero-g airplanes or drop towers. Most of the time classical superconducting solenoids are operated to perform such experiments, which lead to a poor quality of the gravity compensation due to the non-ideal shape of the current and field distribution. In order to improve the quality of simulated microgravity, scientists need to build novel ground-based systems fully dedicated to magnetic levitation. The magnetic design of these levitation apparatuses would be based on theoretical studies of magnetic forces and associated field distributions. The work presented in this paper demonstrates the possibility of producing a magnetic force on paramagnetic and diamagnetic materials that is constant, thus providing a uniform gravity compensation, along a segment in a 3D geometry. These results come from both the decomposition in spher...

Design and Optimization by zn Complex Function of Magnet Electric Poles in order to obtain Magnetic Levitation

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.