E. Augé, Voyage au coeur de la matière, Paris: Belin-CNRS, 2002.

Y. Ajima, The MQXA quadrupoles for the LHC low-beta insertions, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.550, issue.3, pp.499-513, 2003.
DOI : 10.1016/j.nima.2005.04.092

A. and A. Large, Ion Collider Experiment

M. Anerella, The RHIC magnet system, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.499, issue.2-3, pp.280-315, 2003.
DOI : 10.1016/S0168-9002(02)01940-X

F. M. Asner, High field superconducting magnets, 1999.

W. Ansorge, Some basic design parameters of the ISR SC quadrupole, 1973.

A. Asner, On a semi-analytical method for field and force calculation in coil ends of cylindrical aperture superconducting dipole and quadrupole magnets, pp.86-94, 1986.

B. Bellesia, Correlation between magnetic field quality and mechanical components of the Large Hadron Colider main dipole, 2006.

B. Bellesia, Field quality in low-superconducting quadrupoles and impact on the beam dynamics for the large hadron collider upgrade, 2007.

B. Bellesia, Random Errors in superconducting dipoles, Proceeding of European Particle Accelerator Conference, 2006.

R. A. Beth, An Integral Formula for Two???Dimensional Fields, Journal of Applied Physics, vol.38, issue.12, pp.4689-4692, 1967.
DOI : 10.1063/1.1782086

J. Billan, Construction of a prototype superconducting quadrupole magnet for high luminosity insertion at the CERN intersecting storage ring, CERN Yellow Report, pp.76-92, 1976.

F. Borgnolutti, 130 MM aperture quadrupoles for the LHC luminosity upgrade, 2007 IEEE Particle Accelerator Conference (PAC), 2007.
DOI : 10.1109/PAC.2007.4440208

F. Borgnolutti, Nouveaux quadrupoles à grande ouverture pour l'accroissement de la luminosité du LHC, Poster présenté à Neuvièmes Journées de Cryogénie et Supraconductivité à, pp.25-27, 2009.

F. Borgnolutti, Analytic Estimates of Magnetic Energy in Superconducting Quadrupoles, IEEE Transactions on Applied Superconductivity, vol.18, issue.4, pp.1774-1780, 2008.
DOI : 10.1109/TASC.2008.2007271

F. Borgnolutti, Reproducibility of the Coil Positioning in ${\rm Nb}_{3}{\rm Sn}$ Magnet Models Through Magnetic Measurements, IEEE Transactions on Applied Superconductivity, vol.19, issue.3, pp.1100-1105, 2009.
DOI : 10.1109/TASC.2009.2018530

F. Borgnolutti, A Method for Coil Design of Superconducting Quadrupole Based on Sector Coils and Fourier Transform, To be presented at the Magnet Technology Conference to be held in Hefei, 2009.

F. Borgnolutti, Quadrupole design study for the LHC Phase-I Upgrade, LHC IR Upgrade Working Group, vol.14, 2008.

F. Borgnolutti, Update on the coil cross-section of the low-beta quadrupole, LHC IR Upgrade Working Group 18, 2008.

R. Bossert, Construction experience with MQXB quadrupole magnets built at Fermilab for the LHC interaction regions, IEEE Transactions on Appiled Superconductivity, vol.13, issue.2, pp.1297-1300, 2003.
DOI : 10.1109/TASC.2003.812653

R. Bosset, Development of TQC01, a 90 mm<tex>$hboxNb_3hbox Sn$</tex>Model Quadrupole for LHC Upgrade Based on SS Collar, IEEE Transactions on Applied Superconductivity, vol.16, issue.2, pp.370-373, 2006.
DOI : 10.1109/TASC.2006.871320

L. Bottura, Field errors decay and "snap-back" in LHC model dipoles, IEEE Transactions on Appiled Superconductivity, vol.7, issue.2, pp.602-605, 1997.
DOI : 10.1109/77.614576

L. Bottura, A practical fit for the critical surface of NbTi, IEEE Transactions on Appiled Superconductivity, vol.10, issue.1, pp.1054-1057, 2000.
DOI : 10.1109/77.828413

L. Bottura, Standard Analysis Procedures for Field Quality Measurement of the LHC Magnets, CERN-LHC Project Document LHC-XMT-ES-0001 rev 0.2, 2001.

H. Brechna, Superconducting Magnet Systems, 1973.
DOI : 10.1063/1.3069061

O. Burning, The LHC main ring, CERN-LHC Design Report, 2004.

S. Caspi, Fabrication and Test of TQS01???A 90 mm ${\rm Nb}_{3}{\rm Sn}$ Quadrupole Magnet for LARP, IEEE Transactions on Applied Superconductivity, vol.17, issue.2, p.1122, 2007.
DOI : 10.1109/TASC.2007.899244

M. L. China, Comparative study of heat transfer from Nb-Ti and Nb3Sn coils to He II, Phys. Rev. Spec. Top. Accel. Beams, vol.11, 2008.

W. Cooper, Fermilab Tevatron quadrupoles, IEEE Transactions on Magnetics, vol.19, issue.3, pp.1372-1377, 1983.
DOI : 10.1109/TMAG.1983.1062268

E. D. Courant, Theory of the Alternating ?Gradient Synchrotron, Science Direct- Annals of Physics, vol.281, pp.1-2, 1957.

W. G. Davies, The theory of the measurement of magnetic multipole fields with rotating coil magnetometers, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.311, issue.3, pp.399-436, 1992.
DOI : 10.1016/0168-9002(92)90637-J

A. Devred, Investigation of wire motion in superconducting magnets, IEEE Trans. Magn, vol.27, issue.2, pp.2132-2135, 1991.

A. Devred, Review of superconducting dipole and quadrupole magnets for particle accelerators, DAPNIA/STCM 99-24, 1999.

A. Devred and D. Trassart, Magnetic Field Produced by a Single Current Line near or within a Ferromagnetic Cylinder or Tube, CERN Departemental Report, 2005.

A. Devred, Practical low-temperature superconductors for electromagnets, CERN Yellow Report, pp.2004-2010, 2004.

E. Durand, Magnetostatique, Masson et Cie, 1968.

J. W. Ekin, effect of transverse compressive strain on the critical current and upper critical field of Nb3Sn, J. Appl. Phys, vol.62, issue.12, 1987.

J. W. Ekin, Strain Effects in Superconducting Compounds, Adv. Cryo. Eng. (Materials), vol.30, pp.823-836, 1984.
DOI : 10.1007/978-1-4613-9868-4_90

S. Feher, Development and Test of LARP Technological Quadrupole (TQC) Magnet, IEEE Transactions on Applied Superconductivity, vol.17, issue.2, 2007.
DOI : 10.1109/TASC.2007.898420

P. Ferracin, Field quality analysis of the next generation IR quadrupole for the LHC, Proceedings of the 2003 Bipolar/BiCMOS Circuits and Technology Meeting (IEEE Cat. No.03CH37440), 2003.
DOI : 10.1109/PAC.2003.1288748

P. Ferracin, Modeling of random geometric errors in superconducting magnets with applications to the CERN Large Hadron Collider, Physical Review Special Topics - Accelerators and Beams, vol.10, issue.12, p.112403, 2000.
DOI : 10.1109/77.828177

P. Fessia, Parametric Analysis of Forces and Stresses in Superconducting Quadrupole Sector Windings, IEEE Transactions on Applied Superconductivity, vol.17, issue.2, pp.1269-1272, 2007.
DOI : 10.1109/TASC.2007.898523

P. Fessia, Parametric Analysis of Forces and Stresses in Superconducting Quadrupole Sector Windings, IEEE Transactions on Applied Superconductivity, vol.17, issue.2, 2007.
DOI : 10.1109/TASC.2007.898523

P. J. Ferry, Analysis of the Performance of the Eight Superconducting Quadrupoles for the Lep Low-Beta Insertions, 1989.
DOI : 10.1007/978-94-009-0769-0_43

P. Granieri, Development of the Cable Insulation for the LHC Triplet Upgrade Phase-I " , Presented in a TE seminar at CERN in, 2009.

R. Gupta, Estimating and adjusting field quality in superconducting accelerator magnets, Proceeding of Particle Accelerator Conference, 1996.
DOI : 10.2172/1119480

R. Gupta, Tuning shims for high field quality in superconducting magnets, IEEE Transactions on Magnetics, vol.32, issue.4, 1996.
DOI : 10.1109/20.508569

R. W. Hanft, Studies of time dependence of fields in Tevatron superconducting dipole magnets, IEEE Transactions on Magnetics, vol.25, issue.2, pp.1647-1651, 1989.
DOI : 10.1109/20.92616

J. Herrera, Random Errors in the Magnetic Field Coefficients of Superconducting Magnets, Proceeding of Particle Accelerator Conference, 1985.
DOI : 10.1109/TNS.1985.4334470

J. Herrera, Random errors in the magnetic field coefficients of superconducting quadrupoles magnets, 1987.

G. A. Kirby, Design of the 70 mm twin aperture superconducting quadrupole for the LHC dump insertion, IEEE Transactions on Appiled Superconductivity, vol.7, issue.2, pp.562-565, 1996.
DOI : 10.1109/77.614566

V. V. Kashikhin, Field quality study in Nb 3 Sn accelerator magnets, Proceeding of Particle Accelerator Conference, 2005.

J. P. Koutchouk, A Solution for Phase-one Upgrade of the LHC Low-Beta Quadrupoles based on Nb-Ti, 2007.

M. J. Lamm, Nb/sub 3/Sn accelerator magnet development around the world, IEEE Transactions on Appiled Superconductivity, vol.13, issue.2, pp.1278-1283, 2003.
DOI : 10.1109/TASC.2003.812646

M. J. Lamm, Test results of Fermilb-built quadrupoles for the LHC interaction regions, Proceeding of European Particle Accelerator Conference, 2006.

. Lhcb, The Large Hadron Collider Beauty experiment

A. Madur, Contribution à la métrologie magnétique dans les multipoles d'accélèrateurs : Les quadrupoles du Synchrotron Soleil, 2006.

R. Meinke, Superconducting magnet system for HERA, IEEE Transactions on Magnetics, vol.27, issue.2, pp.1728-1734, 1991.
DOI : 10.1109/20.133525

R. Ostojic, Conceptual Design of the LHC Interaction Region Upgrade: Phase-I, 2008.

R. Ostojic, The Construction of the Low-Beta Triplets for the LHC, Proceeding of Particle Accelerator Conference, 2005.

R. Ostojic, Low-Beta quadrupole designs for the LHC luminosity upgrade, Proceeding of Particle Accelerator Conference, 2005.

F. Regis and P. Fessia, Study of the quadrupole collar structure, LHC IR Upgrade Working Group, vol.14, 2008.

L. Rossi and E. Todesco, Electromagnetic design of superconducting quadrupoles, Physical Review Special Topics - Accelerators and Beams, vol.9, issue.10, 2006.
DOI : 10.1063/1.1662353

L. Rossi, Course on the LHC luminosity upgrade, CERN academic training, 2009.

S. Russenschuck and C. Lhc-, ROXIE: A Computer Code for the Integrated Design of Accelerator Magnets, 1999.

S. Russenschuck, Electromagnetic design and mathematical optimization methods in magnet technology

S. Russenschuck, Oral presentation gave in the framework of the LHC IR Upgrade Working Group, 2009.

G. Sabbi, Design Studies of ${\hbox{Nb}}_{3}{\hbox{Sn}}$ High-Gradient Quadrupole Models for LARP, IEEE Transactions on Applied Superconductivity, vol.17, issue.2, pp.1051-1054, 2007.
DOI : 10.1109/TASC.2007.897292

P. R. Sarma, General coil-shape in superconducting quadrupole magnets for generating the perfect field, Nuc. Inst. And Meth, vol.568, issue.2, 2006.

P. R. Sarma, Coil shape of a two-fold symmetric perfect superconducting quadrupole for use in common-coil twin magnets, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.564, issue.1, 2006.
DOI : 10.1016/j.nima.2006.04.035

W. Scandal, Random errors induced by the superconducting windings in the LHC dipoles, IEEE Transactions on Appiled Superconductivity, vol.10, issue.1, 2000.
DOI : 10.1109/77.828184

E. E. Schmidt, Magnetic Field Data on Fermilab Energy Saver Quadrupoles, IEEE Trans. Nuc. Sci, issue.4, 1983.

K. and ?. H. Mess, Superconducting accelerator magnets, 1996.
DOI : 10.1142/3219

URL : http://www.worldscientific.com/doi/pdf/10.1142/9789814261029_fmatter

S. Snfilippo, Axis Measurements, Field Quality and Quench Performance of the First LHC Short Straight Sections, IEEE Transactions on Appiled Superconductivity, vol.15, issue.2, 2005.
DOI : 10.1109/TASC.2005.849504

T. Sen, Second generation high gradient quadrupoles for the LHC interaction regions, PACS2001. Proceedings of the 2001 Particle Accelerator Conference (Cat. No.01CH37268), 2001.
DOI : 10.1109/PAC.2001.988131

K. Sugita, Analytical calculation of field error due to radial coil distortions of the LHC low-beta quadrupole magnets, IEEE Transactions on Appiled Superconductivity, vol.12, issue.1, 2002.
DOI : 10.1109/TASC.2002.1018733

L. T. Summers, A model for the prediction of Nb/sub 3/Sn critical current as a function of field, temperature, strain, and radiation damage, IEEE Transactions on Magnetics, vol.27, issue.2, 1991.
DOI : 10.1109/20.133608

E. Todesco, Field Harmonic, US Particle Accelerator School, 20090.

E. Todesco, Field Quality in Low-Beta Superconducting Quadrupoles and Impact on the Beam Dynamics for the Large Hadron Collider Upgrade, Phys. Rev. Spec. Top. Accel. Beams, vol.10, p.62401, 2007.

D. Tommasini and D. Richter, New Cable Insulation Scheme Improving Heat Transfer to Superfluid Helium in Nb-Ti Superconducting Accelerator Magnets, Proceeding of European Particle Accelerator Conference, 2008.

S. Turner, Measurement and alignement of accelerator and detector magnets, Cern Accelerator School, 1997.

G. V. Velev, Field Quality Measurements and Analysis of the LARP Technology Quadrupole Models, IEEE Transactions on Applied Superconductivity, vol.18, issue.2, pp.184-187, 2008.
DOI : 10.1109/TASC.2008.922272

G. V. Velev, Magnetic field measurement of the LHC inner triplet quadrupole produced at Fermilab, Proceeding of European Particle Accelerator Conference, 2004.

A. Vv, Poission-Superfish, group of codes supported by the Los-Alamos National Laboratory Under U.s. Government contract W-7405-ENG-36

J. Wei, Field quality evaluation of the superconducting magnets of the Relativistic Heavy Ion Collider, Proceedings Particle Accelerator Conference, 1995.
DOI : 10.1109/PAC.1995.504691

E. Wildner, Parametric study of energy deposition in the LHC inner triplet for the phase I upgrade, EPAC, 2008.

N. Martin and . Wilson, Superconducting Magnets, 1983.

R. R. Wilson, The Tevatron, Physics Today, vol.13, issue.10, p.763, 1978.
DOI : 10.1109/TMAG.1977.1059312

URL : https://hal.archives-ouvertes.fr/in2p3-00509098

R. Wolf, Analytical calculation of field errors due to small and random coil motion in cosine-theta type accelerator magnets

A. V. Zlobin, Nb 3 Sn accelerator magnet technology at Fermilab, Proceeding of Particle Accelerator Conference, 2007.

A. V. Zlobin, Aperture limitation for 2 nd generation Nb3Sn LHC IR quadrupoles, Proceeding of Particle Accelerator Conference, 2003.