The SCFD task: Performance of a Nb3Sn Superconducting Quadrupole in an External Solenoid Field

Transcription

1 The SCFD task: Performance of a Nb3Sn Superconducting Quadrupole in an External Solenoid Field O. Delferrière 1, M. Durante 1, F. Kircher 1, O. Napoly 1, M. Segreti 1 December 30, 2008 Abstract The magnetic feasibility of the ILC interaction region based on a large aperture large gradient superconducting quadrupole magnet embedded in the field of a detector solenoid is investigated. Connected to this issue, the status of the fabrication at CEA-Saclay of a 211 T/m Nb3Sn quadrupole is described, and the progress in the design and optimisation of the ILD (former LCD) detector solenoid is reported. This report is the deliverable of the EUROTeV Superconducting Final Doublet technology R&D task (SCFD) and gives an overview of the results. 1 IRFU/SACM, CEA-Saclay, Gif-sur-Yvette, France - 1 -

2 1 Introduction The SCFD task was to deliver the test of the high gradient performance and mechanical stability of a Nb3Sn superconducting large aperture quadrupole in a external field of 2 T parallel to its axis. This test is motivated by the need to operate a large gradient superconducting doublet a few meters from to the interaction point of the ILC linear collider in order to achieve small beam spot sizes and to deliver a large luminosity. The last quadrupole magnet is consequently embedded in the large field region of the detector solenoid designed to produce 4 T peak field in the inner central region of the detector. It is therefore essential to check that the maximum magnetic field on the quadrupole conductor stays significantly below the critical magnetic field corresponding to its the operating current density (see Fig.1). In a first approximation, the module of the applied magnetic field can be calculated from the orthogonal superposition of the longitudinal 4 T solenoid field to the transverse maximum field on the quadrupole straight section. However, this approximation assumes that both magnets are infinitely long and ignores the end field or fringe field magnitude and orientation. Actually, in the quadrupole region the solenoid field bears a non-zero radial component which may add linearly to the quadrupole field, while the quadrupole return conductor at both ends generates a field which is not purely transverse. This issue can therefore be studied by a 3D magnetic calculation taking into account the size and orientation of the solenoid field in the quadrupole region, and the realistic fields of the quadrupole ends. Such a calculation, described in Section 3, should ideally be complemented by an experimental test of a high gradient quadrupole embedded in a large solenoid field, as envisioned at CEA-Saclay using the quadrupole prototype whose construction is described in Section 2. This quadrupole is made of a Nb3Sn conductor developed for the ITER project which leads to higher critical fields that the standard NbTi conductor technology (see Fig.1). Finally, in Section 4, the design and optimisation of the 4 T solenoid of the LDC-ILD detector concept, is described. Figure 1: Maximum magnetic field on the quadrupole coils for 0 and 4 T external longitudinal field B S as compared to B vs. J critical lines for the NbTi and ITER-like Nb3Sn conductors

3 2 Status of the fabrication of the large aperture Nb3Sn quadrupole at CEA-Saclay Although it is an independent R&D project which has not been funded by the EUROTeV programme, it is worth reviewing the status of the construction of the Nb3Sn superconducting quadrupole prototype which was foreseen to undergo the high field test described in the introduction. The design parameters of the quadrupole prototype are as follows: Length 1 m Aperture diameter 56 mm Gradient 211 T/m Current A Peak field on conductor 7.65 T The coils are made of two layers of Nb3Sn conductors developed for the ITER project with a critical current density J c =765 A/mm2 at 12 T and 4.2 K, leading to higher critical fields that the standard NbTi conductor technology at both 4.2 K and 1.8 K operating temperatures (see Fig.1). The cross-section of the quadrupole cold mass (see Fig.2) is based on the LHC arc quadrupoles developed at CEA-Saclay using NbTi conductors. The 1 m long prototype (see Fig.3) will be tested at high gradient at both 4.2 K and 1.8 K temperatures in dedicated cryostat in the horizontal test cryogenic station which was used for the first LHC two-in-one 3 m long quadrupole prototypes about 10 years ago. Figure 2: Cross-section of the Nb3Sn quadrupole cold mass

4 Figure 3: CAD 3D models of the Nb3Sn quadrupole magnet (top) in its Helium tank (bottom). Two dummy coils and six certified coils have been manufactured between August 2004 and February While one coil was damaged during fabrication, two coils with short circuit have been successfully repaired in April 2007 by inserting additional insulating kapton foils between the faulty cables. This technique which is routine for NbTi cables, was applied successfully for the first time on very brittle Nb3Sn cables. The four best coils have been assembled and collared in November 2007 (see Fig. 4). Figure 4: Nb3Sn quadrupole magnet (return end) - 4 -

5 Warm field measurements of the magnet made early 2008 confirmed the absence of shortcircuit and the viability of the assembled quadrupole cold mass. Cold tests at high current will establish if the coil repair operations have degraded the superconductor, or not. The cryostating of the cold mass in its LHe tank including cryogenic and electric connections (see Fig.5) has then been realized and finally the quadrupole has been inserted in the horizontal test cryostat at Saclay in December 2008 (see Fig.6). Figure 5: Cryostating of the cold mass for Nb3Sn quadrupole The cold test at high gradient (211 T/m) will be performed in the spring of 2009 at 4.2 K and 1.8 K. Figure 6: Quadrupole cold mass in Helium tank ready for test in the horizontal test station - 5 -

6 3 Magnetic field calculations of the solenoid-quadrupole configuration 3.1 Preparation of the experimental test The test of the high gradient performance and mechanical stability of a Nb3Sn superconducting large aperture quadrupole in a external field of 2 T parallel to its axis was originally foreseen in the warm bore of a 2 T MNR solenoid. However this coil has been destroyed by a major electrical breakdown in It was then foreseen to make this test with an 8 T facility SEHT using a 1 m long superconducting coil assembled at CEA-Saclay for the NeuroSpin project. The 1 m long quadrupole would have been inserted vertically half-way along the 1 m long solenoid (see Fig.7) operated from 2 T up to 4 T to allow a complete study of the superposition of the quadrupole transverse and end fields with the solenoid field, representative of the ILC final doublet conditions under various values of l*. In order to prepare these tests, a finite element modelling of the quadrupole have been done with the code OPERA 3D (see Fig.8). This modelling has allowed magnetic calculations of the quadrupole inside of the 2 T-MNR solenoid and the 4 T solenoid to be completed (see Fig.9), including the calculation of the forces applied on the poles and their resultant. This is a necessary step to design the quadrupole support structure in the test cryostat and to check that forces applied on the solenoid coil are safe. These calculations have been repeated in the case of the stronger 8 T SEHT coil as reported (in French) in the Appendix. Since the cold test of the quadrupole will fall out of the EUROTeV programme duration ( ), the experimental test in an external field is cancelled. Figure 7: Vertical test configuration of the Nb3Sn quadrupole inserted in the 4T solenoid

7 Figure 8: Finite element OPERA-3D model of both ends of the Nb3Sn quadrupole prototype (top) and 0.5 mt boundary (bottom). Figure 9: Magnetic 3 Model of the 2 T MNR coil and quadrupole - 7 -

8 3.2 Magnetic field calculations of the solenoid-quadrupole configuration The priority was set in 2006 to calculating the maximum magnetic field on the conductor the last quadrupole QD0, using the current conceptual design of the European Large Detector Concept (LDC) (see Fig. 10). The objective is to determine the quadrupole conductor technology, standard NbTi or advanced Nb3Sn if this field is larger than 10 T, and hence the quadrupole engineered design. With the assumed l*=4 m, the quadrupole is embedded in the fringe field of the 6.6 m long solenoid coil. Figure 11 shows the OPERA 3D model of this magnetic configuration and the challenge posed by this calculation in term of using a mesh compatible with the respective sizes of the solenoid and quadrupole coils. Figure 12 shows the magnitude of the magnetic field on every element of the quadrupole coils as a result of this calculation. The maximum field is of the order of 8.0 T, which is small enough to validate the NbTi conductor technology for the construction of the final doublet quadrupoles. This OPERA3D model and their calculation techniques will later be used to derive the field map of the ILC interaction region in order to accurately calculate the incoming beam transport. It is foreseen to repeat the model with the other detector solenoids (SiD) and to eventually introduce a crossing-angle. This important result was later confirmed by a simple 2 D calculation of the solenoid field alone, namely its longitudinal component B z along the axis (see Fig.13) and, related to it through the Maxwell equation B= 0, its radial component B r (see Fig.14). Figure 10: Conceptual design of the LDC detector - 8 -

9 Figure 11: Magnetic 3D modelling of the ILC-LDC superconducting solenoid with the final QD0 quadrupole inserted at l* = 4m. Figure 12: Magnitude of the magnetic field on the quadrupole coils embedded in the LDC solenoid From these field profiles, one concludes on the one hand that the longitudinal component of the solenoid field is below 2 T in quadrupole region for l* <3 m, while, on the other hand, the radial component of the solenoid field is more than two orders of magnitude smaller that the 7.65 T peak field on the quadrupole alone, and hence negligible. Adding quadratically the longitudinal 2 T to the 7.65 T transverse components, one reproduces a peak field of about 8 T on the quadrupole coil as obtained in the 3D calculation

10 Figure 13: Magnetic field profile along the axis (r=0) of the LDC solenoid Figure 14: Radial magnetic field profile at the quadrupole bore radius along the LDC solenoid In conclusion, thanks to the OPERA3D Modeller license, a complete magnetic 3D calculation of the insertion of a 250 T/m superconducting final focus quadrupole in the LDC (then ILD) detector 4 T solenoid magnet has been performed. It has shown that for l* > 3m the added longitudinal and radial components of the solenoid fringe field are small enough not to exceed the critical magnetic field on the quadrupole coils even for a NbTi conductor. 4 Design and optimisation of the LDC-ILD detector solenoid Optimisation of the European Large Detector Concept (LDC) solenoid was aimed at achieving a homogeneous 4 T field in the central TPC region of the detector while reducing the costs e.g. reducing the Iron yoke in the calorimeter end cap, and adapting to the

11 calorimeter design (see Fig.15). This work was continued in 2007 and 2008 in the context of the merging of the LDC and Asian GLD detector designs into the so-called ILD detector concept. Figure 15: Magnetic 3D modelling of the ILC-LDC superconducting solenoid New magnetic calculations have been done with the ILD Collaboration LoI parameters summarized below: Magnetic field : B 0 = 4 T nominal, 3.5 T operation Internal coil radius : R int = mm External coil radius : R ext = mm Length : L = ( ) mm Stray fields at 3.5 T: Bext 200 z=10 m from I.P. Bext 200 at (Rout m) in the radial direction A solution, so called ILD-v2, which meets the specifications, has been found (see Fig.16). This work has been presented at the ILD workshop at Cambridge (Great Britain) in September

12 B z (r=0) [T] B(z) (8m<r<9.5m) [T] Figure 16: ILD-v2 detector solenoid design at 4 T 5 Conclusion This task did not deliver the cold test of the Nb3Sn superconducting quadrupole embedded in the 2-4 T solenoid field. The main reason is that the time needed to build the quadrupole was underestimated due to manpower resources and technical problems. Although these problems have been overcome, the cold test of the quadrupole will fall out of the EUROTeV contract duration. However, the 3D magnetic and mechanical modelling efforts initiated by this task, both for the quadrupole and for the solenoid magnets, lead the way to a successful investigation of the ILC interaction region properties. Firstly, it was shown that final focus quadrupole doublets fabricated from the cheap and well proven NbTi conductor technology would be able to sustain the external magnetic field of the 4 T solenoid field foreseen in the LDC-ILC detector with 20% operational margin. Secondly, the design and the optimisation of this solenoid, namely the coil and its Iron yoke, were also made possible by the resources available for this task thus producing a continuously improving design over the EUROTeV period. It has allowed the European LDC collaboration to propose a solid conceptual design at the basis of the proposal for the ILD detector Letter of Intend, merging the LDC and GLD collaborations. This design has been recently improved to include new requirements like stray field limits. Acknowledgement This work is supported by the Commission of the European Communities under the 6 th Framework Programme Structuring the European Research Area, contract number RIDS Appendix: Forces applied to the 8 T coil SEHT in presence of the Nb3Sn quadrupole

13 COMMISSARIAT À L ÉNERGIE ATOMIQUE DEPARTEMENT D ASTROPHYSIQUE, DE PHYSIQUE DES PARTICULES, DE PHYSIQUE NUCLÉAIRE ET DE L INSTRUMENTATION ASSOCIÉE Service d'ingénierie des Systèmes DIRECTION DES SCIENCES DE LA MATIÈRE Emetteur JM Baze Note de Calcul Projet SEHT Ref : DAPNIA/SIS/888/06 JMB Destinataires : M. Durante,Ph Chesny,P. Vedrine FORCES VUES DANS LA STATION SEHT EN PRESENCE DU QUADRIPOLE NB3SN 1. Calcul des densités de courant sur les pôles Sensibilité a un décalage des axes solénoïde et Qpôle axes confondus Qpôle décalé de 10cm par rapport à l axe du solénoïde de 10 cm dans la direction OY pôle en court circuit?? Calcul inverse : action d un Q pôle sur le solénoïde L induction due au pôle Z Les forces Calcul de l influence du Q pôle complet...4 Pour un pole à 90 degrés du précédent (inversion du sens de I)...4 Pour l ensemble des poles Inductance du Q pôle (avec l aide du professeur FP Juster ) Energie stockée Inductance...5 P A 20/ JMBaze Statut indice date rédacteur vérificateur approbateur DAPNIA/SIS/888/06/JMB 1/5 date 22/09/2006 Fichier SEHT/Note_forces

14 1. Calcul des densités de courant sur les pôles Ce calcul a été fait au préalable dans le cadre de la modélisation du Qpôle On a donc injecté un courant total de A dans le câble Figure 1-1 Répartition des courants dans le pôles Les différences dans les têtes viennent du mode de calcul : résolution d un problème de potentiel sur les brins, la densité de courant se renforce dans l intérieur des coudes. Il n est pas possible de rendre compte de la transposition des câbles à l intérieur du Rutherford. Néanmoins l intégrale du courant est conservé dans les sections droites ce qui doit conduire a une erreur faible (dans le cas présent) Cet aimant est placé dans le champ du solénoïde de la station développant un champ au centre de 8T ( Nota ce champ n est pas purement axial vu le rapport longueur ouverture du solénoïde). Si le champ max du solénoïde est inferieur il suffit de faire une règle de 3 les forces étant proportionnelles à Bsol ) Aucune présence de fer doux dans le système 2. Sensibilité à un décalage des axes solénoïde et Qpôle On suppose ici le Qpôle en situation normale de fonctionnement Comme il n y a pas de fer l intégrale de Jq*Bsq sur le volume des conducteurs donne la distribution des forces sur les pôles 2.1. axes confondus Dans cette configuration les forces vues par les pôles s équilibrent parfaitement Résultante générale en Newtons E E E Qpôle décalé de 10cm par rapport à l axe du solénoïde de 10 cm dans la direction OY Les forces restent négligeables De toute façon il est impensable d en arriver a ces extrémités et dans ce cas il est inutile de recalculer l effet d un pôle en court circuit DAPNIA/SIS/888/06/JMB 2/5 date 22/09/2006 Fichier SEHT/Note_forces

15 pôle en court circuit?? En l absence de tout cahier des charge et information en provenance du SACM au sujet d éventuelles situations exceptionnelles On examine les cas d un pôle en court circuit ( Ici le pôle supérieur haut ) Dans ces conditions il apparaît une force transverse Z X Y Figure 2-1 distribution des forces sur le pole RESULTANTE FORCES 9.339E E E E+04 RESULTANTE MOMENTS E E E E Calcul inverse : action d un Q pôle sur le solénoïde 3.1. L induction due au pôle Z+ Z Y Y Figure 3-1 Le champ du Qpôle sur le solénoïde DAPNIA/SIS/888/06/JMB 3/5 date 22/09/2006 Fichier SEHT/Note_forces

16 3.2. Les forces Figure 3-2 Les forces du pôle Z+ sur le solénoïde RESULTANTE FORCES E E E E+04 RESULTANTE MOMENTS E E E E+04 On constate une différence entre les résultats des deux calculs qui est due certainement au peu de raffinement du maillage du solénoïde mais l ordre de grandeur est correct 3.3. Calcul de l influence du Q pôle complet Dans la mesure ou le maillage du solénoïde est régulier et si le Q pôle est centré sur l axe du solénoïde on peut calculer l action générale par de simples rotations des champs de forces et inversions de signes Pour un pole à 90 degrés du précédent (inversion du sens de I) Figure 3-3 Force dues au pôle a 90 degrés du précédent DAPNIA/SIS/888/06/JMB 4/5 date 22/09/2006 Fichier SEHT/Note_forces

17 Pour l ensemble des poles Figure 3-4 Forces dues a l'ensemble des 4 pôles Le comportement mécanique du solénoïde peut être abordé a partir de cette distribution des forces ( il faudra y adjoindre évidement sa contribution propre ) Nota les forces calculées ici sont relatives a un solénoïde donnant 8T au centre et a un Qpole voyant un courant de 11800A donc a rectifier si ces valeurs sont ne sont inferieures 4. Inductance du Q pôle (avec l aide du professeur FP Juster ) C est un sous produit des modélisations effectues pour NB3Sn 4.1. Energie stockée A partir du potentiel vecteur produit par le Q pôle sur lui même on calcule l énergie stockée soit L intégrale. Adv 1 2 J. Adv J donne J pour 1 quart de pôle Donc l énergie totale stockée est (0.5*7127.8) * 4*4 = J 4.2. Inductance C est également 1/2LI 2 avec I = Ampères D ou L = H soit 0.8 mh DAPNIA/SIS/888/06/JMB 5/5 date 22/09/2006 Fichier SEHT/Note_forces