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Mechanical design of the superconducting solenoid package for the SARAF-linac project
Nuclear Inst. and Methods in Physics Research, A 955 (2020) 163312
Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
Mechanical design of the superconducting solenoid package for the SARAF-linac project F. Rossi a ,∗, B. Gastineau a , M. Jacquemet b , S. Ladegaillerie a , F. Leseigneur a , C. Madec a , A. Madur a , N. Pichoff a a b
IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France GANIL, CEA, Université Paris-Saclay, F-14076 Caen, France
ARTICLE
INFO
Keywords: Solenoid Superconducting magnet Cryogenic Composite Mechanical design Finite elements
ABSTRACT The Soreq Applied Research Accelerator Facility (SARAF) in Israel will provide an intense source of fast neutrons and radioactive nuclei for neutron applications, to explore rare nuclear reactions and produce new types of radiopharmaceuticals for nuclear medicine. CEA Paris-Saclay is in charge of the design, construction and commissioning of this superconducting linear particle accelerator (linac) to produce the first particle beams in 2022. The superconducting linac is part of the SARAF accelerator and it will be equipped with twenty identical solenoid packages arranged in four 5-metre long cryomodules; they are located between the cavities and they ensure the beam control. The solenoid package is a complex mechanical system and it is designed to operate at cryogenic temperatures. It comprises the main solenoid coil with an integrated square flux density of 3.5 T2 m , two lateral shielding coils to reduce the fringe fields on the cavities as well as two pairs of steering coils. This ensemble is enclosed in a stainless steel helium vessel. In this study, we present the mechanical design of the first prototype of the solenoid package with a particular focus on the main coil, whereby the superconducting wire (Nb–Ti/Cu) is wound and cured on two extremity flanges made of epoxy reinforced with glass cloth (G-10). The modelling of the solenoid components is carried out using Finite Element Analysis (FEA) and the results of simulations are used to assess the structural integrity of the components. Moreover, an extensive literature review is conducted to collect the mechanical properties at cryogenic temperature of the composite materials used for the construction. Finally, the results of the experimental validation of the first solenoid prototype are presented. The experimental campaign is carried out using a cryostat designed on purpose to reproduce both the final operating temperature and magnetic field.
1. Introduction The Soreq Applied Research Accelerator Facility (SARAF), under construction at Soreq Nuclear Research Center, is conceived as an Israeli national infrastructure for applied research and training in various areas of nuclear science and engineering [1]. Began in 2003, it is expected to be completed in 2023. The high ion current enables generation, via nuclear reactions, of high fluxes of fast neutrons. These last ones can be slowed down to energies similar to those of neutrons from research reactors. SARAF is designed to serve as a model for the possible replacement of research reactors by environmentally friendly facilities that do not make use of fissile materials. Applications at SARAF will include neutron-based imaging, nuclear and particle physics research, radiopharmaceuticals studies, development and production. ∗
In the linear particle accelerator, the beam is accelerated in ultrahigh vacuum (10−7 Pa) through different acceleration stages and collides with a target to produce neutrons (Fig. 1). The Super-Conducting Linac (SCL) is in charge of accelerating the beams to their final energy; it is made of four cryomodules and they are housing the accelerating cavities made of Niobium as well as the solenoids operating at cryogenic temperatures (Fig. 2). Since during the acceleration the beam is naturally growing and deviating, the superconducting coils in the solenoid packages combine the function of focusing and steering the beam. Designed to operate at very low temperatures and with high magnetic fields, the magnet package is a very complex mechanical system, whereby reinforced plastics are used to assure the electrical insulation between the superconducting coils and their metallic supports, as well as to carry very high structural loads. In most of the cases, these parts are mechanically coupled with materials having different
Corresponding author. E-mail address: [email protected] (F. Rossi).
https://doi.org/10.1016/j.nima.2019.163312 Received 22 October 2019; Received in revised form 6 December 2019; Accepted 17 December 2019 Available online 19 December 2019 0168-9002/© 2019 Elsevier B.V. All rights reserved.
F. Rossi, B. Gastineau, M. Jacquemet et al.
Nuclear Inst. and Methods in Physics Research, A 955 (2020) 163312
Fig. 1. Acceleration scheme of the SARAF linac (top). Superconducting linac made of four 5 m long cryomodules (bottom).
Fig. 2. Cryomodule housing the accelerating cavities made of Niobium and the magnet packages.
thermal expansions, which in turn may produce regions of high stress
successful design. This paper presents a detailed modelling analysis
concentrations in the components during the severe cooling down.
of the main components of a superconducting magnet package for a
Therefore, the prediction of the structural behaviour is crucial for a
particle accelerator, with particular focus on the inner solenoid where 2
F. Rossi, B. Gastineau, M. Jacquemet et al.
Nuclear Inst. and Methods in Physics Research, A 955 (2020) 163312
Fig. 3. Magnet package components and cross-section view.
Fig. 4. Self-supporting main coil with extremity flanges and electrical insulating layer made of G-10.
the extremity flanges are made of glass-reinforced epoxy. Given the
without any additional internal support or reinforcement, will be called hereafter ‘‘self-supporting’’. As a result of an extensive literature review, the material properties at cryogenic temperatures are presented in the manuscript and used throughout the finite element study to predict the mechanical behaviour at the normal operating mode. Using the results of the simulations, different failure criteria are then implemented to assess the structural integrity of all the components. Finally, the construction
structural loading on the main coil, resulting from the magnetic field and the differential thermal expansion of the materials when the operating conditions are reached, the numerical analysis will show that the main coil can withstand the loads without any additional bobbin made of metal, whose main purpose would be just to improve the overall stiffness. This mechanical solution, where the coil is carrying the loads 3
F. Rossi, B. Gastineau, M. Jacquemet et al.
Nuclear Inst. and Methods in Physics Research, A 955 (2020) 163312
The main solenoid is a self-supporting coil where the extremity flanges are made of G-10, a fibreglass laminate where multiple layers of glass cloth are stacked and soaked in epoxy resin; given the fabrication process, it is an orthotropic material (Fig. 4). G-10 is a grade designation for glass epoxy laminates, like FR-4 that is mainly used in electronics and detectors for particle physics research [4]. The superconducting wire has a diameter of 0.5 mm; it is wound on a central spool and confined between the two composite flanges during the winding process as described in [5]. The number of turns defines the final diameter of the solenoid and an additional layer of epoxy with glass fabric is added on the external surface of the coil to improve the overall electrical insulation. After the curing process in the oven, the spool is removed and the self-supporting solenoid is shown in Fig. 5. A central support made of stainless steel is assuring the accurate positioning of the two shielding coils and it is designed to house the four steering coils that are wound on separate permanent spools. The insulation thickness for both the shielding and steering coil is 1 mm. The BPM-tank head one-piece machined block is the common face used to align as well as to sustain the main and shielding coil supports; the beam pipe is welded to it. This design solution allows to improve the machining accuracy of the common reference system and to align the geometrical axis of the coils with respect to BPM axis within a coaxiality error of ±0.250 mm. The magnetic axis has been measured at room temperature confirming that it lies within the same tolerance. Fiducial markers are placed on the external surface of the tank and they are used to identify the mechanical axis of the BPM, based on the metrology previously done on a CMM machine. During the integration in the cryomodule, the solenoid packages and the cavities are aligned within a coaxiality error of ±1 mm.
Fig. 5. Extremity flanges mounted on the central spool before winding (left). Self-supporting main coil after curing (right).
and experimental validation of a first solenoid prototype are presented and discussed. 2. The magnet package The magnet package consists of different Nb–Ti/Cu coils enclosed in a tank made of a stainless steel (AISI 316LN) and having an external diameter of 240 mm; the total length of the full package is 344 mm (flange-to-flange), while the aperture diameter is 40 mm. The liquid helium is circulating around the coils and setting the operating temperature at 4.45 K, the secondary vacuum in the cryomodule is assuring the thermal insulation of the helium vessel. The particle beam is travelling in ultra-high vacuum and focused by the main solenoid coil with an integrated square flux density of 3.5 T2 m (this includes a 10% margin on the operating value). The beam is then steered by the steering coils, while the shielding coils are designed to reduce the magnetic fringe field on the neighbouring cavities; the on-axis fringe field of the magnet package is limited to 20 mT at the cavity flange. Finally, a pair of Beam Position Monitors (BPM) [3] mounted on the upstream flange of the helium vessel is contributing to the beam orbit correction process (Fig. 3).
3. Mechanical behaviour of composites at cryogenic temperature Mechanical properties of metals at cryogenic temperatures are widely available in literature [2], while for composites they are less accessible. For the metals shown in Fig. 6, it is worth noting that at low temperatures both the Young’s modulus and the yield strength slightly increase, while the amount of thermal expansion strongly depends on the material considered. Assuming a cooling down from room temperature (293 K) to absolute zero (Fig. 7), the metal that experiences the highest thermal shrinkage is aluminium (0.420%), while the lowest one occurs for titanium (0.140%).
Fig. 6. Young’s modulus (left) and yield strength (right) of metals at cryogenic temperatures [2].
4
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Nuclear Inst. and Methods in Physics Research, A 955 (2020) 163312
mechanical testing under extreme environmental conditions [8]. The mechanical properties of the base metals constituting the superconducting wire are compared to stainless steel (Table 2); Young’s modulus and Poisson’s ratio are evaluated at 4 K, while the material strength is given at room temperature, resulting in an additional (and intentional) safety margin during the final structural assessment. It is worth noting that the thermal contraction of Nb–Ti (0.188%) and copper (0.324%) are quite different. Given these assumptions for the base materials, the mechanical properties for the metallic composite (i.e. the superconducting wire) can be evaluated by applying the rule of mixture (Table 3). Due to the actual volume fraction and the mechanical properties of the base metals, the thermal contractions along the different orthotropic directions are almost equivalent and similar to stainless steel; the Young’s modulus is marginally different along the principal directions either. The structural assessment of the superconducting wire is carried out by using the von Mises criterion for each of the base materials. 4. Numerical modelling and structural assessment A finite element model of the magnet package has been developed in Ansys to study the mechanical behaviour of the superconducting solenoid under normal operating conditions and to assess its structural integrity. The initial geometry designed in Catia has been simplified by removing all the unnecessary features for the modelling (holes, screws, fillets, etc.) in order to improve the overall mesh quality; hexahedral elements with quadratic shape function are used for most of the parts of the magnet package, except for the helium vessel that is modelled with shell elements. Bonded contacts have been defined between the coils and their supports, while the material properties have been assigned on the basis of the assumptions previously made. A mesh sensitivity analysis has been carried out to define the optimal number of elements to have both accurate results and a reasonable computational time; the resulting mesh is constituted of about one million nodes and it is shown in Fig. 8. The structural integrity must be assessed not only under normal operating conditions, but also throughout the entire lifecycle of the mechanical system, therefore a buckling analysis is performed in order to study the loading during the leak-tightness test done to qualify the welding of the helium vessel. As vacuum is generated inside the tank, the ambient pressure results in a compressive stress on the outer shell; the high safety factor calculated for the first buckling mode can assure that no instability will lead to any structural failure of the vessel during this acceptance test. Before activating the superconducting coils, the magnet package is cooled down from room temperature to 4.45 K by pumping liquid helium inside the tank; the absolute pressure of the cryogenic coolant is 2.25 bar. The displacements along the beam axis are shown in Fig. 9; due to the imposed temperature difference, the longitudinal contraction of the vessel is 0.870 mm. The extremity bellows are therefore in charge of both connecting the magnet package to the neighbouring accelerating cavities and compensating the differential deformations inside the cryomodule. The dissimilar thermal expansions of the materials used in the magnet package are responsible of non-negligible stress amplification during the cooling down. The stress field predicted by the finite element model is shown in Fig. 10. It is worth noting that, since the coefficient of thermal expansion of stainless steel is slightly bigger than the one of the superconducting wire, the shielding coils are experiencing a compressive force, while their support a tensile one; the same happens for the steering coils. For both the steel supports and the superconducting coils, the equivalent von Mises stress predicted by FEA is smaller than allowable one. Concerning the self-supporting main solenoid, the superconducting wire is wound and glued on the two extremity flanges made of G-10. Since the thermal expansion in the plane of the glass cloth is similar to that one of Nb–Ti/Cu wire, a negligible stress amplification occurs
Fig. 7. Thermal expansion of metals (top) and composites (bottom) from room temperature to absolute zero [2].
On the other side the thermal expansion of composites is severely affected by the principal directions; since G-10 is an orthotropic material, the shrinkage in the plane of the glass fabric (−0.241%) is about one third of the value along the transversal direction (−0.706%), where the only contribution of epoxy becomes preponderant. Given these considerations, an erroneous definition of the orthotropic directions in the design phase might result in high stress amplifications during severe cooling down, in particular if orthotropic composites are coupled with materials having very different coefficients of thermal expansion. Table 1 is the result of a detailed literary review and summarizes the mechanical properties of G-10 at 4 K; due to the intrinsic orthotropicity of the material, the Young’s modulus and Poisson’s ratio are strongly dependent on the principal directions too. On the other hand, a failure criterion for composite materials at cryogenic temperatures is not thoroughly defined or universally accepted in literature; therefore, the structural assessment in this study is carried out by considering two different criteria: the maximum strain allowable in the plane of reinforcing [6] and the Mohr–Coulomb criterion in the normal direction [7]. Like for metals, both the allowable tensile and shear stress slightly increase as the temperature goes down. It is worth noting that in the experimental study presented in [7], data are not available below 77 K. The superconducting wire is a metal matrix composite, where the Niobium–Titanium (Nb–Ti) filaments are embedded in a copper matrix having a diameter of 0.5 mm. The electric insulation is provided by a 19 μm-thick layer of Formvar enclosing the wire; the use of epoxy as insulator material for electric wires is also a common practice in 5
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Nuclear Inst. and Methods in Physics Research, A 955 (2020) 163312
Fig. 8. Finite element model of the magnet package (∼106 nodes).
Table 1 Mechanical properties of G-10 at 4 K. G-10 laminate 20 12 6 0.17 0.33 0.5 25
Shear modulus [6]
[GPa]
Poisson’s ratio [6]
[–]
Strain allowable in plane of reinforcing [6] Tensile stress allowable normal to reinforcing plane [7] (at room temperature) Shear stress allowable across reinforcing planes [7] (at room temperature)
[%] [MPa]
E1 = E2 E3 G1 = G2 = G3 𝜈12 𝜈13 = 𝜈23 𝜀a1 = 𝜀a2 𝜎a3
[MPa]
𝜏a13 = 𝜏a23
19
Thermal contraction (293 K -> 4 K) [2]
[%]
𝛥L1 ∕L1 = 𝛥L2 ∕L2 𝛥L3 ∕L3
0.241 0.706
Young’s modulus [6]
[GPa]
Table 2 Mechanical properties of Nb–Ti, Cu and AISI 316LN at 4 K.
Young’s modulus Poisson’s ratio Yield strength
[GPa] [–] [MPa]
E 𝜈 𝜎y
Tensile strength
[MPa]
𝜎UTS
Thermal contraction (293 K -> 4 K)
[%]
𝛥L/L
Nb–Ti [9]
Copper OFE [2] (annealed)
AISI 316LN [2] (annealed)
88 0.38 410 [10] (at room temperature) 450 [10] (at room temperature) 0.188
138 0.34 86 [11]
208 0.28 610 [11]
455 [11]
988 [11]
0.324
0.297
Table 3 Mechanical properties of the superconducting wire at 4 K (V = volume fraction). Nb–Ti/Cu wire (VNb−−Ti = 0.74%) Young’s modulus
[GPa]
Shear modulus Poisson’s ratio
[GPa] [–]
Thermal contraction 𝛥L/L (293 K -> 4 K)
[%]
E1 = ENbTiVNbTi + ECu VCu E2 = E3 = (ENbTi ECu )/(ECu VNbTi + ENbTi VCu ) 1/G12 = VNbTi∕GNbTi + VCu ∕GCu 𝜈12 = 𝜈NbTi VNbTi + 𝜈Cu VCu 𝛼1 = 1/E1 (𝛼NbTi ENbTi VNbTi + 𝛼Cu ECu VCu ) 𝛼2 = 𝛼NbTi VNbTi (1 + 𝜈f ) + 𝛼Cu VCu (1 + 𝜈Cu ) – 𝛼1 𝜈12
at the coil-flange interface along the radial direction. On the contrary, the 1-mm-thick layer of G-10 wrapped around the inner and outer surface of the main coil experiences a higher stress intensification in the overlapping area of the extremity flanges. In fact, although both the
117 111 41 0.36 0.280 0.260
flanges and the cylindrical insulations are made of the same material, their thermal expansions along the beam axis are extremely different, since the orthotropic directions are defined differently. The glass cloth embedded in the epoxy of the extremity flanges is perpendicular to 6
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Nuclear Inst. and Methods in Physics Research, A 955 (2020) 163312
Fig. 9. Displacements along the beam axis after the cooling down from room temperature to 4.45 K.
Fig. 10. Predicted stress field in the coils (Nb–Ti/Cu) and their supports (AISI 316LN) after cooling down. Allowable stress: 𝜎y,AISI316LN@4K /1.5 = 407 MPa and 𝜎y,Cu@4K /1.5 = 58 MPa.
the beam axis, while in the insulating layer it is parallel; therefore, the longitudinal thermal expansion of the flanges is three times bigger, since the contribution of the epoxy matrix is more important in this direction. Nevertheless, both the maximum strain criterion in the plane of reinforcing and the Mohr–Coulomb criterion in the normal direction are satisfied for all the G-10 structural parts (Fig. 11). The magnetic field can be predicted in Ansys by considering the current density in the main and the shielding coils (300 A/mm2 ) as well as the steering coils (250 A/mm2 ); the magnetic forces are then imported in the structural model as body force density and shown in Fig. 12. It is worth noting that, due to the presence of the steering coils,
the magnetic field is not symmetrical and therefore the displacements are not either. Finally, the normal operating conditions in the cryomodule are investigated by considering in the finite element model of the magnet package both the cooling down and the coil powering; based on the stress intensity field predicted by the modelling (Fig. 13), all the failure criteria used to assess the structural integrity of the mechanical system are satisfied (Fig. 14). 7
F. Rossi, B. Gastineau, M. Jacquemet et al.
Nuclear Inst. and Methods in Physics Research, A 955 (2020) 163312
Fig. 11. Structural assessment for G-10 parts after cooling down, according to the Mohr–Coulomb and maximum allowable strain criteria.
Fig. 12. Body force density as result of the magnetic field (left) and corresponding coils displacements (right).
5. Prototype construction and experimental validation
the series production; this task has been outsourced to the external company ‘‘Elytt Energy’’ in Bilbao (Spain). Based on the design developed at CEA Paris-Saclay and presented in this paper, some minor modifications have been done by the firm, aimed at improving the overall machining and the assembly procedure of the mechanical pieces constituting the
In order to validate the concept and the corresponding numerical modelling, the construction of a prototype is necessary before starting 8
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Nuclear Inst. and Methods in Physics Research, A 955 (2020) 163312
Fig. 13. Predicted stress field in the coils (Nb–Ti/Cu) and their supports (AISI 316LN) under normal operating conditions (after cooling down and coil powering). Allowable stress: 𝜎y,AISI316LN@4K /1.5 = 407 MPa and 𝜎y,Cu@4K /1.5 = 58 MPa.
Fig. 14. Structural assessment for G-10 parts under normal operating conditions (after cooling down and coil powering), according to the Mohr–Coulomb and maximum allowable strain criteria.
magnet package. The same company has been in charge of defining
before the final welding of the helium vessel. As requested by CEA,
the cable routing inside the tank and the electrical connections for
Elytt has carried out a quench analysis to show that the specifications
the power supplies. Fig. 15 shows the magnet package fully assembled
provided for the hot spot temperature during quench (<150 K for the 9
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Nuclear Inst. and Methods in Physics Research, A 955 (2020) 163312
Fig. 15. Mechanical supports of the main, steering (left) and shielding coils (right).
Fig. 16. Acceptance tests for the magnet package: leak-tightness test and integration in the cryostat to reproduce the final operating conditions (temperature and coil powering).
main and shielding coils, <40 for the steerers) are met. The numerical study has been done separately for each coil, by developing a finite element model where the boundaries are considered adiabatic (i.e. no quench back can occur) and the quench is initiated by imposing locally an initial temperature rise. The prototype has been delivered at CEA Paris-Saclay in June 2019, just after some preliminary quality tests done at the same company to certify the leak-tightness of the vessel and the electrical continuity of the connections. A cryostat has been designed on purpose to test the superconducting solenoid at CEA Paris-Saclay under the same operating conditions of the cryomodule (temperature and electric current). As shown in Fig. 16, the magnet package is lowered down in the cryogenic vessel and liquid helium is pumped into the tank housing the coils; the secondary vacuum generated inside the cryostat assures the thermal insulation. When the operating temperature of 4.45 K is reached, the
superconducting coils are powered on and generating a maximum magnetic field of 6.4 T at the centre. The test current has been 91 A which corresponds to 110% of the design value, while the quench current reached during testing has been 95 A, thus resulting in a margin to quench of 15% with respect to the design value (note that the design value is already 10% above the operating value). Throughout all the entire duration of the test campaign, the thermal, electric and magnetic values obtained have been shown to be extremely stable and meet the technical specifications, thus finally validating the overall design of the magnet package. 6. Conclusions The superconducting magnet package for the SARAF linac project is a very complex mechanical system and it is designed to operate at very 10
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Nuclear Inst. and Methods in Physics Research, A 955 (2020) 163312
low temperatures and with high magnetic fields. Reinforced plastics are used to assure the electrical insulation between the superconducting coils and their metallic supports, but also to carry very high structural loads. In particular, the novel design of the main solenoid is based on a self-supporting coil, whereby the extremity flanges are made of glass-reinforced epoxy (G-10). In addition, this orthotropic composite is mechanically coupled with other materials having dissimilar coefficient of thermal expansions. Given the severe cooling down necessary to reach the normal operating mode, the most highly stressed regions in the components have been designed by carefully identifying/defining the orthotropic directions during the design phase. The mechanical properties of composite materials at cryogenic temperatures, which are not widely available in literature, have been collected and presented in this paper. Given this extensive literary review, a detailed FE model has been built to study accurately the mechanical behaviour of the magnet package as well as to predict the stress field induced by different material shrinkage during the cooling down from room temperature to 4.45 K. The normal operating conditions, at which the coils are powered on and generating the high magnetic field, have also been investigated in the simulations. The maximum stresses predicted and computed by the FE analysis have been subsequently plugged into the failure criteria for safe-life assessment. Two different failure criteria have been used for glass-reinforced plastics, the maximum strain criterion in the plane of reinforcing and the Mohr–Coulomb criterion in the normal direction. The predictions indicate that all the various components fully satisfy the structural integrity criteria. Finally, the validation of both the design and numerical modelling have been carried out by constructing an experimental prototype of the superconducting solenoid. The first magnet package has been built by ‘‘Elytt Energy’’ in Bilbao (Spain), and then tested in a cryostat developed by CEA Paris-Saclay, where the actual operating conditions of the cryomodule have been reproduced (both temperature and magnetic field). Given the promising results of the experimental validation, the series production of twenty (plus two spares) additional superconducting magnet packages for the SARAF linac is expected to be launched shortly.
CRediT authorship contribution statement F. Rossi: Conceptualization, Methodology, Formal analysis, Investigation, Writing - original draft, Writing - review & editing, Visualization, Supervision. B. Gastineau: Conceptualization, Methodology, Validation, Writing - review & editing, Visualization, Supervision, Project administration, Funding acquisition. M. Jacquemet: Resources, Supervision, Project administration, Funding acquisition. S. Ladegaillerie: Resources, Supervision . F. Leseigneur: Conceptualization, Methodology. C. Madec: Resources, Supervision, Project administration. A. Madur: Conceptualization, Methodology, Formal analysis. N. Pichoff: Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition. Acknowledgements The authors sincerely thank the all the members of the SARAF working group. Special thanks go to ‘‘Elytt Energy’’ in Bilbao (Spain) for the production of the first prototype of the magnet package that has been successfully tested at CEA Paris-Saclay. References [1] I. Mardor, et al., The soreq applied research accelerator facility (SARAF) – overview, research programs and future plans, Eur. Phys. J. A 54 (2018) 91. [2] J.W. Ekin, Experimental Techniques for Low Temperature Measurements, Oxford University Press, 2006. [3] P. Forck, et al., Beam Position Monitors, CERN Accelerator School, 2008. [4] F. Rossi, J. Elman, B. Jose, Mechanical modelling of the micromegas detectors for the atlas new small wheel, Compos. Struct. 207 (2019) 53–61. [5] S. Sanz, Fabrication and testing of the first magnet package prototype for the srf linac of LIPAC, in: Proceedings of IPAC2011, San Sebastian, Spain, 2011. [6] Structural Design Criteria for ITER Magnet Components, 2004. [7] K. Kitamura, Cryogenic shear fracture tests of interlaminar organic insulation for a forced-flow superconducting coil, IEEE Trans. Magn. 30 (4) (1994). [8] M.G. Tarantino, L. Weber, A. Mortensen, Effect of hydrostatic pressure on flow and deformation in highly reinforced particulate composites, Acta Mater. 117 (2016) 345–355. [9] K.M. Wilson, Mechanical Cavity Design for 100 MV Upgrade Cryomodule, IPAC2013. [10] ASTM, Standard Specification for Titanium and Titanium Alloy, 2011. [11] C.L. Goodzeit, Superconducting Accelerator Magnets – An Introduction to Mechanical Design and Construction Methods, Brookhaven National Laboratory, 2001.
Data availability statement The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.
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Contents lists available at ScienceDirect
Nuclear Inst. and Methods in Physics Research, A journal homepage: www.elsevier.com/locate/nima
Mechanical design of the superconducting solenoid package for the SARAF-linac project F. Rossi a ,∗, B. Gastineau a , M. Jacquemet b , S. Ladegaillerie a , F. Leseigneur a , C. Madec a , A. Madur a , N. Pichoff a a b
IRFU, CEA, Université Paris-Saclay, F-91191 Gif-sur-Yvette, France GANIL, CEA, Université Paris-Saclay, F-14076 Caen, France
ARTICLE
INFO
Keywords: Solenoid Superconducting magnet Cryogenic Composite Mechanical design Finite elements
ABSTRACT The Soreq Applied Research Accelerator Facility (SARAF) in Israel will provide an intense source of fast neutrons and radioactive nuclei for neutron applications, to explore rare nuclear reactions and produce new types of radiopharmaceuticals for nuclear medicine. CEA Paris-Saclay is in charge of the design, construction and commissioning of this superconducting linear particle accelerator (linac) to produce the first particle beams in 2022. The superconducting linac is part of the SARAF accelerator and it will be equipped with twenty identical solenoid packages arranged in four 5-metre long cryomodules; they are located between the cavities and they ensure the beam control. The solenoid package is a complex mechanical system and it is designed to operate at cryogenic temperatures. It comprises the main solenoid coil with an integrated square flux density of 3.5 T2 m , two lateral shielding coils to reduce the fringe fields on the cavities as well as two pairs of steering coils. This ensemble is enclosed in a stainless steel helium vessel. In this study, we present the mechanical design of the first prototype of the solenoid package with a particular focus on the main coil, whereby the superconducting wire (Nb–Ti/Cu) is wound and cured on two extremity flanges made of epoxy reinforced with glass cloth (G-10). The modelling of the solenoid components is carried out using Finite Element Analysis (FEA) and the results of simulations are used to assess the structural integrity of the components. Moreover, an extensive literature review is conducted to collect the mechanical properties at cryogenic temperature of the composite materials used for the construction. Finally, the results of the experimental validation of the first solenoid prototype are presented. The experimental campaign is carried out using a cryostat designed on purpose to reproduce both the final operating temperature and magnetic field.
1. Introduction The Soreq Applied Research Accelerator Facility (SARAF), under construction at Soreq Nuclear Research Center, is conceived as an Israeli national infrastructure for applied research and training in various areas of nuclear science and engineering [1]. Began in 2003, it is expected to be completed in 2023. The high ion current enables generation, via nuclear reactions, of high fluxes of fast neutrons. These last ones can be slowed down to energies similar to those of neutrons from research reactors. SARAF is designed to serve as a model for the possible replacement of research reactors by environmentally friendly facilities that do not make use of fissile materials. Applications at SARAF will include neutron-based imaging, nuclear and particle physics research, radiopharmaceuticals studies, development and production. ∗
In the linear particle accelerator, the beam is accelerated in ultrahigh vacuum (10−7 Pa) through different acceleration stages and collides with a target to produce neutrons (Fig. 1). The Super-Conducting Linac (SCL) is in charge of accelerating the beams to their final energy; it is made of four cryomodules and they are housing the accelerating cavities made of Niobium as well as the solenoids operating at cryogenic temperatures (Fig. 2). Since during the acceleration the beam is naturally growing and deviating, the superconducting coils in the solenoid packages combine the function of focusing and steering the beam. Designed to operate at very low temperatures and with high magnetic fields, the magnet package is a very complex mechanical system, whereby reinforced plastics are used to assure the electrical insulation between the superconducting coils and their metallic supports, as well as to carry very high structural loads. In most of the cases, these parts are mechanically coupled with materials having different
Corresponding author. E-mail address: [email protected] (F. Rossi).
https://doi.org/10.1016/j.nima.2019.163312 Received 22 October 2019; Received in revised form 6 December 2019; Accepted 17 December 2019 Available online 19 December 2019 0168-9002/© 2019 Elsevier B.V. All rights reserved.
F. Rossi, B. Gastineau, M. Jacquemet et al.
Nuclear Inst. and Methods in Physics Research, A 955 (2020) 163312
Fig. 1. Acceleration scheme of the SARAF linac (top). Superconducting linac made of four 5 m long cryomodules (bottom).
Fig. 2. Cryomodule housing the accelerating cavities made of Niobium and the magnet packages.
thermal expansions, which in turn may produce regions of high stress
successful design. This paper presents a detailed modelling analysis
concentrations in the components during the severe cooling down.
of the main components of a superconducting magnet package for a
Therefore, the prediction of the structural behaviour is crucial for a
particle accelerator, with particular focus on the inner solenoid where 2
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Fig. 3. Magnet package components and cross-section view.
Fig. 4. Self-supporting main coil with extremity flanges and electrical insulating layer made of G-10.
the extremity flanges are made of glass-reinforced epoxy. Given the
without any additional internal support or reinforcement, will be called hereafter ‘‘self-supporting’’. As a result of an extensive literature review, the material properties at cryogenic temperatures are presented in the manuscript and used throughout the finite element study to predict the mechanical behaviour at the normal operating mode. Using the results of the simulations, different failure criteria are then implemented to assess the structural integrity of all the components. Finally, the construction
structural loading on the main coil, resulting from the magnetic field and the differential thermal expansion of the materials when the operating conditions are reached, the numerical analysis will show that the main coil can withstand the loads without any additional bobbin made of metal, whose main purpose would be just to improve the overall stiffness. This mechanical solution, where the coil is carrying the loads 3
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The main solenoid is a self-supporting coil where the extremity flanges are made of G-10, a fibreglass laminate where multiple layers of glass cloth are stacked and soaked in epoxy resin; given the fabrication process, it is an orthotropic material (Fig. 4). G-10 is a grade designation for glass epoxy laminates, like FR-4 that is mainly used in electronics and detectors for particle physics research [4]. The superconducting wire has a diameter of 0.5 mm; it is wound on a central spool and confined between the two composite flanges during the winding process as described in [5]. The number of turns defines the final diameter of the solenoid and an additional layer of epoxy with glass fabric is added on the external surface of the coil to improve the overall electrical insulation. After the curing process in the oven, the spool is removed and the self-supporting solenoid is shown in Fig. 5. A central support made of stainless steel is assuring the accurate positioning of the two shielding coils and it is designed to house the four steering coils that are wound on separate permanent spools. The insulation thickness for both the shielding and steering coil is 1 mm. The BPM-tank head one-piece machined block is the common face used to align as well as to sustain the main and shielding coil supports; the beam pipe is welded to it. This design solution allows to improve the machining accuracy of the common reference system and to align the geometrical axis of the coils with respect to BPM axis within a coaxiality error of ±0.250 mm. The magnetic axis has been measured at room temperature confirming that it lies within the same tolerance. Fiducial markers are placed on the external surface of the tank and they are used to identify the mechanical axis of the BPM, based on the metrology previously done on a CMM machine. During the integration in the cryomodule, the solenoid packages and the cavities are aligned within a coaxiality error of ±1 mm.
Fig. 5. Extremity flanges mounted on the central spool before winding (left). Self-supporting main coil after curing (right).
and experimental validation of a first solenoid prototype are presented and discussed. 2. The magnet package The magnet package consists of different Nb–Ti/Cu coils enclosed in a tank made of a stainless steel (AISI 316LN) and having an external diameter of 240 mm; the total length of the full package is 344 mm (flange-to-flange), while the aperture diameter is 40 mm. The liquid helium is circulating around the coils and setting the operating temperature at 4.45 K, the secondary vacuum in the cryomodule is assuring the thermal insulation of the helium vessel. The particle beam is travelling in ultra-high vacuum and focused by the main solenoid coil with an integrated square flux density of 3.5 T2 m (this includes a 10% margin on the operating value). The beam is then steered by the steering coils, while the shielding coils are designed to reduce the magnetic fringe field on the neighbouring cavities; the on-axis fringe field of the magnet package is limited to 20 mT at the cavity flange. Finally, a pair of Beam Position Monitors (BPM) [3] mounted on the upstream flange of the helium vessel is contributing to the beam orbit correction process (Fig. 3).
3. Mechanical behaviour of composites at cryogenic temperature Mechanical properties of metals at cryogenic temperatures are widely available in literature [2], while for composites they are less accessible. For the metals shown in Fig. 6, it is worth noting that at low temperatures both the Young’s modulus and the yield strength slightly increase, while the amount of thermal expansion strongly depends on the material considered. Assuming a cooling down from room temperature (293 K) to absolute zero (Fig. 7), the metal that experiences the highest thermal shrinkage is aluminium (0.420%), while the lowest one occurs for titanium (0.140%).
Fig. 6. Young’s modulus (left) and yield strength (right) of metals at cryogenic temperatures [2].
4
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mechanical testing under extreme environmental conditions [8]. The mechanical properties of the base metals constituting the superconducting wire are compared to stainless steel (Table 2); Young’s modulus and Poisson’s ratio are evaluated at 4 K, while the material strength is given at room temperature, resulting in an additional (and intentional) safety margin during the final structural assessment. It is worth noting that the thermal contraction of Nb–Ti (0.188%) and copper (0.324%) are quite different. Given these assumptions for the base materials, the mechanical properties for the metallic composite (i.e. the superconducting wire) can be evaluated by applying the rule of mixture (Table 3). Due to the actual volume fraction and the mechanical properties of the base metals, the thermal contractions along the different orthotropic directions are almost equivalent and similar to stainless steel; the Young’s modulus is marginally different along the principal directions either. The structural assessment of the superconducting wire is carried out by using the von Mises criterion for each of the base materials. 4. Numerical modelling and structural assessment A finite element model of the magnet package has been developed in Ansys to study the mechanical behaviour of the superconducting solenoid under normal operating conditions and to assess its structural integrity. The initial geometry designed in Catia has been simplified by removing all the unnecessary features for the modelling (holes, screws, fillets, etc.) in order to improve the overall mesh quality; hexahedral elements with quadratic shape function are used for most of the parts of the magnet package, except for the helium vessel that is modelled with shell elements. Bonded contacts have been defined between the coils and their supports, while the material properties have been assigned on the basis of the assumptions previously made. A mesh sensitivity analysis has been carried out to define the optimal number of elements to have both accurate results and a reasonable computational time; the resulting mesh is constituted of about one million nodes and it is shown in Fig. 8. The structural integrity must be assessed not only under normal operating conditions, but also throughout the entire lifecycle of the mechanical system, therefore a buckling analysis is performed in order to study the loading during the leak-tightness test done to qualify the welding of the helium vessel. As vacuum is generated inside the tank, the ambient pressure results in a compressive stress on the outer shell; the high safety factor calculated for the first buckling mode can assure that no instability will lead to any structural failure of the vessel during this acceptance test. Before activating the superconducting coils, the magnet package is cooled down from room temperature to 4.45 K by pumping liquid helium inside the tank; the absolute pressure of the cryogenic coolant is 2.25 bar. The displacements along the beam axis are shown in Fig. 9; due to the imposed temperature difference, the longitudinal contraction of the vessel is 0.870 mm. The extremity bellows are therefore in charge of both connecting the magnet package to the neighbouring accelerating cavities and compensating the differential deformations inside the cryomodule. The dissimilar thermal expansions of the materials used in the magnet package are responsible of non-negligible stress amplification during the cooling down. The stress field predicted by the finite element model is shown in Fig. 10. It is worth noting that, since the coefficient of thermal expansion of stainless steel is slightly bigger than the one of the superconducting wire, the shielding coils are experiencing a compressive force, while their support a tensile one; the same happens for the steering coils. For both the steel supports and the superconducting coils, the equivalent von Mises stress predicted by FEA is smaller than allowable one. Concerning the self-supporting main solenoid, the superconducting wire is wound and glued on the two extremity flanges made of G-10. Since the thermal expansion in the plane of the glass cloth is similar to that one of Nb–Ti/Cu wire, a negligible stress amplification occurs
Fig. 7. Thermal expansion of metals (top) and composites (bottom) from room temperature to absolute zero [2].
On the other side the thermal expansion of composites is severely affected by the principal directions; since G-10 is an orthotropic material, the shrinkage in the plane of the glass fabric (−0.241%) is about one third of the value along the transversal direction (−0.706%), where the only contribution of epoxy becomes preponderant. Given these considerations, an erroneous definition of the orthotropic directions in the design phase might result in high stress amplifications during severe cooling down, in particular if orthotropic composites are coupled with materials having very different coefficients of thermal expansion. Table 1 is the result of a detailed literary review and summarizes the mechanical properties of G-10 at 4 K; due to the intrinsic orthotropicity of the material, the Young’s modulus and Poisson’s ratio are strongly dependent on the principal directions too. On the other hand, a failure criterion for composite materials at cryogenic temperatures is not thoroughly defined or universally accepted in literature; therefore, the structural assessment in this study is carried out by considering two different criteria: the maximum strain allowable in the plane of reinforcing [6] and the Mohr–Coulomb criterion in the normal direction [7]. Like for metals, both the allowable tensile and shear stress slightly increase as the temperature goes down. It is worth noting that in the experimental study presented in [7], data are not available below 77 K. The superconducting wire is a metal matrix composite, where the Niobium–Titanium (Nb–Ti) filaments are embedded in a copper matrix having a diameter of 0.5 mm. The electric insulation is provided by a 19 μm-thick layer of Formvar enclosing the wire; the use of epoxy as insulator material for electric wires is also a common practice in 5
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Fig. 8. Finite element model of the magnet package (∼106 nodes).
Table 1 Mechanical properties of G-10 at 4 K. G-10 laminate 20 12 6 0.17 0.33 0.5 25
Shear modulus [6]
[GPa]
Poisson’s ratio [6]
[–]
Strain allowable in plane of reinforcing [6] Tensile stress allowable normal to reinforcing plane [7] (at room temperature) Shear stress allowable across reinforcing planes [7] (at room temperature)
[%] [MPa]
E1 = E2 E3 G1 = G2 = G3 𝜈12 𝜈13 = 𝜈23 𝜀a1 = 𝜀a2 𝜎a3
[MPa]
𝜏a13 = 𝜏a23
19
Thermal contraction (293 K -> 4 K) [2]
[%]
𝛥L1 ∕L1 = 𝛥L2 ∕L2 𝛥L3 ∕L3
0.241 0.706
Young’s modulus [6]
[GPa]
Table 2 Mechanical properties of Nb–Ti, Cu and AISI 316LN at 4 K.
Young’s modulus Poisson’s ratio Yield strength
[GPa] [–] [MPa]
E 𝜈 𝜎y
Tensile strength
[MPa]
𝜎UTS
Thermal contraction (293 K -> 4 K)
[%]
𝛥L/L
Nb–Ti [9]
Copper OFE [2] (annealed)
AISI 316LN [2] (annealed)
88 0.38 410 [10] (at room temperature) 450 [10] (at room temperature) 0.188
138 0.34 86 [11]
208 0.28 610 [11]
455 [11]
988 [11]
0.324
0.297
Table 3 Mechanical properties of the superconducting wire at 4 K (V = volume fraction). Nb–Ti/Cu wire (VNb−−Ti = 0.74%) Young’s modulus
[GPa]
Shear modulus Poisson’s ratio
[GPa] [–]
Thermal contraction 𝛥L/L (293 K -> 4 K)
[%]
E1 = ENbTiVNbTi + ECu VCu E2 = E3 = (ENbTi ECu )/(ECu VNbTi + ENbTi VCu ) 1/G12 = VNbTi∕GNbTi + VCu ∕GCu 𝜈12 = 𝜈NbTi VNbTi + 𝜈Cu VCu 𝛼1 = 1/E1 (𝛼NbTi ENbTi VNbTi + 𝛼Cu ECu VCu ) 𝛼2 = 𝛼NbTi VNbTi (1 + 𝜈f ) + 𝛼Cu VCu (1 + 𝜈Cu ) – 𝛼1 𝜈12
at the coil-flange interface along the radial direction. On the contrary, the 1-mm-thick layer of G-10 wrapped around the inner and outer surface of the main coil experiences a higher stress intensification in the overlapping area of the extremity flanges. In fact, although both the
117 111 41 0.36 0.280 0.260
flanges and the cylindrical insulations are made of the same material, their thermal expansions along the beam axis are extremely different, since the orthotropic directions are defined differently. The glass cloth embedded in the epoxy of the extremity flanges is perpendicular to 6
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Fig. 9. Displacements along the beam axis after the cooling down from room temperature to 4.45 K.
Fig. 10. Predicted stress field in the coils (Nb–Ti/Cu) and their supports (AISI 316LN) after cooling down. Allowable stress: 𝜎y,AISI316LN@4K /1.5 = 407 MPa and 𝜎y,Cu@4K /1.5 = 58 MPa.
the beam axis, while in the insulating layer it is parallel; therefore, the longitudinal thermal expansion of the flanges is three times bigger, since the contribution of the epoxy matrix is more important in this direction. Nevertheless, both the maximum strain criterion in the plane of reinforcing and the Mohr–Coulomb criterion in the normal direction are satisfied for all the G-10 structural parts (Fig. 11). The magnetic field can be predicted in Ansys by considering the current density in the main and the shielding coils (300 A/mm2 ) as well as the steering coils (250 A/mm2 ); the magnetic forces are then imported in the structural model as body force density and shown in Fig. 12. It is worth noting that, due to the presence of the steering coils,
the magnetic field is not symmetrical and therefore the displacements are not either. Finally, the normal operating conditions in the cryomodule are investigated by considering in the finite element model of the magnet package both the cooling down and the coil powering; based on the stress intensity field predicted by the modelling (Fig. 13), all the failure criteria used to assess the structural integrity of the mechanical system are satisfied (Fig. 14). 7
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Fig. 11. Structural assessment for G-10 parts after cooling down, according to the Mohr–Coulomb and maximum allowable strain criteria.
Fig. 12. Body force density as result of the magnetic field (left) and corresponding coils displacements (right).
5. Prototype construction and experimental validation
the series production; this task has been outsourced to the external company ‘‘Elytt Energy’’ in Bilbao (Spain). Based on the design developed at CEA Paris-Saclay and presented in this paper, some minor modifications have been done by the firm, aimed at improving the overall machining and the assembly procedure of the mechanical pieces constituting the
In order to validate the concept and the corresponding numerical modelling, the construction of a prototype is necessary before starting 8
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Fig. 13. Predicted stress field in the coils (Nb–Ti/Cu) and their supports (AISI 316LN) under normal operating conditions (after cooling down and coil powering). Allowable stress: 𝜎y,AISI316LN@4K /1.5 = 407 MPa and 𝜎y,Cu@4K /1.5 = 58 MPa.
Fig. 14. Structural assessment for G-10 parts under normal operating conditions (after cooling down and coil powering), according to the Mohr–Coulomb and maximum allowable strain criteria.
magnet package. The same company has been in charge of defining
before the final welding of the helium vessel. As requested by CEA,
the cable routing inside the tank and the electrical connections for
Elytt has carried out a quench analysis to show that the specifications
the power supplies. Fig. 15 shows the magnet package fully assembled
provided for the hot spot temperature during quench (<150 K for the 9
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Fig. 15. Mechanical supports of the main, steering (left) and shielding coils (right).
Fig. 16. Acceptance tests for the magnet package: leak-tightness test and integration in the cryostat to reproduce the final operating conditions (temperature and coil powering).
main and shielding coils, <40 for the steerers) are met. The numerical study has been done separately for each coil, by developing a finite element model where the boundaries are considered adiabatic (i.e. no quench back can occur) and the quench is initiated by imposing locally an initial temperature rise. The prototype has been delivered at CEA Paris-Saclay in June 2019, just after some preliminary quality tests done at the same company to certify the leak-tightness of the vessel and the electrical continuity of the connections. A cryostat has been designed on purpose to test the superconducting solenoid at CEA Paris-Saclay under the same operating conditions of the cryomodule (temperature and electric current). As shown in Fig. 16, the magnet package is lowered down in the cryogenic vessel and liquid helium is pumped into the tank housing the coils; the secondary vacuum generated inside the cryostat assures the thermal insulation. When the operating temperature of 4.45 K is reached, the
superconducting coils are powered on and generating a maximum magnetic field of 6.4 T at the centre. The test current has been 91 A which corresponds to 110% of the design value, while the quench current reached during testing has been 95 A, thus resulting in a margin to quench of 15% with respect to the design value (note that the design value is already 10% above the operating value). Throughout all the entire duration of the test campaign, the thermal, electric and magnetic values obtained have been shown to be extremely stable and meet the technical specifications, thus finally validating the overall design of the magnet package. 6. Conclusions The superconducting magnet package for the SARAF linac project is a very complex mechanical system and it is designed to operate at very 10
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low temperatures and with high magnetic fields. Reinforced plastics are used to assure the electrical insulation between the superconducting coils and their metallic supports, but also to carry very high structural loads. In particular, the novel design of the main solenoid is based on a self-supporting coil, whereby the extremity flanges are made of glass-reinforced epoxy (G-10). In addition, this orthotropic composite is mechanically coupled with other materials having dissimilar coefficient of thermal expansions. Given the severe cooling down necessary to reach the normal operating mode, the most highly stressed regions in the components have been designed by carefully identifying/defining the orthotropic directions during the design phase. The mechanical properties of composite materials at cryogenic temperatures, which are not widely available in literature, have been collected and presented in this paper. Given this extensive literary review, a detailed FE model has been built to study accurately the mechanical behaviour of the magnet package as well as to predict the stress field induced by different material shrinkage during the cooling down from room temperature to 4.45 K. The normal operating conditions, at which the coils are powered on and generating the high magnetic field, have also been investigated in the simulations. The maximum stresses predicted and computed by the FE analysis have been subsequently plugged into the failure criteria for safe-life assessment. Two different failure criteria have been used for glass-reinforced plastics, the maximum strain criterion in the plane of reinforcing and the Mohr–Coulomb criterion in the normal direction. The predictions indicate that all the various components fully satisfy the structural integrity criteria. Finally, the validation of both the design and numerical modelling have been carried out by constructing an experimental prototype of the superconducting solenoid. The first magnet package has been built by ‘‘Elytt Energy’’ in Bilbao (Spain), and then tested in a cryostat developed by CEA Paris-Saclay, where the actual operating conditions of the cryomodule have been reproduced (both temperature and magnetic field). Given the promising results of the experimental validation, the series production of twenty (plus two spares) additional superconducting magnet packages for the SARAF linac is expected to be launched shortly.
CRediT authorship contribution statement F. Rossi: Conceptualization, Methodology, Formal analysis, Investigation, Writing - original draft, Writing - review & editing, Visualization, Supervision. B. Gastineau: Conceptualization, Methodology, Validation, Writing - review & editing, Visualization, Supervision, Project administration, Funding acquisition. M. Jacquemet: Resources, Supervision, Project administration, Funding acquisition. S. Ladegaillerie: Resources, Supervision . F. Leseigneur: Conceptualization, Methodology. C. Madec: Resources, Supervision, Project administration. A. Madur: Conceptualization, Methodology, Formal analysis. N. Pichoff: Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition. Acknowledgements The authors sincerely thank the all the members of the SARAF working group. Special thanks go to ‘‘Elytt Energy’’ in Bilbao (Spain) for the production of the first prototype of the magnet package that has been successfully tested at CEA Paris-Saclay. References [1] I. Mardor, et al., The soreq applied research accelerator facility (SARAF) – overview, research programs and future plans, Eur. Phys. J. A 54 (2018) 91. [2] J.W. Ekin, Experimental Techniques for Low Temperature Measurements, Oxford University Press, 2006. [3] P. Forck, et al., Beam Position Monitors, CERN Accelerator School, 2008. [4] F. Rossi, J. Elman, B. Jose, Mechanical modelling of the micromegas detectors for the atlas new small wheel, Compos. Struct. 207 (2019) 53–61. [5] S. Sanz, Fabrication and testing of the first magnet package prototype for the srf linac of LIPAC, in: Proceedings of IPAC2011, San Sebastian, Spain, 2011. [6] Structural Design Criteria for ITER Magnet Components, 2004. [7] K. Kitamura, Cryogenic shear fracture tests of interlaminar organic insulation for a forced-flow superconducting coil, IEEE Trans. Magn. 30 (4) (1994). [8] M.G. Tarantino, L. Weber, A. Mortensen, Effect of hydrostatic pressure on flow and deformation in highly reinforced particulate composites, Acta Mater. 117 (2016) 345–355. [9] K.M. Wilson, Mechanical Cavity Design for 100 MV Upgrade Cryomodule, IPAC2013. [10] ASTM, Standard Specification for Titanium and Titanium Alloy, 2011. [11] C.L. Goodzeit, Superconducting Accelerator Magnets – An Introduction to Mechanical Design and Construction Methods, Brookhaven National Laboratory, 2001.
Data availability statement The raw/processed data required to reproduce these findings cannot be shared at this time as the data also forms part of an ongoing study.
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