Abstract: Nb3Sn magnets are presently built for the HL-LHC accelerator upgrade and are developed for the Future Circular Collider study. The knowledge of the Nb3Sn strain state distribution in these magnets is required in order to predict their ultimate performance limit. We have measured the Nb3Sn residual strain distribution in an 11 T dipole accelerator magnet coil. Ambient temperature Nb3Sn strain maps across 11 T dipole coil cross sections were acquired by means of fast high energy synchrotron x-ray diffraction. Using complementary neutron diffraction measurements the Nb3Sn residual strain and stress was measured in the four largest conductor blocks of a massive 11 T dipole coil segment.
Abstract: The knowledge of the temperature-induced changes of the superconductor volume and of the thermomechanical behavior of the different coil and tooling materials is required for predicting the coil geometry and the stress distribution in the coil after the Nb3Sn reaction heat treatment. In this paper, we have measured the Young's and shear moduli of the HL-LHC 11 T Nb3Sn dipole magnet coil and reaction tool constituents during in situ heat cycles with the dynamic resonance method. The thermal expansion behaviors of the coil components and of a free standing Nb3Sn wire were compared based on dilation experiments.
Abstract: We have directly measured, for the first time, the Nb3Sn and Cu loading strains and stresses in 11 T dipole coil segments upon compressive loading using neutron diffraction. For this purpose a load frame that enables rotation of the sample load axis with respect to the neutron scattering geometry was installed in the Stress-Spec beamline at the Heinz Maier-Leibnitz FRM II neutron source. The neutron diffraction data suggests that the magnet coil wound of Rutherford type cables can be considered as a fibre reinforced composite material. In the axial load direction the load is mainly carried by the Nb3Sn filaments and the composite stiffness can be estimated by the rule of mixtures assuming iso-strain conditions in all composite constituents. Under transverse compression the fully annealed Cu provides an isotropic pressure around the Nb3Sn filaments. The transverse load stresses in the Cu and Nb3Sn are similar, indicating iso-stress behaviour of the coil constituents under transverse compression. The broadening of the Nb3Sn diffraction peaks above critical stress values indicates reversible and irreversible Nb3Sn loading stress effects.
Abstract: For next-generation accelerator magnets for fields beyond those achievable using Nb–Ti, Nb3Sn is the most viable superconductor. The high luminosity upgrade for the Large Hadron Collider (HL-LHC) marks an important milestone as it will be the first project where Nb3Sn magnets will be installed in an accelerator. Nb3Sn is a brittle intermetallic, so magnet coils are typically wound from composite strands containing ductile precursors before heat treating the wire components to form Nb3Sn. However, some mechanical assembly is still required after the coils have been heat-treated. In this paper, we present direct evidence of cracking of the brittle Nb3Sn filaments in a prototype dipole that resulted in degraded magnet performance. The cracking of the Nb3Sn, in this case, can be attributed to an issue with the collaring process that is required in the assembly of dipole accelerator magnets. Metallographic procedures were developed to visualize cracks present in the cables, along with quantitative image analysis for location-based crack analysis. We show that the stresses experienced in the damaged coil are above the critical damage stress of Nb3Sn conductor, as evidenced by a measured Cu stabilizer hardness of 85 HV0.1, which is higher than the Cu stabilizer hardness in a reference Nb3Sn cable ten-stack that was subjected to a 210 MPa transverse compression. We also show that once the collaring procedure issue was rectified in a subsequent dipole, the Nb3Sn filaments were found to be undamaged, and the Cu stabilizer hardness values were reduced to the expected levels. This paper provides a post-mortem verification pathway to analyze the damage, provides strand level mechanical properties, which could be beneficial for improving model prediction capabilities. This method could be applied beyond Nb3Sn magnets to composite designs involving high work hardening materials.
Abstract: The Nb3Sn superconductor in accelerator magnets must resist high mechanical stresses. In order to better understand the effect of the coil impregnation system on the stresses exerted on the strain-sensitive Nb3Sn superconductor, we have measured the elastic strain evolution in the conductor constituents under externally applied loads. For this purpose, a dedicated load frame that enables rotation of the sample load axis with respect to the neutron scattering geometry was installed in the Stress-Spec beamline at the neutron source Heinz Maier-Leibnitz FRM II. The Nb3Sn- and Cu-loading strains were measured in situ by neutron diffraction under monotonic and cyclic compressive loading. So-called ten-stack samples composed of Nb3Sn Rutherford type cables with different impregnation and coil blocks extracted from an 11 T dipole short model coil were investigated.
Abstract: Mit Hilfe des Begriffes der elastischen Polarisierbarkeit konnen die elastischen Konstanten des makroskopisch isotropen Vielkristalls aus den Einkristallkonstanten exakt ausgerechnet werden. Im Falle des Aggregats aus kubischen Kristalliten, in dem die Bestimmung des Kompressionsmoduls trivial ist, folgt der Schubmodul aus einer Gleichung 3. Grades [Gl. (22)], in der Kombinationen der Einkristallhauptkonstanten als Koeffizienten auftreten. Die experimentellen Vergleichswerte weichen von den berechneten etwas ab, was beweist, das die Experimente nicht den von der Theorie geforderten idealen Bedingungen genugt haben. Weitere Anwendungsmoglichkeiten der Methode werden besprochen.
Abstract: INTRODUCTION Residual Stress: Friend or Foe? Historical Development of Stress Measurement by Diffraction Special Characteristics of Neutron Strain Measurement Nature and Origin of Residual Stress Effects of Residual Stress FUNDAMENTALS OF NEUTRON DIFFRACTION Introduction Scattering and Absorption of Neutrons and X-Rays by Atoms Neutron Diffraction from Crystalline Solids Penetration of Neutron Beams Effects of Lattice Vibrations Extinction, Texture, and Multiple Scattering DIFFRACTION TECHNIQUES AND INSTRUMENT DESIGN Neutron Sources Diffractometers for Strain Measurement Neutron Detectors The Instrumental Resolution Instrument Gauge Volumes Sampled Gauge Volume and Effective Measurement Position Specialized Instruments for Strain Measurement PRACTICAL ASPECTS OF STRAIN MEASUREMENT USING NEUTRON DIFFRACTION Introduction Measurement of Diffraction Bragg Peak Profile Analyzing Bragg Peak Profiles Accuracy of Diffraction Peak Center Determination Analysis of Complete Diffraction Profiles for Strain Strain-Free Reference Reproducibility Tests INTERPRETATION AND ANALYSIS OF LATTICE STRAIN DATA Inferring Stresses from Lattice Strains Introduction to Mechanics of Crystallite Deformation Elastic Anisotropy of Single Crystals The Bulk Elastic Response of Polycrystals hkl-Specific Response in a Polycrystal Undergoing Elastic Deformation hkl-Specific Response in a Polycrystal Undergoing Plastic Deformation APPLICATIONS TO PROBLEMS IN MATERIALS SCIENCE AND ENGINEERING Introduction Welded Structures Composites and Other Multiphase Materials Plastically Deformed Components and Materials Near-Surface Stresses In Situ and Through-Process or Life Studies THE FUTURE SYMBOLS AND ABBREVIATIONS GLOSSARY APPENDICES Note on Reactor Flux Spectrum Relation between the Centroid of Sampled Gauge Volume and Translator Reading Points for Consideration When Making a Neutron Diffraction Stress Measurement Macroscopic Scattering Cross-Sections of All Elements Index
Abstract: Critical current and flux pinning densities have been determined for a series of Nb3Sn, V3Ga, Nb3Ge, and NbTi conductors as a function of uniaxial tensile strain in magnetic fields ranging from 4 to 19 T. An empirical relationship has been found at 4.2 K that describes these data over the entire range of field under both compressive and tensile strain. The pinning force F has been found to obey a scaling law of the form F = [B c2 ∗(ϵ)] n f(b) , where Bc2∗ is the strain-dependent upper-critical field determined from high-field critical-current measurements and f(b) is a function only of the reduced magnetic field b B/B c2 ∗ . The detailed shape of f(b) depends on the super-conducting material and reaction conditions, but n was found to be nearly constant for a given type of superconductor. For Nb3Sn conductors n = 1 ± 0.3, for multifilamentary V3Gan≅1.3, for CVD-Nb3Ge tape n≅1.6, and for multifilamentary NbTi n≅3.3. The importance of this relationship is that, for these conductors at least, it is possible to measure F at one strain and then immediately be able to predict F (and thus the critical current) at other strain levels simply by scaling the results by [Bc2∗(ϵ)]n. Part I of this paper presents the basic uniaxial-strain scaling relationship and focuses on its application to Nb3Sn conductors. The strain scaling law with n = 1 ± 0.3 was found to hold for all Nb-Sn based conductors examined thus far, including commercial-multifilamentary conductors, extremely fine-filament composites, partially-reacted specimens, ‘insitu’ conductors, and Nb-Hf/Cu-Sn-Ga conductors. The detailed dependence of Bc2∗ on strain was-found to be nearly universal for highly-reacted commercial Nb3Sn specimens, greatly simplifying the application of the scaling law to this group of practical superconductors. These results are discussed within the context of flux pinning models and a general scaling relation is proposed which unifies the usual temperature-scaling relation with this strain-scaling relation.
Abstract: The Large Hadron Collider is working at about half its design value, limited by the defective splices of the magnet interconnections. While the full energy will be attained after the splice consolidation in 2014, CERN is preparing a plan for a Luminosity upgrade (High Luminosity LHC) around 2020 and has launched a pre-study for exploring an Energy upgrade (High Energy LHC) around 2030. Both upgrades strongly rely on advanced accelerator magnet technology, requiring dipoles and quadrupoles of accelerator quality and operating fields in the 11-13 T range for the luminosity upgrade and 16-20 T range for the energy upgrade. The paper will review the last ten year of Nb3Sn accelerator magnet R&D and compare it to the needs of the upgrades and will critically assess the results of the Nb3Sn and HTS technology and the planned R&D programs also based on the inputs of first year of LHC operation.
Abstract: Bulk samples covering the entire homogeneity range of the Nb-Sn A15-phase were prepared by a new method: levitation melting under high argon pressure. The variations of the lattice parameter, superconducting transition temperature, resistivity and critical field slope were measured as a function of composition. A low-temperature X-ray diffraction study was undertaken in order to fix the compositional limit of the tetragonal phase. The theoretical expectations for the critical field slopes at the transition temperature, Tc, based on actually-observed alloy parameters, were found to be in good agreeement with measured values.