Mechanical characterisation of Nb3Sn Rutherford cable stacks

Nb3Sn Rutherford cables are used in CERN’s superconducting 11 T dipole and MQXF quadrupole magnets, which are proposed for the instantaneous luminosity (rate of particle collisions) upgrade of the Large Hadron Collider (LHC) by a factor of five to a High Luminosity-Large Hadron Collider (HL-LHC). Nb3Sn-based conductors are the key technology for the envisioned Future Circular Collider (FCC) with an operating magnetic dipole field of 16 T. The baseline superconductor of the LHC dipole magnets is Nb–Ti, whereas an operation above 10 T is not possible due to the current carrying performance limitations of this superconductor at higher magnetic fields. Therefore, a superconducting material such as Nb3Sn has to be used with proven performance capabilities of 10 T and above. The conductor choice towards Nb3Sn-based cables affects the magnet manufacturing process, as it requires a heat treatment up to 650°C, an epoxy resin impregnation and introduces mechanical diffculties as the superconducting filaments are brittle and strain sensitive. A mechanical over loading of the filaments lead to irreversible conductor damage. The designs of 11 and 16 T magnets are supposed to push the conductor towards its mechanical and electrical performance limitations. The magnetic field induced forces on the current carrying conductor are balanced by mechanical pre-loading of the magnet. Thereby the highest controlled mechanical pre-load for the 11 T dipole magnet is set at ambient temperature. The mechanical stress limits of Nb3Sn-based cables have been investigated at cryogenic temperatures. The material strength and stiffness of the cable insulation system, formed by glass-fibre-reinforced resin, is increased at low temperatures. The ultimate stress values, determined at cryogenic temperature, are therefore not conservative. The ultimate stress limitation of the insulated conductor is assumed to be lower at ambient temperature. The cable limitations at ambient temperature need to be known for the ongoing magnet manufacturing process and also for future design approaches. Furthermore, the compressive stress–strain behaviour of a coil conductor block at ambient temperature is the key material characteristic, in order to recalculate the stress level in the coil during the assembly process. Existing approaches using an indirect strain measurement method provide uncertainties in the low-strain regime, which is the essential strain range for a material compound consisting of major fractions composed of heat-annealed copper and epoxy resin. Compressive stress–strain data of an impregnated conductor block are required, based on a direct strain measurement system, as available data have been collected on samples based on a different strand type and insulation system. The elaborated direct strain measurements can be correlated to strain gauge data, measured directly on a coil. The stress distribution in a Nb3Sn Rutherford cable need to be understood and validated to understand strain-induced degradation effects in the insulated conductor. This knowledge can also help to optimise the stress distribution envisioned magnet designs. The stress–strain state in the copper and Nb3Sn phase of a loaded conductor block has to be determined experimentally. This dissertation describes a test protocol and first elaborated results on the investigated stress limitations of a Nb3Sn Rutherford cable under homogeneous load applied in transversal direction. The compressive stress–strain behaviour of impregnated Nb3Sn Rutherford cable stacks was investigated experimentally. This includes a detailed report on the sample manufacturing process, measurements performed and validation of results through a comparison with the elaborated data of cable stacks extracted from a coil. The presented results from neutron diffraction measurements of loaded cable stacks allow the determination of the stress–strain level of the copper and Nb3Sn phase in the impregnated conductor. The relevant measured results have been recalculated with numerical calculations based on the Finite Element Method (FEM).:1. Introduction 1 1.1. The LHC and the HL-LHC project 1.2. The FCC study 1.3. Superconducting materials for accelerator magnets 1.4. Multi-filamentary wires and Rutherford cables 1.5. Coil manufacturing process 1.6. Magnet coil assembly 1.7. Objectives of this thesis 2. Theory: fundamental principles 17 2.1. Analytical calculation: sector coil dipole 2.2. Mechanical behaviour of composite materials 2.3. Failure criteria and strength hypotheses for materials 2.4. Compressive tests 2.5. Fundamental principles of Neutron scattering 2.5.1. Test apparatus and measurement method 2.5.2. Lattice plane and Miller indices 2.5.3. Bragg diffraction and interference 2.5.4. Diffraction-based strain calculation 2.5.5. Diffraction-based stress calculation 2.6. Fundamental principles of FEM 3. Homogeneous transversal compression of Nb3Sn Rutherford cables 3.1. Superconducting cable test stations 3.2. The FRESCA test facility and specific sample holder 3.3. The sample description 3.4. Experimental procedure 3.5. Review of existing contact pressure measurement system 3.6. Compressive test station 3.7. Validation of the pressure-sensitive films 3.8. Press punch 3.9. Improvement of the contact stress distribution 3.9.1. First test: cable pressed between the bare tools 3.9.2. Second test: tool shimmed with a soft Sn96Ag4 3.9.3. Third test: tool shimmed with a soft Sn60Pb40 3.9.4. Fourth test: tool shimmed with a soft indium 3.9.5. Fifth test: tool shimmed with a polyimide film 3.10. Test results 3.11. Conclusion 4. Material characterisation by a compression test 4.1. Test set-ups for compressive tests and validation 4.2. Sample preparation 4.3. Compressive stress–strain measurement 4.4. Ten-stack sample stiffness estimation-based composite theories 4.5. Dye penetration test on loaded and unloaded samples 4.6. Conclusion 5. Neutron diffraction measurements 80 5.1. Test set-up for neutron diffraction measurement 5.2. The samples 5.3. Experiment: lattice stress–strain measurements 5.4. Conclusion 6. Simulation and modelling of Nb3Sn cables 6.1. The models 6.2. The 2D simulation results 6.3. The 3D simulation results 6.4. Conclusion 7. Comprehensive summary 7.1. Summary 7.2. Critical review 7.3. Next steps Appendix 113 A. Calculation of the magnetic field components in a sector coil without iron B. Approaches for the determination of diffraction elastic constants C. Manufacturing drawings D. FEM calculation results of the 2D model E. FEM calculation results of the 3D model F. Source Codes Bibliograph

Isogeometric Boundary Elements in Electromagnetism: Rigorous Analysis, Fast Methods, and Examples

We present a new approach to three-dimensional electromagnetic scattering problems via fast isogeometric boundary element methods. Starting with an investigation of the theoretical setting around the electric field integral equation within the isogeometric framework, we show existence, uniqueness, and quasi-optimality of the isogeometric approach. For a fast and efficient computation, we then introduce and analyze an interpolation-based fast multipole method tailored to the isogeometric setting, which admits competitive algorithmic and complexity properties. This is followed by a series of numerical examples of industrial scope, together with a detailed presentation and interpretation of the results

Multipatch Approximation of the de Rham Sequence and its Traces in Isogeometric Analysis

We define a conforming B-spline discretisation of the de Rham complex on multipatch geometries. We introduce and analyse the properties of interpolation operators onto these spaces which commute w.r.t. the surface differential operators. Using these results as a basis, we derive new convergence results of optimal order w.r.t. the respective energy spaces and provide approximation properties of the spline discretisations of trace spaces for application in the theory of isogeometric boundary element methods. Our analysis allows for a straightforward generalisation to finite element methods

Systemic physiology augmented functional near-infrared spectroscopy: a powerful approach to study the embodied human brain.

In this Outlook paper, we explain why an accurate physiological interpretation of functional near-infrared spectroscopy (fNIRS) neuroimaging signals is facilitated when systemic physiological activity (e.g., cardiorespiratory and autonomic activity) is measured simultaneously by employing systemic physiology augmented functional near-infrared spectroscopy (SPA-fNIRS). The rationale for SPA-fNIRS is twofold: (i) SPA-fNIRS enables a more complete interpretation and understanding of the fNIRS signals measured at the head since they contain components originating from neurovascular coupling and from systemic physiological sources. The systemic physiology signals measured with SPA-fNIRS can be used for regressing out physiological confounding components in fNIRS signals. Misinterpretations can thus be minimized. (ii) SPA-fNIRS enables to study the embodied brain by linking the brain with the physiological state of the entire body, allowing novel insights into their complex interplay. We envisage the SPA-fNIRS approach will become increasingly important in the future

The Role of Systemic Physiology in Individual Hemodynamic Responses Measured on the Head Due to Long-Term Stimulation Involving Colored Light Exposure and a Cognitive Task: An SPA-fNIRS Study

In our previous investigations using systemic physiology augmented functional near-infrared spectroscopy (SPA-fNIRS) neuroimaging, we found larger variability between subjects in changes of cerebral hemodynamics and oxygenation induced by an intricate experimental paradigm involving colored light exposure and a cognitive task. We aimed to investigate the role the activity of the systemic physiology has on individual variations in the fNIRS data. Thirty-two healthy subjects (17 female, 15 male and age: 25.5 ± 4.3 years) were exposed to blue and red light for 9 min (colored light exposure, CLE) while performing a verbal fluency task (VFT). We found that (i), at the group level, the visual cortex showed a stronger deoxyhemoglobin concentration response during blue light exposure than during red light exposure, and (ii) this relationship was influenced by individually different baseline blood pressure values. Furthermore, we found other correlations between changes in fNIRS signals and changes in systemic physiology. Our study demonstrates the usefulness and necessity of the SPA-fNIRS approach to gain insights into the individual variability of hemodynamic responses measured with fNIRS, especially in the case of an intricate experimental paradigm (i.e., CLE-VFT) as used in our study

The Role of Systemic Physiology in Individual Hemodynamic Responses Measured on the Head Due to Long-Term Stimulation Involving Colored Light Exposure and a Cognitive Task: An SPA-fNIRS Study.

In our previous investigations using systemic physiology augmented functional near-infrared spectroscopy (SPA-fNIRS) neuroimaging, we found larger variability between subjects in changes of cerebral hemodynamics and oxygenation induced by an intricate experimental paradigm involving colored light exposure and a cognitive task. We aimed to investigate the role the activity of the systemic physiology has on individual variations in the fNIRS data. Thirty-two healthy subjects (17 female, 15 male and age: 25.5 ± 4.3 years) were exposed to blue and red light for 9 min (colored light exposure, CLE) while performing a verbal fluency task (VFT). We found that (i), at the group level, the visual cortex showed a stronger deoxyhemoglobin concentration response during blue light exposure than during red light exposure, and (ii) this relationship was influenced by individually different baseline blood pressure values. Furthermore, we found other correlations between changes in fNIRS signals and changes in systemic physiology. Our study demonstrates the usefulness and necessity of the SPA-fNIRS approach to gain insights into the individual variability of hemodynamic responses measured with fNIRS, especially in the case of an intricate experimental paradigm (i.e., CLE-VFT) as used in our study