[en] The next generation of superconducting accelerator magnets will most likely use a brittle conductor (such as Nb₃Sn), generate fields around 18 T, handle forces that are 3-4 times higher than in the present LHC dipoles, and store energy that starts to make accelerator magnets look like fusion magnets. To meet the challenge and reduce the complexity, magnet design will have to be more innovative and better integrated. The recent design of several high field superconducting magnets have now benefited from the integration between CAD (e.g. ProE), magnetic analysis tools (e.g. TOSCA) and structural analysis tools (e.g. ANSYS). Not only it is now possible to address complex issues such as stress in magnet ends, but the analysis can be better detailed an extended into new areas previously too difficult to address. Integrated thermal, electrical and structural analysis can be followed from assembly and cool-down through excitation and quench propagation. In this paper we report on the integrated design approach, discuss analysis results and point out areas of future interest

[en] Dipole magnets with fields beyond 16T will require superconducting coils that are at least 40 mm thick, an applied pres-stress around 150 MPa and a protection scheme for stored energy in the range of 1-2 MJ/m. The coil size will have a direct impact on the overall magnet cost and the stored energy will raise new questions on protection. To reduce coil size and minimize risk, the coil may have to be graded. Grading is achieved by splitting the coil into several layers with current densities that match the short sample field in each layer. Grading, especially at high fields, can be effective; however it will also significantly raise the stress. In this paper we report on the results of a study on the coil size and field relation to that of the stress and stored energy. We then extend the results to graded coils and attempt to address high stress issues and ways to reduce it

[en] At the LHC upgrade luminosity of 10³⁵ cm^-2 s^-1, collision product power in excess of a kW is deposited in the inner triplet quadrupoles. The quadrupole field sweeps secondary particles from pp-collisions into the superconducting (SC) coils, concentrating the power deposition at the magnetic mid-planes. The local peak power density can substantially exceed the conductor quench limits and reduce component lifetime. Under these conditions, block-coil geometries may result in overall improved performance by removing the superconductor from the magnetic mid-planes and/or allowing increased shielding at such locations. First realistic energy deposition simulations are performed for an interaction region based on block-coil quadrupoles with parameters suitable for the LHC upgrade. Results are presented on distributions of power density and accumulated dose in the inner triplet components as well as on dynamic heat loads on the cryogenic system. Optimization studies are performed on configuration and parameters of the beam pipe, cold bore and cooling channels. The feasibility of the proposed design is discussed

[en] Knowledge of the three-dimensional strain state induced in the superconducting filaments due to loads on Rutherford cables is essential to analyze the performance of Nb₃Sn magnets. Due to the large range of length scales involved, we develop a hierarchical computational scheme that includes models at both the cable and strand levels. At the Rutherford cable level, where the strands are treated as a homogeneous medium, a three-dimensional computational model is developed to determine the deformed shape of the cable that can subsequently be used to determine the strain state under specified loading conditions, which may be of thermal, magnetic, and mechanical origins. The results can then be transferred to the model at the strand/macro-filament level for rod restack process (RRP) strands, where the geometric details of the strand are included. This hierarchical scheme can be used to estimate the three-dimensional strain state in the conductor as well as to determine the effective properties of the strands and cables from the properties of individual components. Examples of the modeling results obtained for the orthotropic mechanical properties of the Rutherford cables are presented.

[en] During the CERN Accelerator School 'Superconductivity for accelerators', the students were divided into 18 groups, and 6 different exercises (case studies), involving the design and analysis of superconducting magnets and RF cavities, were assigned. The problems covered a broad spectrum of topics, from properties of superconducting materials to operation conditions and general dimensions of components. The work carried out by the students turned out to be an extremely useful opportunity to review the material explained during the lectures, to become familiar with the orders of magnitude of the key parameters, and to understand and compare different design options. We provide in this paper a summary of the activities related to the case studies on superconducting magnets and present the main outcomes

[en] We present two techniques used in the analysis of voltage tap data collected during recent tests of superconducting magnets developed by the Superconducting Magnet Program at Lawrence Berkeley National Laboratory. The first technique was used on a quadrupole to provide information about quench origins that could not be obtained using the time-of-flight method. The second technique illustrates the use of data from transient flux imbalances occurring during magnet ramping to diagnose changes in the current-temperature margin of a superconducting cable. In both cases, the results of this analysis contributed to make improvements on subsequent magnets.

[en] NbTi accelerator dipoles are limited to magnetic fields (H)of about 10 T, due to an intrinsic upper critical field(Hc2) limitation of 14 T. To surpass this restriction, prototype Nb3Sn magnets are being developed which have reached 16 T. We show that Nb3Sn dipole technology is practically limited to 17 to 18 T due to insufficient high field pinning, and intrinsically to 20 to 22 T due to Hc2 limitations. Therefore, to obtain magnetic fields approaching 20 T and higher, a material is required with a higher Hc2 and sufficient high field pinning capacity. A realistic candidate for this purpose is Bi-2212, which is available in round wires and sufficient lengths for the fabrication of coils based on Rutherford-type cables. We initiated a program to develop the required technology to construct accelerator magnets from 'wind-and-react' (W and R) Bi-2212 coils. We outline the complications that arise through the use of Bi-2212, describe the development paths to address these issues, and conclude with the design of W and R Bi-2212sub-scale magnets

[en] NbTi accelerator dipoles are limited to magnetic fields (H) of about 10 T, due to an intrinsic upper critical field (Hc2) limitation of 14 T. To surpass this restriction, prototype Nb3Sn magnets are being developed which have reached 16 T. We show that Nb3Sn dipole technology is practically limited to 17 to 18 T due to insufficient high field pinning, and intrinsically to 20 to 22 T due to Hc2 limitations. Therefore, to obtain magnetic fields approaching 20 T and higher, a material is required with a higher Hc2 and sufficient high field pinning capacity. A realistic candidate for this purpose is Bi-2212, which is available in roundwires and sufficient lengths for the fabrication of coils based on Rutherford-type cables. We initiated a program to develop the required technology to construct accelerator magnets from 'wind-and-react' (W and R) Bi-2212 coils. We outline the complications that arise through the use of Bi-2212, describe the development paths to address these issues, and conclude with the design of W and R Bi-2212 sub-scale magnets

[en] It can be shown that, by superposing two solenoid-like thin windings that are oppositely skewed (tilted) with respect to the bore axis, the combined current density on the surface is 'cos-theta' like and the resulting magnetic field in the bore is a pure dipole. As a proof of principle, such a magnet was designed, built and tested as part of a summer undergraduate intern project. The measured field in the 25mm bore, 4 single strand layers using NbTi superconductor, exceeded 1 T. The simplicity of this high field quality design, void of typical wedges end-spacers and coil assembly, is especially suitable for insert-coils using High Temperature Superconducting wire as well as for low cost superconducting accelerator magnets for High Energy Physics. Details of the design, construction and test are reported

[en] The random part of the integral field harmonics in a series of superconducting magnets has been used in the past to identify the reproducibility of the coil positioning. Using a magnetic model and a MonteCarlo approach, coil blocks are randomly moved and the amplitude that best fits the magnetic measurements is interpreted as the reproducibility of the coil position. Previous values for r.m.s. coil displacements for Nb-Ti magnets range from 0.05 to 0.01 mm. In this paper, we use this approach to estimate the reproducibility in the coil position for Nb₃Sn short models that have been built in the framework of the FNAL core program (HFDA dipoles) and of the LARP program (TQ quadrupoles). Our analysis shows that the Nb₃Sn models manufactured in the past years correspond to r.m.s. coil displacements of at least 5 times what is found for the series production of a mature Nb-Ti technology. On the other hand, the variability of the field harmonics along the magnet axis shows that Nb3Sn magnets have already reached values similar to these obtained for Nb-Ti ones.