Centre d'études et d'expertise sur les risques, l'environnement, la mobilité et l'aménagement

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Abstract-A number of models for the critical surface of Nb 3 Sn, and in general A15 superconductors, have been developed in the past years. This paper compares the most common parameterizations using consistent notation. Although the parameterizations appear dissimilar at first sight, they are in reality all based on a fit of the normalized pinning force vs. the reduced field, and have similar scalings for the critical field and critical temperature based on a Unified Scaling Law. In this paper we take the various parameterizations as a basis for a generic scaling proposed for the characterization and production follow-up of the ITER Nb 3 Sn strands. The accuracy of the scaling is estimated using the fitting residuals on various sets of I C (B T ) data available in literature. We discuss the results, and give our view of the work towards a unified, practical parameterization.

The critical current density of the Nb 3 Sn superconductor is strongly dependent on the strain applied to the material. In order to investigate this dependence, it is a common practice to measure the critical current of Nb 3 Sn strands for different values of applied axial strain. In the literature, several models have been proposed to describe these experimental data in the reversible strain region. All these models are capable of fitting the measurement results in the strain region where data are collected, but tend to predict unphysical trends outside the range of data, and especially for large strain values. In this paper we present a model of a new strain function, together with the results obtained by applying the new scaling law on relevant datasets. The data analyzed consisted of the critical current measurements at 4.2 K that were carried out under applied axial strain at Durham University and the University of Geneva on different strand types. With respect to the previous models proposed, the new scaling function does not present problems at large strain values, has a lower number of fitting parameters (only two instead of three or four), and is very stable, so that, starting from few experimental points, it can estimate quite accurately the strand behavior in a strain region where there are no data. A relationship is shown between the proposed strain function and the elastic strain energy, and an analogy is drawn with the exponential form of the McMillan equation for the critical temperature.

Abstract-Recent advancements in the critical current density ( ) of Nb 3 Sn conductors, coupled with a large effective filament size, have drawn attention to the problem of magneto-thermal instabilities. At low magnetic fields, the quench current of such high Nb 3 Sn strands is significantly lower than their critical current because of the above-mentioned instabilities. An adiabatic model to calculate the minimum current at which a strand can quench due to magneto-thermal instabilities is developed. The model is based on an 'integral' approach already used elsewhere [1]. The main difference with respect to the previous model is the addition of the self-field effect that allows to describe premature quenches of non-magnetized Nb 3 Sn strands and to better calculate the quench current of strongly magnetized strands. The model is in good agreement with experimental results at 4.2 K obtained at Fermilab using virgin Modified Jelly Roll (MJR) strands with a low Residual Resistivity Ratio (RRR) of the stabilizing copper. The prediction of the model at 1.9 K and the results of the tests carried out at CERN, at 4.2 K and 1.9 K, on a 0.8 mm Rod Re-Stack Process (RRP) strand with a low RRR value are discussed. At 1.9 K the test revealed an unexpected strand performance at low fields that might be a sign of a new stability regime.

High critical current density Nb 3 Sn wires (J c > 2500 A/mm 2 at 4.2 K and 12 T) are the conductors considered for next generation accelerator magnets. At present, the large magnetization of these strands is a concern within the scientific community because of the impact it might have on the magnet field quality. In order to characterize the magnetic behavior of these wires, an extensive campaign of magnetization measurements was launched at CERN. Powder In Tube (PIT) strands by Bruker-EAS and Restacked Rod Process (RRP ® ) strands by Oxford Superconducting Technology (OST) were measured between 0 T and 10.5 T at different temperatures (ranging from 1.9 K to 14.5 K). The samples, based on strands with different subelements dimensions (35 to 80 μm), were measured with a Vibrating Sample Magnetometer (VSM). The experimental data were analyzed to: 1) calculate the effective filament size and the optimal parameters for the pinning force scaling law; 2) define the field-temperature region where there are flux jumps. It was found that the flux-jump can limit the maximum magnetization of the Nb 3 Sn wires and that the maximum magnetization at higher temperatures can be larger than the one at lower temperatures. In this paper the experimental results and the analysis are reported and discussed. The experimental data were analyzed to: 1) calculate the effective filament size and the optimal parameters for the pinning force scaling law; 2) define the field-temperature region where there are flux jumps. It was found that the flux-jump can limit the maximum magnetization of the Nb 3 Sn wires and that the maximum magnetization at higher temperatures can be larger than the one at lower temperatures. In this paper the experimental results and the analysis are reported and discussed.