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A Computational Procedure for Assessing I$_c$($\varepsilon$) in Nb$_3$Sn/Bi-2212 Hybrid Magnets

A. D'Agliano, A. V. Zlobin, I. Novitski, G. Vallone, P. Ferracin, E. Barzi, S. Donati, V. Giusti

TL;DR

This work presents a computational procedure to assess I$_C$(B,T,ε) in a FNAL 4-layer Bi-2212/Nb$_3$Sn hybrid dipole by applying a strand-level heterogeneous Rutherford cable model in ANSYS APDL. Nb$_3$Sn I$_C$ scaling is combined with a strain function s(ε) derived from invariants of the area-averaged strand strain, while Bi-2212 degradation follows a transverse-pressure–based law defined by Ω(ε). The magnetic analysis provides bore-field distributions across powering configurations, which feed a simplified mechanical model to predict conductor strains and the corresponding I$_C$ degradation, revealing that Bi-2212 experiences less degradation than Nb$_3$Sn under the optimal configuration due to the SMCT design. The approach yields a versatile framework for evaluating conductor integrity and optimizing future high-field hybrid magnets across alternative geometries. The results indicate a bore-field of about 14.4 T in degraded operation with the optimal currents, demonstrating feasibility and guiding design choices for magnet performance beyond 16 T.

Abstract

The critical current of superconductors is commonly measured by testing unloaded wires under an external magnetic field. While stressed by intense Lorentz forces, the existing HTS/LTS superconductors are prone to a reduction in critical current before reaching their structural mechanical limit. In this work, the magnetic and mechanical analysis of the FNAL 4-layer Bi-2212/Nb$_3$Sn hybrid dipole magnet is reported, aimed at predicting the critical current degradation for both the superconductors during powering at 16 T. All the Rutherford cables in the coils of the hybrid magnet were modeled at the strand level in Ansys APDL with the heterogeneous cable model. Utilizing this detailed geometry, it was possible to evaluate the effects of strain on the critical current degradation for both the Nb$_3$Sn and Bi-2212 superconductors under the intense Lorentz forces. The analysis presented in this paper integrates strain-dependent critical current laws, with parameters derived from experimental data, to simulate the hybrid magnet's performance for all possible current-powering configurations. The proposed methodology enables a detailed assessment of conductor integrity and I$_C$($\varepsilon$) reduction in existing hybrid magnet designs, providing a versatile and rigorous framework for optimizing future high-field hybrid magnets.

A Computational Procedure for Assessing I$_c$($\varepsilon$) in Nb$_3$Sn/Bi-2212 Hybrid Magnets

TL;DR

This work presents a computational procedure to assess I(B,T,ε) in a FNAL 4-layer Bi-2212/NbSn hybrid dipole by applying a strand-level heterogeneous Rutherford cable model in ANSYS APDL. NbSn I scaling is combined with a strain function s(ε) derived from invariants of the area-averaged strand strain, while Bi-2212 degradation follows a transverse-pressure–based law defined by Ω(ε). The magnetic analysis provides bore-field distributions across powering configurations, which feed a simplified mechanical model to predict conductor strains and the corresponding I degradation, revealing that Bi-2212 experiences less degradation than NbSn under the optimal configuration due to the SMCT design. The approach yields a versatile framework for evaluating conductor integrity and optimizing future high-field hybrid magnets across alternative geometries. The results indicate a bore-field of about 14.4 T in degraded operation with the optimal currents, demonstrating feasibility and guiding design choices for magnet performance beyond 16 T.

Abstract

The critical current of superconductors is commonly measured by testing unloaded wires under an external magnetic field. While stressed by intense Lorentz forces, the existing HTS/LTS superconductors are prone to a reduction in critical current before reaching their structural mechanical limit. In this work, the magnetic and mechanical analysis of the FNAL 4-layer Bi-2212/NbSn hybrid dipole magnet is reported, aimed at predicting the critical current degradation for both the superconductors during powering at 16 T. All the Rutherford cables in the coils of the hybrid magnet were modeled at the strand level in Ansys APDL with the heterogeneous cable model. Utilizing this detailed geometry, it was possible to evaluate the effects of strain on the critical current degradation for both the NbSn and Bi-2212 superconductors under the intense Lorentz forces. The analysis presented in this paper integrates strain-dependent critical current laws, with parameters derived from experimental data, to simulate the hybrid magnet's performance for all possible current-powering configurations. The proposed methodology enables a detailed assessment of conductor integrity and I() reduction in existing hybrid magnet designs, providing a versatile and rigorous framework for optimizing future high-field hybrid magnets.

Paper Structure

This paper contains 11 sections, 1 equation, 8 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Methodology
  3. Heterogeneous Rutherford cable model
  4. Critical Current Scaling Law - Nb$_3$Sn
  5. Critical Current Degradation Law - Bi-2212
  6. Magnet Design
  7. Magnetic assumptions
  8. Mechanical Analysis
  9. Mechanical Structure
  10. Mechanical Results
  11. Conclusion

Figures (8)

  • Figure 1: Schematic representation of the 4-layer hybrid magnet in dipole configuration, with the insert coil made of Bi-2212 Rutherford cable (Bi-SMCT1) and the outer cosine-theta coil in Nb$_3$Sn.
  • Figure 2: Cross-section of the heterogeneous Rutherford cable model for the Bi-2212 (top) and Nb$_3$Sn (bottom) superconductors (cables are not in scale).
  • Figure 3: Normalized I$_C$ degradation $\Omega$($\varepsilon$) (at 4.2 K, 11 T) as a function of the area-averaged strain state in the Bi-2212 Rutherford cable strands due to transverse pressure.
  • Figure 4: I$_C$(B) curves of the Bi-2212 (blue) and Nb$_3$Sn (red) superconductors at 4.2 K with the load-lines of: powering HTS insert only (grey), powering LTS outsert only (orange), hybrid dipole in series powering configuration (green), and optimal load-lines for both HTS and LTS conductors (thin black lines).
  • Figure 5: Mechanical structure and materials of the hybrid dipole magnet implemented in ANSYS to compute the mechanical analysis.
  • ...and 3 more figures