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

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.