Computation of the Reversible Critical Current Degradation in Nb $_{3}$Sn Rutherford Cables for Particle Accelerator Magnets

Superconducting coils limit current is usually measured on unloaded short samples of strands extracted from the same cable used to wound the coil. However, the critical current density of Nb$_{3}$Sn strands is strongly dependent on the applied strain. This dependence is well reproduced by the so-called exponential scaling laws on strands subject to uniaxial loading. Unfortunately, no standard procedure exists to apply these laws under the complex stress condition experienced by the strands inside Rutherford cables for particle accelerator magnets. As a consequence, an empirical limit from magnet tests was set in the past: 150–200 MPa of maximum equivalent stress within the coil, considered as a block of uniform material. It is not clear how this number relates with the actual stress/strain state in the strands and if it is possible in magnet applications to infer the coil degradation from single strands tests. In this context, this paper presents a model to estimate the critical current degradation of superconducting coils as a function of the applied strain. The model results were compared against the critical current degradation measured on impregnated cable stacks subject to transverse pressure.