Modelling V-I Measurements of Nb$_3$Sn Accelerator Magnets With Conductor Degradation

In the framework of the High-Luminosity Large Hadron Collider (HL-LHC) project, 11 T dipole and MQXF quadrupole magnets employing Nb$_3$Sn technology have been tested in short and long test configurations. Nb$_3$Sn magnets are more sensitive than Nb-Ti magnets to a potential degradation of their conductors during production, testing, and cycling operation. At CERN, new diagnostic tools and measurement procedures have been developed to investigate, in detail, the performance of Nb$_3$Sn accelerator type magnets. This is accomplished by V-I measurements extracted from voltage taps on conductor sections as well as entire coils. A leading hypothesis for the cause of decaying voltages on current plateaus of the V-I measurements is the presence of an inhomogeneous defect in the Rutherford cable. Current redistribution for bypassing such defects takes place through a current diffusion process, which leads to a decaying voltage over the affected cable sections. Using the simulation software THEA, the general behavior of this phenomenon has been studied. Good qualitative agreement is found between simulation and magnet test results.