Development of a Current Fit Function for NbTi to be Used for Calculation of Persistent Current Induced Field Errors in the LHC Main Dipoles

A new fit function for the critical current density of superconducting NbTi cables for the LHC main dipoles is presented. Existing fit functions usually show a good matching of the very low field range, but produce a current density which is significantly too small for the intermediate and high field range. Consequently the multipole range measured at cold is only partially reproduced and loops from current cycling do not match. The presented function is used as input for the field quality calculation of a complete magnet cross-section including arbitrary current cycling and all hysteresis effects. This way allows to trace a so-called finger-print of the cable combination used in the LHC main bending magnets. The finger-print pattern is a consequence of the differences of the measured superconductor magnetization of cables from different manufacturers. The simulation results have been compared with measurements at cold obtained from LHC main dipoles and a very good agreement for low and intermediate field values could be observed.