Determination of a Fit Function for the Critical Current Density for NbTi Cables used in LHC Main Bending Magnets

For the construction of the LHC at CERN the main dipoles and the superconducting cables are produced in industry. As part of the quality control the field quality of the magnets is measured both at warm and at cold conditions at CERN. In superconducting accelerator magnets field errors are mainly created by the positioning of the conductors, but also by so-called persistent currents. These currents are linked to the superconductor magnetization and they are an inevitable property of type II superconducting materials. The superconductor magnetization behavior of each strand used for the LHC main dipoles is tested at CERN and the cable has to be approved before use. It has been observed that the dependency of the superconductor magnetization on the applied magnetic induction is different for the different manufacturers. Based on the magnetization measurements and the critical state model the persistent current effects can be calculated by means of a model for superconducting filaments. For this thesis the intersecting ellipse model is used which is implemented in the CERN field computation program ROXIE and is used for the calculation of the expected field errors in the LHC magnets. In this work a new fit function for the critical current density of NbTi cables for the LHC main dipoles is presented. This newly developed fit function is used as input for the existing sc model and complete magnet cross-sections have been calculated. The simulation results have been compared with measurements at cold of the LHC main dipoles. A very good agreement with measurements for small and intermediate field values could be observed.