Modified Bean Model and FEM Method Combined for Persistent Current Calculation in Superconducting Coils

Field variations in the LHC superconducting magnets, e. g. during the ramping of the magnets, induce magnetization currents in the superconducting material, the so-called persistent currents that do not decay but persist due to the lack of resistivity. This paper describes a semi-analytical hysteresis model for hard superconductors, which has been developed for the computation of the total field errors arising from persistent currents. Since the superconducting coil is surrounded by a ferromagnetic yoke structure, the persistent current model is combined with the finite element method (FEM), as the non-linear yoke can only be calculated numerically. The used finite element method is based on a reduced vector potential formulation that avoids the meshing of the coil while calculating the part of the field arising from the source currents by means of the Biot-Savart Law. The combination allows to determine persistent current induced field errors as function of the excitation and for arbitrarily shaped iron yokes. The model has been implemented into the ROXIE program and is tested using the LHC dipole magnet as an example.