Superconductor Magnetization Modeling for the Numerical Calculation of Field Errors in Accelerator Magnets

Superconducting magnets are obligatory today in order to provide the high magnetic fields that are needed for the acceleration of heavy particles in particle accelerators. The coils of such magnets are made of type II superconducting material and are exposed to a changing magnetic field which induces a so-called persistent current. Persistent currents are bipolar screening currents that do not decay, but persist due to the lack of resistivity in the superconductor. This way, they are the source of a superconductor magnetization in the coil which disturbs the field quality in the magnet aperture. In the framework of this thesis, a macroscopic superconductor model for the calculation of the magnetization of a thin superconducting cylinder of type II material has been developed. The model considers the dependency of the induced current density on the applied field as well as the local distribution of the magnetic induction within the superconductor. Both, the one-dimensional case of a homogeneous change of an external field as well as the case of rotating magnetic inductions with arbitrary excercising angles in the plane are considered. The repercussion of the screening field on the applied field is considered by means of a fixed-point iteration. A relaxation method accelerates and stabilizes the convergence of the iteration. Hysteresis effects that occur in the superconductor in case of a change in the external field are fully re-produced. The model has been incorporated into the CERN field computation program ROXIE and in such a way is combined with numerical methods as the coupled method of finite elements and boundary elements. This way, the calculation of field errors resulting from non-linear materials as used in accelerator magnets, is possible in combination with the superconductor model. The model has been verified by comparing the calculated field errors with measurements for various magnet types, typically for use in particle accelerators, today. Different methods for compensating the persistent current effect are discussed and one method of inserting a ferromagnetic sheet has been tested and experimentally confirmed the predicted compensatory effect.