A vector hysteresis model for superconducting filament magnetization in accelerator magnets

Magnetic field changes in the coils of superconducting magnets are shielded from the filaments' core by so-called persistent currents which can be modeled by means of the critical state model. This paper presents a semianalytical two-dimensional model of the filament magnetization due to persistent currents for changes of the magnitude of the magnetic induction and its direction while taking the field dependence of the critical current density into account. The model is combined with numerical field computation for the calculation of field errors in superconducting magnets. The filament magnetization and the field errors in a nested orbit corrector magnet for the large hadron collider project at CERN have been calculated as an example.