Computation of the Magnetization of Type II Superconductors for Potential Beam Screen Coatings of the Future Circular Collider

High-temperature superconductor coatings have been proposed for the reduction of the beam coupling impedance for the future circular collider's hadron-hadron (FCC-hh) option. These coatings are, however, prone to hysteretic magnetization due to the ramp of the external magnet field. We present a mathematical formulation and implementation of Bean's model, which is a simplified, phenomenological model of persistent current loops and magnetization. After validating the model on simplified, analytically accessible examples, it is applied to the FCC setup under various conditions. The conclusion is that the magnetization might impair the magnetic field quality strongly for a complete coating, but a coating in the form of stripes can be a feasible tradeoff between field quality and impedance reduction.