Numerical modeling of critical-state magnetization in type-II superconducting cylinders under parallel and transverse magnetic field

In this paper we extensively analyze the magnetization of superconducting bulk cylinders in parallel and transverse magnetic field. We use analytic formulations with different Jc(B) dependencies, and compare the magnetization to 2D and 3D numerical computations for finite geometries with different aspect ratios. This subject is a basic study for understanding the hysteretic losses in a cylindrical geometry, which is the typical geometry occurring in superconducting wires and cables. The shift of the peak of the magnetization cycle is always reproduced by FEM 2D and 3D, as a consequence of considering the local field in the Jc(B). Using different Jc(B) dependencies and different cylinder aspect ratio, we have reproduced the behavior of the magnetization in parallel fields, checking simulation results versus analytical calculations. In this framework we also developed the analytic behavior of the magnetization in parallel fields using the generalized Kim model. Finally, for a cylinder in a perpendicular magnetic configuration, we found that 2D numerical simulations, once suitably scaled, are in agreement to 3D simulations.