A hybrid FPM/BEM scalar potential formulation for field calculation in nonlinear magnetostatic analysis of superconducting accelerator magnets

Abstract

A new hybrid numerical method for the solution of nonlinear magnetostatic problems in accelerator magnets is proposed. The methodology combines the Fragile Points Method (FPM) and the Boundary Element Method (BEM). The FPM is a Galerkin-type meshless method employing for field approximation simple, local, and discontinuous point – based interpolation functions. Because of the discontinuity of these functions, the FPM can be considered as a meshless discontinuous Galerkin formulation where numerical flux corrections are employed for the treatment of local discontinuity inconsistencies. The FPM possesses the advantages of a mesh-free method, evaluates with high accuracy field gradients, and treats nonlinear magnetostatic problems by utilizing, for the same problem, fewer nodal points than the Finite Element Method (FEM). In the present work, the nonlinear ferromagnetic material of an accelerator magnet is treated by the FPM, while the BEM is employed for the infinitely extended, surrounding air space. The proposed hybrid scheme is based on the scalar potential formulation of Mayergouz et.al (1987), also used in the BEM/BEM and FEM/BEM schemes of Rodopoulos et al. (2019, 2020). The applicability of the method is demonstrated with the solution of representative 2-D magnetostatic problems and the obtained numerical results are compared to those provided by the FEM/BEM scheme of Rodopoulos et al. (2020), as well as by the commercial FEM package ANSYS. Finally, the magnetic field utilized for stable bending of the particles’ trajectory in a 16 Tesla dipole magnet design for the Future Circular Collider (FCC) project of CERN is accurately evaluated with the aid of the proposed here FPM/BEM scheme.