Numerical calculation of the saturation induced field errors in the main dipole of CERN's future large hadron collider

A survey of the main magnetostatic field problems arising in context with superconducting (SC) magnets is presented. The cardinal point is the treatment of the complicated coil shapes in the Finite Element (FE)-model. The total Vector Potential (VP)-formulation has an important drawback when applying it to coil-dominated accelerator magnets. Since the coil structure is part of the FE-mesh a detailed description of the coil is hardly possible. By introducing a reduced VP the coil structure can be eliminated from the FE-mesh. Furthermore, the extension of the 2D reduced VP-formulation to three dimensions is presented. A formulation with node-based elements requires the continuity of the normal component of the divergence of the VP on the material boundaries between iron and air. In the 2D-formulation this continuity condition is implicitly satisfied since the divergence of the VP is identically zero. In order to overcome these convergence problems a rather new type of FEs, namely edge-elements are applied. An estimation of the integrated harmonics in the magnet ends of the LHC main dipole is given. Conclusions are presented concerning the applicability of this class of FE-formlations to SC accelerator magnets. (author)