A Semi-Analytical Method for a Fast Estimation of the Magnetostatic Forces Acting on Tokamak Components

High-intensity magnetic fields in tokamak structures for nuclear fusion generate significant ferromagnetic forces that must be properly estimated for a reliable design of the mechanical structures. Accurate numerical modeling of these electromagnetic problems is likely to entail high computational costs due to the complexity of the geometries and the need to account for nonlinear material behavior. However, electromagnetic forces are not the only loads acting on tokamaks, as other phenomena, such as seismic forces, must also be considered in their design. Therefore, it is highly beneficial to develop coarse estimates of the electromagnetic loads in order to compare their magnitude with that of other loads. Such estimates are useful not only in the early stages of design, but also in the final design phase, particularly if these forces prove to be negligible. To this end, this paper proposes a semi-analytical method to quickly estimate the forces acting on ferromagnetic components located outside the vessel. The method is based on the calculation of the magnetization by means of a well-established integral method after a coarse discretization of the volume occupied by the ferromagnetic materials. The proposed method is implemented in computational routines made available within this paper, enabling the estimation of these forces even for users who lack the expertise required to operate commercial simulation tools. The method is applied to case studies related to some export components of the ITER tokamak, and the validation is carried out with reference to the accurate numerical solutions provided by both commercial and in-house simulation tools.