Nonlinear three-port magnetic-circuit elements for simulating bending magnets

Abstract

Purpose The purpose of this paper is to show that constructing magnetic equivalent circuits (MECs) for simulating accelerator magnets is possible by defining a three-port magnetic element for modelling the T-shape field distribution, where the flux leaves the yoke and enters the aperture. Design/methodology/approach A linear three-port magnetic element is extracted from an analytical field solution and can be represented by a number of two-port elements. Its nonlinear counterpart is obtained as a combination of the corresponding nonlinear two-port elements. An improved nonlinear three-port element is developed on the basis of an embedded nonlinear one-dimensional finite element model. Findings The T-shaped field distribution comes together with a complicated interplay between the saturation of the ferromagnetic yoke parts and flux leaking to the aperture. This is more accurately modelled by the improved nonlinear three-port magnetic element. Research limitations/implications MECs have a limited validity range, especially for configurations where a high saturation level and fringing flux effects coexist. Practical implications The results of the paper appeal to be careful with applying nonlinear MECs for simulating bending magnets. Originality/value A new nonlinear three-port magnetic element for ferromagnetic yoke parts with T-shaped flux distribution has been developed.