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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.

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.

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.

MECs have a limited validity range, especially for configurations where a high saturation level and fringing flux effects coexist.

The results of the paper appeal to be careful with applying nonlinear MECs for simulating bending magnets.

A new nonlinear three-port magnetic element for ferromagnetic yoke parts with T-shaped flux distribution has been developed.