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Purpose The aim of this paper is to present a method for calculating the electromagnetic fields, forces and current density distribution using Fourier series for a two-dimensional quasi steady state model consisting of a conducting uniform plate moving relative to an arbitrary current source with time harmonic excitation. Design/methodology/approach The presented solution is valid for an arbitrary source. A specific source is chosen consisting of a single coil made up of two-time harmonic current filaments. The solutions are derived and presented in a form that allows its expansion to include an arbitrary number of spatially shifted coils conducting arbitrary harmonic currents. Findings The analytical solution is compared to simulations produced using commercial finite element analysis software, ANSYS Maxwell2D and COMSOL, and is found to be in good agreement. The analytical solution provides a direct method to analyze the spatial harmonics in the system and can be computationally significantly faster especially at high relative speeds between the primary source and conducting plate. Originality/value The presented Fourier series solution is applied to simple 2-D model of a single coil with AC current excitation moving relative to a conducting plate. An analytical solution and analysis of this system has not been presented before, to the authors’ knowledge, using Fourier series or any other method.

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To describe the wide range of possible applications of high temperature superconductors (HTSCs) (e.g. magnetic bearings, levitation systems or electrical machines) several appropriate calculation algorithms have been developed. They determine the force interaction between a superconductor and any even multidimensional magnetic field excitation system. Especially good agreements between experiments and computed results have been obtained for the Vector‐Controlled Model, which seems to be the best approximation of the macroscopic superconductivity behaviour. The validation of this model by means of measurements makes it a powerful tool for the design and optimisation of any HTSC application in the field of force generation. It can be used not only for the designing of levitation applications, but also to help the understanding of the flux penetration, flux trapping and magnetisation of bulk superconductors in non‐uniform magnetic fields. By means of this model, the force interaction between superconductors and external magnetic fields for practical multi‐polar configurations, e.g. superconducting levitation systems or inherently stable superconducting bearings has been determined. Furthermore, the time dependency of the forces taking flux flow and flux creep into account, can be considered.

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