3D analytical calculation of forces between linear Halbach-type permanent-magnet arrays

In the analytical calculation of magnetic and mechanical quantities of Halbach systems, the authors use the Fourier-series approximation because the exact calculations are more difficult. In this work, the interaction forces between linear Halbach arrays are analytically calculated thanks to our recent development 3D exact calculation of forces between two cuboidal magnets with parallel and perpendicular magnetization. We essentially describe the way to separately calculate the forces between two magnets. between one magnet and a Halbach array and between two Halbach systems.