A semi-analytical method for the design of coil-systems for homogeneous magneto-static field generation

Abstract

This paper proposes a simple semi-analytical method for designing coil-systems for homogeneous magnetostatic field generation. The homogeneity of the magnetic field and the average magnitude of the magnetic flux density inside of the volume of interest are the objective functions chosen for the selection of the coil-system geometry (size and location), number of coils and the number of turns of each winding. The spatial distribution of the magnetostatic field is estimated superposing the magnetic induction numerically computed from the analytical expression of the magnetic field generated by each coil, obtained using the Biot-Savart's law and the current filament method. The homogeneous magnetic field is synthesized using an iterative algorithm based on TABU search with geometric constraints, which varies the design parameters of the windings to meet the requirements. The number of turns of each coil and gauge of wire used for the windings is adjusted automatically in order to achieve the target average magnitude of the magnetic induction under the constraints imposed by power consumption. This method was used to design a coil arrangement that can generate up to 10 mT within a volume 0.5 m×0.5 m×1 m with 99% of spatial homogeneity, with square loops of length less than or equal to 1.5 m, and with a power dissipated by Joule effect less than or equal to 1 W per coil. The synthesized magnetic field distribution was validated using Finite Element Method simulation, showing a good correspondence between the objective values and the simulated fields. This method is an alternative to design magnetic field exposure systems over large volumes such as those used in bioelectromagnetics applications.