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

This paper proposes a simple semi-analytical method for designing coil-systems for homogeneous magnetostatic fleld generation. The homogeneity of the magnetic fleld and the average magnitude of the magnetic ∞ux 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 fleld is estimated superposing the magnetic induction numerically computed from the analytical expression of the magnetic fleld generated by each coil, obtained using the Biot-Savart's law and the current fllament method. The homogeneous magnetic fleld 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 10mT within a volume 0:5m£0:5m£1m with 99% of spatial homogeneity, with square loops of length less than or equal to 1.5m, and with a power dissipated by Joule efiect less than or equal to 1W per coil. The synthesized magnetic fleld distribution was validated using Finite Element Method simulation, showing a good correspondence between the objective values and the simulated flelds. This method is an alternative to design magnetic fleld exposure systems over large volumes such as those used in bioelectromagnetics applications.