Optimization of a Coil System for Generating Uniform Magnetic Fields inside a Cubic Magnetic Shield

Ultra-low magnetic fields have drawn lots of attention due to their important role in scientific and technological research. The combination of a magnetic shield and an active compensation coil is adopted in most high performance magnetically shielded rooms. Special consideration needs to be taken in the coil design since the magnetic shield significantly affects the uniformity of the magnetic field that is generated by the coil. An analytical model for the magnetic field calculation of the coil inside a cubic magnetic shield is proposed based on the generalized image method, which is validated by finite element analysis. A novel design method of the coil used in a cubic magnetic shield with a large homogeneous volume is proposed. The coil parameters are optimized to obtain a large cubic uniform volume with desired total deviation rate by discretizing the central volume in the coil. In the desired total deviation rate, the normalized usable volume of the new coil increases by 70% when compared with the Merritt coil. A coil system is developed according to the parameters obtained based on this method. The magnetic flux density and practical deviation rate of the coil are measured to validate the accuracy of this model and the feasibility of the design method. The experimental magnetic flux density agrees well with the analytical value. The maximum practical deviation rate of uniform volume of 0.8 x 0.8 x 0.8 m is in good agreement with the theoretical design value, taking into account the experiment errors.