Optimal design of thick-walled circular coils for uniform magnetic field generation

Uniform magnetic field coils are widely used as electromagnetic equipment in industrial, medical, and research applications, with Helmholtz coils being a common configuration among them. For applications requiring relatively high magnetic field (~mT), Helmholtz coils typically feature a large coil cross-section. However, this characteristic makes them unsuitable for describing the magnetic field generated by a current loop model in the design process. In this work, we model the magnetic field of a large cross-section Helmholtz coil system, often referred to as a thick-walled Helmholtz coil. By employing a genetic algorithm, we transform the design problem of Helmholtz coil into a constrained optimization problem. Subsequently, we propose a method for reverse designing a Helmholtz coil based on constraints on the target magnetic field. Finite element simulations verify the accuracy of the established magnetic field calculation model in describing the magnetic field generated by the thick-walled Helmholtz coil. Moreover, the designed Helmholtz coil effectively meets the design constraints and objectives. This method addresses the issue of significant errors in calculating the magnetic field and its uniformity resulting from the cross-section effect during the design of thick-walled Helmholtz coils. Furthermore, it satisfies the constraints for coil operating time and lightweight design.