Design of Self-Shielded Gradient Coil Based on an Improved PSO Algorithm

To address the severe coupling between the gradient coil and the magnetic shielding system in atomic sensor systems, we propose a self-shielded gradient coil with significantly reduced nonlinear error, designed using an improved Particle Swarm Optimization (PSO) algorithm. The proposed design effectively suppresses the coupling between the self-shielded gradient coil and the magnetic shielding device, while simultaneously generating a gradient magnetic field with substantially reduced nonlinear error. The self-shielded gradient coil consists of eight pairs of coils carrying antiparallel currents and arranged symmetrically with respect to the origin. This configuration produces a gradient magnetic field at the coil center while ensuring rapid decay of the magnetic field outside the coil region. After optimizing the coil positions, current magnitudes, and current directions using a Modified-Weight PSO (MW-PSO) algorithm, numerical simulations are conducted. Compared with gradient coils optimized using the classical PSO algorithm, the magnetic field deviation is reduced from 4 × 10^-3 to 1 × 10^-5, representing an improvement of two orders of magnitude. The proposed optimization approach provides an effective solution for the development of core components capable of high-precision gradient magnetic field generation and compensation in atomic sensor systems.