Global optimal design of longitudinal gradient magnetic field coils based on a modified PSO algorithm in micro atomic sensors

Micro atomic sensors have broad application prospects for their small volume and high accuracy. The inhomogeneity of the magnetic field limits the accuracy and resolution of atomic sensors. In order to realize field corrections, this paper presents a global optimization method for the design of gradient coils to produce arbitrary longitudinal gradient fields, which transforms the design of the gradient coils into a nonlinear optimization problem. Then the optimized parameters of coils are acquired through a modified particle swarm optimization algorithm with acceleration coefficients and inertia weights changing as power functions of iterations. This global optimization method combines derivatives at the origin with field relative errors in the whole target space. An analytical model of arbitrarily gradient fields and field relative errors spatial distribution is introduced by the Taylor series expansions. Numerical simulation results show that the gradient coils designed through the global optimization method effectively reduce the maximum relative errors, compared with the Maxwell coil, the Francoise coil and the gradient coils designed through the local optimization method. The decoupling design for even-order gradient field coils is also proposed through the global optimization method. Experimental results prove the correctness and effectiveness of the numerical simulation results.