Design of superconducting shim coils for a 400 MHz NMR using nonlinear optimization algorithm

A set of superconducting shim coils for a 400 MHz nuclear magnetic resonance spectrometer was designed, analyzed and constructed. A nonlinear optimization algorithm was employed for the calculation of the optimal conductor shapes and positions of superconducting shim coils. In the optimization, a number of system parameters, including field errors, axial size of coils and spherical harmonics have been constrained to acceptable levels. The results have the property of combining best field quality and also controlling the desired harmonics terms strength. The proposed methodology can also be used to design superconducting and resistive shim coils for other homogeneous magnet systems.