A Numerical Analysis on Gradient Coils in Nuclear Magnetic Resonance for Imaging

A mathematical discussion is introduced to describe the gradient coils characterizing the NMRI system. A comparison between the physical laws characterizing the magnetic field of winding coils and a magnetohydrodynamic analysis is built up. The requirements for gradient coil performance are described and analyzed. Design methods are characterized by mathematical manipulation to reduce the nonlinearities that make the magnetic field not suitable for image extraction. A mathematical study has been shown to represent the Golay’s pairs as generators of linear magnetic fields. The entire study shows how the choice of the magnetic field pattern inside the NMRI can occur by choosing the proper geometrical parameters that are a function of the nonlinearities involved in the gradient coils design.