Longitudinal gradient coils with enhanced radial uniformity in restricted diameter: Single-current and multiple-current approaches.

An important requirement for a gradient coil is that the uniformity of the generated magnetic field gradient should be maximal within the active volume of the coil. For a cylindrical geometry, the radial uniformity of the gradient turns critic, particularly in cases where the gradient-unit has to be designed to fit into the inner bore of a compact magnet of reduced dimensions, like those typically used in fast-field-cycling NMR. In this paper we present two practical solutions aimed to fulfill this requirement. We propose a matrix-inversion optimization algorithm based on the Biot-Savart law, that using a proper cost function, allows maximizing the uniformity of the gradient and power efficiency. The used methodology and the simulation code were validated in a single-current design, by comparing the computer simulated field map with the experimental data measured in a real prototype. After comparing the obtained results with the target field approach, a multiple-element coil driven by independent current sources is discussed, and a real prototype evaluated. Opposed equispaced independent windings are connected in pairs conforming an arrangement of independent anti-Helmholtz units. This last coil seizes 80% of its radial dimension with a gradient uniformity better than 5%. The design also provides an adaptable region of uniformity along with adjustable coil efficiency.