Biplanar gradient coil design by simulated annealing

Simulated annealing has been applied to the design of biplanar gradient coils for use in NMR microscopy. This method allows a variety of coil parameters to be considered, such as homogeneity over a specified region of interest (ROI), power dissipation, and efficiency. Chosen parameters are represented in an overall figure of merit which is then minimized by the simulated annealing approach. Unlike most analytical techniques which rely on the use of the stream function, with this technique the coil properties are calculated directly from the wire positions, so there is no stage of approximation between current density and the actual coil design. Using this technique, we have designed biplanar x and z gradient coils for use in an 11.7-T NMR microscope. In each case, the coils were composed of straight wire units. The plane spacing was set at 10 mm and the ROI was a central cube of side 6 mm. Starting from a design generated using the target field approach, simulated annealing was applied with the aim of minimizing the ratio of power dissipation per unit current to the square root of coil efficiency while maintaining adequate gradient homogeneity. The efficiency and power dissipation per unit current of the resulting x and z coils were 117 mT m^–1 A^–1 and 0.1 W A^–2, and 99 mT m^–1 A^–1 and 0.4 W A^–2, respectively.