Multilayer Gradient Coil Design

In standard cylindrical gradient coils consisting of wires wound in a single layer, the rapid increase in coil resistance with efficiency is the limiting factor in achieving very large magnetic field gradients. This behavior results from the decrease in the maximum usable wire diameter as the number of turns is increased. By adopting a multilayer design in which the coil wires are allowed to spread out into multiple layers wound at increasing radii, a more favorable scaling of resistance with efficiency is achieved, thus allowing the design of more powerful gradient coils with acceptable resistance values. By extending the theory used to design standard cylindrical gradient coils, we have developed mathematical expressions which allow the design of multilayer coils, and the evaluation of their performance. These expressions have been used to design a four-layer,z-gradient coil of 8 mm inner diameter, which has an efficiency of 1.73 Tm⁻¹A⁻¹, a resistance of 1.8 Ω, and an inductance of 50 μH. This coil produces a gradient which deviates from linearity by less than 5% within a central cylindrical region of 4.5 mm length and 4.5 mm diameter. A coil has been constructed from this design and tested in simple imaging and pulsed gradient spin echo experiments. The resulting data verify the predicted coil performance, thus demonstrating the advantages of using multilayer coils for experiments requiring very large magnetic field gradients.