In standard cylindrical gradient coils consisting of wires wound iments can be generated by specially designed superconductin a single layer, the rapid increase in coil resistance with efficiency ing magnets (3), but also occur naturally in the fringe fields is the limiting factor in achieving very large magnetic field gradiof conventional high field superconducting magnets. Chang ents. This behavior results from the decrease in the maximum et al. used an ''anti-Helmholz'' arrangement of superconusable wire diameter as the number of turns is increased. By adoptducting coils, which gives a gradient of approximately 180 ing a multilayer design in which the coil wires are allowed to Tm 01 , in a variety of experiments carried out on systems spread out into multiple layers wound at increasing radii, a more with low mobility (3). The maximum rate of change of field favorable scaling of resistance with efficiency is achieved, thus with position below a 400-MHz, 89-mm bore superconductallowing the design of more powerful gradient coils with accepting magnet is about 60 Tm 01 (4). Such gradients in the able resistance values. By extending the theory used to design stray field have been widely employed in STRAFI (4) experstandard cylindrical gradient coils, we have developed mathematical expressions which allow the design of multilayer coils, and the iments and in diffusion measurements (5). Use of these evaluation of their performance. These expressions have been used systems in gradient generation has the advantage of giving to design a four-layer, z-gradient coil of 8 mm inner diameter, large, highly stable gradients over reasonably large volumes, which has an efficiency of 1.73 Tm 01 A 01 , a resistance of 1.8 V, but the disadvantage of only providing a fixed magnitude and an inductance of 50 mH. This coil produces a gradient which gradient which cannot be switched off. The permanent presdeviates from linearity by less than 5% within a central cylindrical ence of the gradient poses severe lower limits on the bandregion of 4.5 mm length and 4.5 mm diameter. A coil has been width of the RF pulses which must be used in NMR expericonstructed from this design and tested in simple imaging and ments and also restricts the range of pulse sequences which pulsed gradient spin echo experiments. The resulting data verify can be implemented. Magnetic field gradients of similar the predicted coil performance, thus demonstrating the advantages magnitude, which can be rapidly switched on and off, and of using multilayer coils for experiments requiring very large magvaried in magnitude offer some considerable advantages. netic field gradients.