A target field approach to optimal coil design

Using a Fourier-Bessel expansion of the magnetic field generated by currents flowing on a cylinder, the relationship between current and field may be inverted. Hence the current density required to generate a specified target field Bz on the surface of a cylinder of smaller radius may be evaluated. Gradient, solenoidal and shim coil designs based on this approach provide exceptionally large usable volumes while remaining compact and, if necessary, of low inductance.