Active shielding of cylindrical saddle-shaped coils: Application to wire-wound RF coils for very low field NMR and MRI

We provide an exact expression for the magnetic field produced by cylindrical saddle-shaped coils and their ideal shield currents in the low-frequency limit. The stream function associated with the shield surface current is also determined. The results of the analysis are useful for the design of actively shielded radio-frequency (RF) coils. Examples pertinent to very low field nuclear magnetic resonance (NMR) and magnetic resonance imaging (MRI) are presented and discussed.