This paper continues the development of a new approach for the design of shim and gradient coils, used in magnetic resonance imaging (MRI) applications. A cylindrical primary coil of radius a and length 2L is placed inside a co-axial shield cylinder of radius b. An active shielding strategy is used to create a desired target field at an arbitrarily specified (cylindrical) location within the primary coil, and to annul the field at a certain radius outside the shield. The form of the interior target field may be chosen arbitrarily by the designer, although zonal and tesseral harmonics are typically used in MRI applications. The method presented here designs coil windings on both the primary and shielding cylinders, to produce fields that conform to the specified interior target field and the annulled field exterior to the shield. An additional feature of the method presented here is that the target field inside the primary coil is matched at two different radii, to improve overall accuracy. The method is illustrated by designing several shielded shim coils, for creating higher order tesseral fields located asymmetrically within the coil. The simpler case of pure zonal fields is discussed separately and applied to the design of some higher order shielded coils. [References: 22]
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