An inverse approach to the design of MRI main magnets

We present a new method for the design of MRI main magnets, based on a variational approach with constraints introduced by Lagrange multipliers. The extrema are located with a combination of analytical and numerical techniques. This method has been tested in the design of non-shielded and actively-shielded magnets. Several representative designs are given. The method is very flexible, having been applied also to the investigation of gradient coils, and could be adapted to the design of other static and quasi-static field systems. It may also be used to consider alternate geometries.>