Limitations of Surface Current Model of Magnetic Field and a Remedy

It is well known that any realistic static magnetic field in a source-free volume can be generated by electric currents on a surface enclosing the volume. The magnetic field generated by surface currents is equivalent to that from magnetic dipoles distributed on the surface and along the surface normal directions. We demonstrate the limitations of the surface current model for instrumentation, and show vertical current loops corresponding to magnetic dipoles along the surface tangential directions may be employed to mitigate these limitations. We consider loop coil elements distributed on a cylindrical surface. A closed-surface array has loops on the entire surface, and an open-surface array does not have loops on the surface of both ends. A coil array may contain only flat elements (each loop is inside the cylindrical surface) or composite elements consisting of three orthogonal loops (one flat loop and two vertical loops) instead of just one flat loop at the location of each element. With computer simulations, the array coils were tested for generating the spatial field pattern of a vertical loop or a linear field gradient. The simulations showed that (1) an open-surface composite loop array produces less errors than a similar flat loop array in generating linear field patterns; the percentage root mean square error (RMSE) of the composite coil loops was 8.46% compared to 21.5% for the similar flat loops; (2) A composite loop array consumes less power than a corresponding flat array. For the open-surface array with a similar number of loops, the power consumption of the composite loop array was 73.9 versus 184 (arbitrary power units) for the flat loop array.