Optimized electromagnetic coil design theory

The authors review the general theory of electromagnetic coil design, the starting point for which is the Biot-Savart equation, which expresses the relationship between current distribution and the resultant static magnetic field. They introduce a reformalization of the Biot-Savar equation which provides for the general design of electromagnetic coils based on surface current distributions. It is demonstrated that this reformalization can be used to optimize the design of electromagnets having restricted length. A method of screened coil design is described. It produces magnetic fields of a particular type optimized on a least-squares basis.<>