Homogeneous magnet design using linear programming

We introduce a technique for designing homogeneous magnets using linear programming, We first show that minimum-power homogeneous magnet design can be cast as a linear programming problem. We also show that the method is applicable to minimum conductor mass superconducting magnet design. The method has several advantages over existing techniques including: it allows complete flexibility in arbitrary geometric constraints on both the coil locations and the shape of the homogeneous volume; it guarantees a globally optimal solution; and it offers rapid computation speed (about 30 s). Three resistive magnet design examples and one shielded superconducting magnet design are presented to illustrate the flexibility of the method.