An optimal design of coaxial coils with constraints on inner and outer multipole magnetic fields

An optimal design method for magnets with double-layered coaxial coils to generate a uniform central magnetic field and a small stray magnetic field has been proposed. To find the optimal current density distribution, we used linear programming with constraints on the multipole field strengths, computed with analytical formulae, of the central and stray fields. The final coil positions were optimized with a quasi-Newton method, again taking into account the inner and outer multipole field strengths.