A Theoretical Model for Designing Superconducting Magnets

A theoretical model for designing a family of dipole magnets suitable for accelerator and other applications is presented here. A general formalism for determining required current density for producing a uniform magnetic field in the region of interest for an arbitrary shaped 2-D magnet has been developed. The current densities required for circular, elliptical, and dumbbell-shaped bores have been derived for obtaining a dipole magnet. The current distributed zone predicted by the theory is, then, discretized by certain number of coil blocks and their actual positions have been optimized. As an illustration, we consider an elliptical bore with two, three, and five blocks, and the corresponding field uniformities have been verified with the standard "POISSON" code. The contributions of higher order multipoles for this arrangement of the conductors are found to be extremely low.