Magnetic- and stress-fields of cylindrical non-uniform current density superconducting coils

Superconducting coils with an inhomogeneous current density distribution yield more field for less volume of superconductor. The advantages of these systems are lower costs and an improved cooling. The latter is important for high field magnets. Mechanical stresses induced by the electromagnetic forces are the limiting factor in designing such coils. The inhomogeneous current field is produced by a set of concentric subcoils. The radial and tensile stresses and the radial displacements in the subcoils are calculated. This calculation requires the field-shape in the coils. An exact calculation shows a linear decrease of the field with the radius in each subcoil. Thus the stress-calculations are very simple and one does not need a computer. As an example this method is applied to a 10 T-magnet with three subcoils. In this case the results of our exact calculation differ from the approximation of Kilbet al., Steklyet al. and from the magnetic pressure estimateB ²/2μ ₀ up to a factor of three.