Analytical stress calculations for magnetic field coils with anisotropic modulus of elasticity

Abstract

Analytical solutions for the radial and tangential stresses in the midplane of long magnetic field coils are derived, for both constant current density and a 1/r current distribution. The elastic anisotropy is contained in the solution as the ratio of the axial and tangential modulus of elasticity. The critical tangential stress is largest at the inner surface for coils with radial transmission of stress; this is greatly reduced if the coil is softer in the radial direction. An outer reinforcing cylinder becomes quite ineffective in this case. The average axial stress in the midplane is calculated for inclusion in Timoshenko's criterion. The authors also calculate the critical stresses in polyhelix coils with equally distributed stress among the layers. These have a modest advantage over radially soft coils only for a large number of layers.