Analysis of Stress Distribution in Helical Coils With Geodesic Windings Based on Virial Theorem

Distributions of stress in helical coils with the geodesic winding based on virial theorem are analyzed theoretically and numerically. A force-balanced coil (FBC) is a multi-pole helical hybrid coil combining toroidal field (TF) coils and a solenoid helically wound on a torus. The combination reduces the net electromagnetic force in the direction of major radius by canceling the centering force due to the TF coil current and the hoop force due to the solenoid current. The FBC concept was extended using the virial theorem which shows that strength of magnetic field is restricted by working stress in the coils and their supporting structure. High-field coils should accordingly have same averaged principal stresses in all directions which is named the virial-limit condition. Recently, we made a model FBC which were neither impregnated with epoxy resin nor reinforced with stainless steel wires. Using acoustic emission measurements, we found that the wires vibrated in response to electromagnetic force changes. Since FBC winding is modulated to reduce the tilting force, the winding is slightly similar to but different from the shortest geodesic trajectory and has no tensile load. In order to reduce the vibration, the geodesic winding is expected to be effective. In this work, we analyze the effect of the winding modulations including the geodesic modulation for the stress distribution of helical windings.