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

Abstract

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.

Edgewise Bending Strain in Helical Coils With Geodesic Windings Based on Virial Theorem

“…8. When b/a exceeds 1.2 in the case of A = 3 and N = 3.9, the direction of curvature vector is reversed, and the coil with a tension is detached from the torus [13]. Therefore, the maximum of torsion in the geodesic coil of N = 3.9 on the torus with A = 3 has the smallest value τ 0.6/a which is similar to τ ave for b/a = 1.2.…”

“…Recently, we proposed a new modulated winding based on a geodesic which can be applied to windings under tension [13]. In order to apply FBC to high-temperature superconducting tapes, the degradation of superconducting properties originating from edgewise bending strain is an important problem [14].…”

Reduced-Size LHD-Type Fusion Reactor with D-Shaped Magnetic Surface

“…Thus, the helical coil winding is expected to be mechanically stable and easy to manufacture. Furthermore, it has been noted [5] that a geodesic winding is very close to a modulated winding for the force balance coil, which reduced the electromagnetic force on the coils, for a circular winding frame. Reduction of the stress working on the coils mitigates engineering problems in reactor construction.…”

“…Geodesic winding on a toroidal surface with a constant major radius R and a constant minor radius a has been studied for superconducting magnetic energy storage [5] to reduce the electromagnetic stress in coil systems.…”

Alpha-Particle Confinement Control of the Geodesic Winding of LHD-Type Fusion Reactors

“…The geodesic winding on a toroidal surface with a constant major radius R and a constant minor radius a was studied for the superconducting magnetic energy storage (SMES) [7] to reduce the electromagnetic stress working in coils systems. In order to express the various types of winding frames with only a few parameters (a 1 , a 2 , a 3 ), we use the following form for the cross-section of the winding frame χ : poloidal angle R 0 : major radius of the helical coil a c : minor radius of the helical coil…”