Force Balance and Stability of Toroidal Helical Coil with Circular Cross Section

Abstract

Stability and force equilibrium of toroidal helical coil with circular cross section were investigated. In this paper, we derived and calculated equations for equilibrium of toroidal helical coil based on an axisymmetric surface current model. The helical coil, which is modulated in such a way that a magnetic surface coincides with the coil surface, can reduce overturning force generated by electromagnetic forces. We analyzed the stability of the toroidally modulated helical coil and confirmed that this modulated configuration is held in equilibrium while it is unstable. This condition means the minimum inductance condition. Moreover, we formulated the relationships between electromagnetic forces and stresses acting on toroidal helical coil with circular cross section, and we compared the stress distributions calculated by the equations with those from finite element method (FEM) analysis.

Time-extended inductive tokamak discharges with differentially-tilted toroidal field coils

“…To address the first of these two problems (EM, or Lorentz, forces), various kinds of modification of the TFCs have been proposed, from an inclination of the meridian planes containing the coils, to a uniform, or differential, azimuthal tilting of part or even the entire profile of the coils [5][6][7][8][9][10][11][12][13][14]. In this paper, which is a continuation of the work presented in [13,14], we consider TFCs with differential tilting (i.e.…”

The differentially-tilted toroidal field coil concept for tokamaks

“…Starting from 1994 up to 2011 a series of papers dealing with the concept of the quasi-force-free helical winding have been published by Japanese authors ( [7][8][9][10][11], to cite a few). While the guiding objective is similar to ours, we follow a different methodology, that is, we look for configurations that optimally tilt the region of the coil under consideration, thus obtaining a tilting that varies around the coil (hence the name "differentially-tilted" coil).…”

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

“…The coils, which are also designed following the modulated winding configuration, can generate strong magnetic field [11] even when the device size is small. However, it is difficult to make a larger device since the tension-free modulated winding configuration is mechanically unstable [12], and requires a great effort for windings.…”