Strain energy minimization in SSC magnet winding

Abstract

Differential geometry provides a natural family of coordinate systems, the Frenet frame, in which to specify the geometric properties of a magnet winding. By a modification of the Euler-Bernoulli thin rod model, the strain energy is defined with respect to this frame. Then, it is minimized by a direct method from the calculus of variations. The mathematics, its implementation in a computer program, and some analysis of a Superconducting Super Collider (SSC) dipole by the program are described.