Theoretical Analysis of the Preload Force for a Tokamak Central Solenoid Coil Structure

A simple one-dimensional analytic formulation is developed for approximate determination of the preload force that must be applied by tie-rods and/or tie-plates for a multimodule central solenoid coil assembly in tokamak devices. The primary purpose of the preload is to ensure that vertical tensile stress does not develop between any two adjacent module coils within the assembly. The absence of the tensile force is a minimal requirement needed to prevent lateral movements of the coils, when friction is the sole means available. An excessive preload, on the other hand, can damage insulation and conductor jackets. The analysis is based on a model system in which the vertical motion of the coil winding is described through representation of the coil conductors and tie-rods/-plates with linear springs. The coupled spring system is represented by a system of simultaneous linear equations, which is solved analytically to obtain the compression force at each spring in terms of the applied preload, electromagnetic forces on the springs, and spring constants. Although this procedure lacks the rigor of complex two- or three-dimensional analyses, it is expected to be able to play some useful role.