Validation and results of an approximate model for the stress of a Tokamak toroidal field coil at the inboard midplane

TL;DR

This paper introduces a fast, approximate analytical model for assessing stress, strain, and displacement in Tokamak toroidal field coils, validated against detailed FEA, enabling rapid design optimization for fusion reactors.

Contribution

The paper presents a new simplified model for TF coil stress analysis that balances speed and accuracy, suitable for iterative design and optimization processes.

Findings

Model's Tresca stress within 10% of FEA results

Enables optimization of fusion pilot plant designs

Sets an upper magnetic field limit of 29 Tesla for steel coils

Abstract

We present the verification, validation, and results of an approximate, analytic model for the radial profile of the stress, strain, and displacement within the toroidal field (TF) coil of a Tokamak at the inner midplane, where stress management is of the most concern. The model is designed to have high execution speed yet capture the essential physics, suitable for scoping studies, rapid evaluation of designs, and in the inner loop of an optimizer. It is implemented in the PROCESS fusion reactor systems code. The model solves a many-layer axisymmetric extended plane strain problem. It includes linear elastic deformation, Poisson effects, transverse-isotropic materials properties, radial Lorentz force profiles, and axial tension applied to layer subsets. The model does not include out-of-plane forces from poloidal field coils. We benchmark the model against 2D and 3D Finite Element Analyses (FEA) using Ansys and COMSOL. We find the Tresca stress accuracy of the model to be within 10\% of the FEA result. We show that this model allows PROCESS to optimize a fusion pilot plant, subject to the TF coil winding pack and coil case yield constraints. This model sets an upper limit on the magnetic field strength at the coil surface of $29$ Tesla for steel TF coil cases, with the practical limit being significantly below this.