Development and validation of multi-physics models for the analysis of superconductive magnets subject to nuclear heating

Tokamaks and Stellarators emerge as leading candidates for achieving controlled fusion reactions through magnetic confinement. Plasma confinement using magnets, a fundamental element in this context, holds particular promise with High-Temperature Superconductors (HTS), which have the potential to revolutionize the fusion industry by overcoming the limitations of Low-Temperature Superconductors (LTS), enabling the development of compact, steady-state fusion power systems. Despite their potential, these complex devices must be maintained at cryogenic temperatures while being in close proximity to a 10^8 K plasma, generating a heat flux in the range of several MW/m^2 due to neutrons produced by DT or DD reactions. Neutrons, in fact, move in the materials losing their kinetic energy by exchanging into thermal energy, and the deposited heat can become relevant in particular dealing with compact devices. Consequently, a comprehensive interdisciplinary multi-physics approach, addressed in this paper, is essential to address magnetic, thermal, mechanical, and cryogenic aspects. The first step of the proposed workflow is to internally generate simplified and consistent CADs from the central spline. This simplification applies to both the cables and the plates of the magnets, resulting in a design that is easy to use for neutronic simulations. In these simulations, the emphasis is on volumes rather than intricate details that could complicate the geometry and meshing process. The goal is to streamline the CAD representation, making it more accessible for neutronic simulations while omitting smaller details that do not significantly impact the simulation outcomes. Open-source software, such as FreeCAD, is employed for this purpose. As a second step, the generated CADs are imported into OpenMC, an open-sourceMonte Carlo code capable of evaluating neutronic flux in 3D geometries. The magnets undergo simulation with a point source representing the plasma, and the resulting heat is non-uniformly distributed on the magnets. The thermal-hydraulic analysis is carried out using OPENSC2, a software presently in development by the MAHTEP group at Politecnico di Torino. OPENSC2 is designed to analyze quench phenomena and thermal-hydraulic behavior. To operate, this tool necessitates 1D inputs for the magnetic self-field – assessed using COMSOL software – and neutronic heating – assessed through OpenMC. The three-dimensional outputs from these software applications undergo post-processing to derive a 1D heat load and magnetic field distribution along the curvilinear coordinate that aligns with the cable length. One notable feature is the tool's ability to predict the behavior of both planar Tokamak coils and non-planar 3D Stellarator superconductors. Two case studies are considered: a generic Tokamak shape and the Helical-Axis Advanced Stellarator (HELIAS), a fusion power reactor with a thermal fusion power of 3000 MW. The versatility of the presented workflow is discussed, as it can handle any geometry by taking only the spline as input. In perspective it will be able to construct the blanket and all the materials between the magnets and the plasma source, adding further depth and relevance to the simulations.