Modeling and correction of 3D error fields in tokamak plasmas.

Controlled thermonuclear fusion holds immense promise as a solution to the medium-term global energy problem. The process is clean, highly secure, and theoretically capable of providing vast amounts of energy. How- ever, achieving nuclear fusion on Earth requires substantial technical and technological efforts. The fuel, called plasma, is made up of charged particles that can be arti- ficially confined to produce nuclear fusion reactions, similar to what happens in the Sun. Two mainly confinement approaches are currently under inves- tigation: inertial confinement, based on the use of high coherence lasers, and magnetic confinement, based on high magnetic fields. The most promis- ing configuration for future commercial reactors is the Tokamak, based on magnetic confinement. These machines have a toroidal geometry, are in prin- ciple axisymmetric and resembling transformers where the plasma serves as the secondary: the excitation of an induced current (on the order of MA) plays a dual role, providing heating (through ohmic dissipation) and controlling the plasma (using external conductors). Three-dimensional effects, known as Error Fields, can significantly impact tokamak performance. Error fields refer to small imperfections or deviations in the symmetry and uniformity of the tokamak’s magnetic fields. These errors can arise from various factors, including manufacturing tolerances, mechanical stress, or electromagnetic interactions. Although these errors may seem minor, they can profoundly affect plasma confinement stability and performance. Presence of error fields can in fact lead to plasma disruptions, causing instabilities and confinement losses. These disruptions not only reduce fusion efficiency but also risk damaging the tokamak’s plasma facing components. In extreme cases, such disruptions can release substantial amounts of energy and heat, potentially damaging the tokamak itself. Researchers and engineers continually work on mitigating error field effects through advanced control techniques and sophisticated magnetic field shaping. Understanding and managing error fields are critical steps in achieving a stable and efficient fusion reactor, providing a clean and virtually limitless energy source for the future. In this thesis a model for the estimation of Error Fields is presented. The approach allows, in a very elegant way, to take into account both assembly and manufacturing uncertainties of the magnetic system. The uncertainties are projected in a suitable functional space of finite dimension, called space of parameters, and a relation between the set of the parameters and, via geometry modelling of the coils, the perturbed field contribute is obtained. In the limit of small perturbations this complex model provides a linear relation suitable for Monte Carlo analysis of the Error fields impact. The procedure has been successfully applied for the estimation of error fields in two tokamaks: the Divertor Tokamak Test (DTT) Facility, the Italian tokamak under construction at the Frascati ENEA Research Center, Rome, and DEMO, the European demonstration power plant. DTT plays a leading role in fusion research, the main aim being to explore alternative solutions for the extraction of the heat generated by the fusion process. Additionally, a technique employing Helmholtz’s theorem is presented. This method acts as a post-processor of the magnetic flux solution of the Grad-Shafranov equation. The procedure, which utilizes a triangular fi- nite element formulation, provides magnetic field results with an accuracy of O(h^2) resulting in reliable inearized models.