Inversion methods for fast-ion diagnostics in fusion plasmas

The present dissertation presents my Ph.D. research on inversion methods for fast-ion diagnostics in fusion plasmas. This work is part of a collaboration between the Technical University of Denmark and École Polytechnique Fédérale de Lausanne. My research focused on developing mathematical methods for solving ill-posed inverse problems in velocity-space tomography applied to synthetic and experimental data from projections of fast-ion velocities, ion cyclotron emission, and fast-ion loss detectors. 

A main objective in diagnostics of fusion plasmas is to determine the fast-ion velocityspace distribution function. As part of my research, a technique called “slowing-down physics regularization” was developed to determine the fast-ion velocity-space distribution function throughout the fusion plasma from projections of velocities of the fast ions. This technique was applied to synthetic data from the TCV tokamak and the W7-X stellarator. 

Extensive modelling of the physical systems is required to determine the fast-ion velocity-space distribution function. In fast-ion parlance, such models are built into a “weight function matrix”. For point-wise determination of the velocities of the fast ions emitting ion cyclotron emission, 2D weight functions and reconstruction techniques using them were developed. 

The ill-posed inverse problem can be solved using regularization methods. Tikhonov regularization has been the standard regularization method in velocity-space tomography for the past decade. Other regularization techniques were investigated and evaluated. In particular, algebraic iterative reconstruction techniques were applied to synthetic and experimental measurements from fast-ion loss detectors and compared with Tikhonov regularization. 

When diagnosing fusion plasmas, simulations are performed to model the physical processes. Measurements from fast-ion loss detectors are simulated using a code called “FILDSIM”. A raised cosine model was proposed as an alternative to the standard Gaussian model. The resulting improvements in weight functions and reconstructions were obtained for the TCV tokamak. A model based on these improvements achieves higher precision and faster calculations, making it possible to compute reconstructions of measurements from fast-ion loss detectors between repeated experiments. 

In addition, neural networks were used to perform velocity-space tomography. Neural networks were trained to suggest an optimal value of the regularization parameter for Tikhonov regularization and to compute reconstructions directly from synthetic and experimental measurements from fast-ion loss detectors. The neural networks provide instantaneous reconstructions of the fast-ion velocity-space distribution function, which can supplement reconstruction methods for diagnostics of fast ions in fusion plasmas and contribute to improved control of fusion plasmas.