Particle scattering in magnetised plasmas: a theoretical and numerical approach

The intricate dynamics of charged particles within plasmas are mainly shaped by their collisional interactions. As a result, it is crucial to address these phenomena through both theoretical and numerical approaches. In pursuit of this objective, this work embarks on reviewing the formal derivation of the Vlasov equation, followed by an extensive exploration of Coulomb scattering, elucidating the Landau collision integral and its underlying characteristics. Furthermore, we delve into the nonconventional neoclassical theory for toroidal systems, providing the theoretical framework for the subsequent numerical findings. Utilizing the ELMFIRE code, gyrokinetic simulations employ a discrete Landau collision integral, ensuring the conservation of energy and momentum. Tailored to conservation laws, a specific binary collision model provides valuable insights into variations in impurity density arising from steep gradients in density and temperature profiles. The analysis compares Landreman-Fülöp- Guszejnov model's theory with neoclassical predictions and ELMFIRE data. Remarkably, within the analytical theory's validity, numerical agreement is 5-10%, especially for δ<0.4 with low charge numbers. Yet, within the pedestal region, the Landreman-Fülöp-Guszejnov framework may not be directly applicable due to pronounced gradients. Furthermore, a novel analysis explores the correlation between turbulent transport and the radial electric field. Using Lower Hybrid (LH) heating operator in an FT-2 tokamak at off-axis and onaxis reveals heightened turbulence at r/a=0.55 during a 70μs simulation. Turbulence induces noticeable fluctuations in the radial electric field profile, with strong high-shearing flow in the former and neoclassical dominance in the latter. These findings align with prior research, suggesting a robust shearing phenomenon, reinstating transport equilibrium. In conclusion, to enhance the central theme of this dissertation, we investigate the formal derivation of a collisional bracket from the Landau collision integral using the metriplectic bracket formulation for dissipative systems. This theoretical framework is then applied to the guiding center Vlasov-Maxwell-Landau model, resulting in a specific collisional bracket that ensures energy and momentum conservation. The implications of this finding are explored within broader frameworks, including the electromagnetic gyrokinetic case, offering a theoretical culmination to this dissertation.