Effects of 3D Ideal MHD Equilibrium Geometry on Neoclassical Properties in Tokamaks: Exploring Bootstrap Current and Impurity Accumulation

This thesis concentrates on investigating the presence of 3D ideal MHD instabilities, particularly a saturated 1/1 ideal internal kink, on neoclassical phenomena such as the bootstrap current and heavy impurity transport. The MHD equilibria are generated using the ideal MHD equilibrium solver \texttt{VMEC} under free-boundary conditions and is used as a basis for the neoclassical calculations performed. The bootstrap current and the parallel flows are examined using the Shaing-Callen 3D neoclassical formulation\cite{ShaingReview}. The examination of equilibria with ideal response to 3D perturbations such as toroidal field ripple and resonant magnetic perturbations (RMPs) is performed. It is found that RMPs and toroidal ripple produce a weak 3D response leading to a bootstrap current profile indistinguishable from axisymmetry. Any additional effects are further obscured by the presence of numerical resonances on q-rational surfaces. It is found, however, that a non-resonant 1/1 ideal internal kink which avoids the q=1 resonance, is well-suited for computation of the bootstrap current density. The bootstrap current is observed to be strongly augmented in the helical core region of the 1/1 internal kink before returning to match the axisymmetric values in the near-axisymmetric region outside the helical core. Explanations for the augmentation of the bootstrap current are provided in an analytical derivation. A similar augmentation is observed for background ion flows as well, including the presence of a finite poloidal flow. Heavy impurities such as tungsten face friction because of the impurity particles colliding with the background ions, and therefore the magnitude of this flow becomes of paramount importance. The \texttt{VENUS-LEVIS} orbit-following code is used to follow the impurity particles with additional effects provided by the centrifugal and Coriolis forces while colliding them in the correct frame of the background ion distribution. This is successfully benchmarked with known results in neoclassical theory concerning impurity transport. Without flows in axisymmetry, an on-axis peaked impurity distribution is observed. With flows, an off-axis peaking of impurities is observed, following known neoclassical expressions. Furthermore, it is found that the impurity accumulation was strongly increased for the combined case of helical core with flows, leading again to a near-axis peaked density profile. The results are compared heuristically with a known peaking formula incorporating the presence of a finite poloidal flow with toroidal flows, and a reasonable agreement is observed.