Study of neoclassical bootstrap current at edge pedestal and verification methods of gyrokinetic code in tokamak geometry

Abstract

This thesis consists of two subjects.

The first subject is a numerical study of the bootstrap current in tokamak plasmas using the drift-kinetic code XGC0.

Bootstrap current $\bf{J}_{b}$ plays an important role in the stability and equilibrium of steep edge pedestal plasma near the magnetic separatrix surface, which has an unconventional and difficult neoclassical property compared to core plasma. Edge pedestal plasma has a narrow passing particle region in the velocity space that can be easily destroyed by Coulomb collisions, and has a widely varying Coulomb collision frequency across the pedestal profile. The drift-kinetic particle code XGC0 equipped with mass-momentum-energy conserving collisions is used to study $\bf{J}_{b}$ in a realistic diverted magnetic field geometry, which confirms the surprising validity of the existing analytic formula (e.g., [O. Sauter et. al., Phys. Plasmas 6, 2834(1999)]) if the pedestal electrons are in weakly collisional deep in the banana collisionality regime. However, if the pedestal electrons are in plateau-collisional regime, a substantial deviation of numerical results from the existing analytic formulas is discovered. When the aspect ratio is large, as in a conventional tokamak, $\bf{J}_{b}$ from XGC0 is significantly less than that from analytic formulas. When the aspect ratio is close to unity as in the NSTX device, the numerical $\bf{J}_{b}$ is significantly greater than the analytic result. A simple modification to the Sauter formula is suggested to bring the analytic fitting formula to a better agreement with the drift-kinetic simulation results in the steep edge pedestal.

The second subject is the method of the manufactured solution for code verification.

Verification is the process of determining that a model implementation accurately represents the developer`s conceptual description of the model and the solution of the model Ref~\cite{AIAA}. Thus, code verification is the process that gives reliab...