Spherical tokamaks (STs) have a particular need for non-inductive start-up methods, due to the limited space for a shielded inboard solenoid. Plasma current start-up assisted by electron Bernstein waves (EBW) has been demonstrated successfully in a number of experiments. The dynamic start-up phase involves a change in field topology, as the initially open magnetic field lines form closed flux surfaces (CFS) under the initiation of a plasma current. This change in field topology will bring about a change in the current drive (CD) mechanism, and, although various mechanisms have been proposed to explain the formation of CFS, no detailed theoretical studies have previously been undertaken.
This thesis reports on the development of a kinetic start-up model for EBW-assisted plasma current start-up in MAST. In order to ensure the model is tractable and computationally manageable, the time evolution of the electron distribution function is studied in zero spatial and two momentum dimensions under several effects thought to be important during start-up.
In order to obtain numerical solutions to the time evolution of the distribution function, a positivity-preserving solution to two-dimensional advection-diffusion equations including mixed derivative terms are required. A numerical scheme for solving these equations is presented, and shown to improve the accuracy of lower-order finite difference schemes.
It is shown that the open magnetic field line configuration allows electrons to freely stream out of the plasma, but that the addition of a small vertical magnetic field leads to the preferential confinement of a selection of electrons and the generation of a plasma current. Collisions then act to ``feed'' this loss mechanism by increasing the parallel momentum of electrons through pitch-angle scattering, leading to greater losses and a greater plasma current. This CD mechanism is shown to be consistent with several experimentally observed effects, providing a theoretical understanding of these effects, while comparisons between simulation and experiment is good.
This work has applications for future STs, as it builds on our current, theoretical understanding of non-inductive plasma current start-up.
