Kinetic ballooning mode studies and the treatment of electromagnetic microinstabilities and turbulence in complex geometry

Magnetically confined thermonuclear fusion is promising as a future power source. However, the viability of fusion power plants is strongly influenced by how well the thermal energy can be confined in the plasma fuel. Often, the dominant process governing confinement is microinstability-driven plasma turbulence. This thesis studies microinstabilities and turbulence using gyrokinetic simulations, which may ultimately inform fusion reactor design and operation. The effect of plasma triangularity on stability in spherical tokamaks (STs) is examined using linear simulations of hypothetical ST equilibria. It is found that the kinetic ballooning mode (KBM), an electromagnetic pressure-driven microinstability, likely prohibits negative triangularity in ST power plants, since negative triangularity closes the "second stability window" for n = infinity ideal magnetohydrodynamic (MHD) ballooning modes. ST equilibria with positive triangularity can access the second stability window, although remain weakly unstable to KBMs. Secondly, microinstabilities are studied for the optimised stellarator Wendelstein 7-X (W7-X). Electrostatic "stability valley" results are reproduced using stella: a gyrokinetic code which offers flexibility in time-marching schemes by using operator splitting. stella is extended to include A_parallel and B_parallel fluctuations linearly using both implicit and explicit schemes. Benchmarking against the code GS2 shows good agreement for electromagnetic tokamak simulations. Using this implementation, the W7-X stability valley at finite beta (=plasma pressure/magnetic pressure) is preliminarily explored. The electromagnetic instabilities observed may be relevant to future W7-X experiments. Finally, a non-interpolating semi-Lagrangian scheme, aiming to efficiently simulate electromagnetic turbulence by eliminating the Courant-Freidrichs-Lewy timestep constraint in nonlinear gyrokinetics, is implemented in stella. A new operator splitting scheme is developed and used to mix single and multi-step numerical methods. Unfortunately, nonlinear tests show low accuracy and currently unexplained numerical instability. Elucidating the reasons for this would be an interesting area of future research.