Open Access Publications from the University of California

## Gyrokinetic Simulation of Plasma Instabilities in the DIII-D Tokamak

Abstract

Fusion energy gives humankind the prospect of nearly unlimited clean energy. To this end future burning plasma experiments are presently under construction, such as the International Thermonuclear Experimental Reactor (ITER). Two potentially significant challenges for ITER are the effects of Edge Localized Modes (ELMs), and energetic particle (EP) transport. While ELMs are benign in present day experiments, extrapolations to reactor scale predict ELM energy fluxes of up to 20 MJ in fractions of a millisecond, which can drastically decrease divertor lifetimes, generate impurities, and erode first wall components. Moreover, EP transport can affect plasma profiles, beam deposition, and current drive, and can erode reactor walls. Due to the strong coupling of EPs with burning thermal plasmas, plasma confinement properties in the ignition regime are some of the most uncertain factors when extrapolating from existing tokamaks to ITER. This work presents advances in addressing the challenges these mechanisms deliver by making use of gyrokinetic simulations of the DIII-D Tokamak.

This thesis presents gyrokinetic simulations of the DIII-D tokamak, via the Gyrokinetic Toroidal Code, with axisymmetric equilibrium show that the reduction in the radial electric field shear at the top of the pedestal during ELM suppression with the $n=2$ resonant magnetic perturbations (RMPs) leads to enhanced drift-wave turbulence and extended turbulence spreading to the top of the pedestal relative to ELMing plasmas with similar RMP and pedestal parameters. The simulated turbulent transport at the top of the pedestal in ELM suppressed conditions is consistent with experimental observations of enhanced turbulence at the top of the pedestal during ELM suppression by the RMPs. These results suggest that enhanced drift-wave turbulence due to reduced $E \times B$ shear at the pedestal top can contribute to the additional transport required to prevent the pedestal growing to a width that is unstable to ELMs.

This thesis also reports verification and validation of linear simulations of Alf {v}en eigenmodes in the current ramp phase of DIII-D L-mode discharge \#159243 using gyrokinetic, gyrokinetic-MHD hybrid, and eigenvalue codes. The verification and validation for the linear simulations of Alf {v}en eigenmodes is the first step to develop an integrated simulation of energetic particles confinement in burning plasmas incorporating multiple physical processes with kinetic effects of both energetic and thermal particles on an equal footing. Using a classical fast ion profile, all simulation codes find that reversed shear Alf {v}en eigenmodes (RSAE) are the dominant instability. The real frequencies from all codes have a coefficient of variation of less than 5\% for the most unstable modes with toroidal mode number $n = 4$ and $5$. If $q_{min}$ is adjusted slightly, within experimental errors, an agreement of within $4.5\%$ and $3.1\%$, for $n = 4$ and $5$ respectively, is found for all codes. The simulated growth rates exhibit greater variation, and simulations find that pressure gradients of thermal plasmas make a significant contribution to the growth rates. Mode structures of the dominant modes agree well among all codes. Moreover, using a calculated fast ion profile that takes into account the diffusion by multiple unstable modes, a toroidal Alf {v}en eigenmode (TAE) with $n=6$ is found to be unstable in the outer edge, consistent with the experimental observations. Variations of the real frequencies and growth rates of the TAE are slightly larger than those of the RSAE. Finally, electron temperature fluctuations and radial phase shifts from simulations show no significant differences with the experimental data for the strong $n = 4$ RSAE, but significant differences for the weak $n = 6$ TAE.