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.

Field-reversed configuration (FRC) is one of the approaches to realizing magnetic fusion due to its engineering simplicity. The recent C2-W experiment showed long-lasting FRC plasmas over 30 ms, with the help of neutral beam injection (NBI) and edge-biasing system. Therefore, understanding the edge-biasing effects on the FRC can be essential to improve the FRC designs and enable the potential active controls. The penetration of the edge biasing applied at the divertor ends can affect the equilibrium potential structure in the scrape-off layer (SOL) of FRC. The first part of the thesis is to establish a formulation that accurately captures both parallel and radial variations of the 2D potential in the SOL under the influence of edge-biasing. A full-f gyrokinetic ion model and a massless electron model are implemented in the GTC-X code to solve for the self-consistent equilibrium potential, given fixed radial potential profiles at the boundaries. Current simulation results implied that accurate electron density and temperature profiles are important in predicting the potential structure in the FRC SOL. The Debye sheath potential and the biasing profiles applied at the boundaries could introduce additional E×B rotation in the FRC SOL. With the equilibrium potential, the turbulent transport in the FRC can be modified due to the added E×B flow shear. Such shearing effects were first studied with an artificial 1D radial equilibrium potential for the ion temperature gradient (ITG) instability in the FRC SOL, which was identified as the dominant source for SOL fluctuations in the C2-W device. Linear δf simulations with adiabatic electrons found that the total shear from both the diamagnetic flow and the equilibrium E×B flow can reduce the linear growth rates and cause a radial tilting of the mode structures in the toroidal plane. Nonlinear simulations further confirmed that the flow shearing significantly decreases ITG saturation and ion heat transport levels. In addition, the self-generated zonal flow shears were also studied and played a similar role to reduce the ITG nonlinear saturation, unless the collisional damping limited the zonal flow level in the SOL. These results may suggest that using a proper edge-biasing profile and minimizing collisions could improve the confinement of the FRC. The full-f scheme developed in the 2D equilibrium simulation was aimed for coupled simulations of the turbulent transport with the self-consistent 2D equilibrium potential. As a starting point, this full-f algorithm had been compared with the δf simulations with periodic boundaries. Future research will involve the full-f simulations with the non-Maxwellian equilibrium distribution functions and open boundary flows in the FRC SOL.

In this work, gyrokinetic simulations in edge plasmas of both tokamaks and field reversed

configurations (FRC) have been carried out using the Gyrokinetic Toroidal Code (GTC) and A New Code (ANC) has been formulated for cross-separatrix FRC simulation.

In the tokamak edge, turbulent transport in the pedestal of an H-mode DIII-D plasma is

studied via simulations of electrostatic driftwaves. Annulus geometry is used and simulations focus on two radial locations corresponding to the pedestal top with mild pressure gradient and steep pressure gradient. A reactive trapped electron instability with typical ballooning mode structure is excited in the pedestal top. At the steep gradient, the electrostatic instability exhibits unusual mode structure, peaking at poloidal angles theta=+- pi/2. Simulations find this unusual mode structure is due to steep pressure gradients in the pedestal but not due to the particular DIII-D magnetic geometry. Realistic DIII-D geometry has a stabilizing effect compared to a simple circular tokamak geometry.

Driftwave instability in FRC is studied for the first time using gyrokinetic simulation. GTC

is upgraded to treat realistic equilibrium calculated by an MHD equilibrium code. Electrostatic local simulations in outer closed flux surfaces find ion-scale modes are stable due to the large ion gyroradius and that electron drift-interchange modes are excited by electron temperature gradient and bad magnetic curvature. In the scrape-off layer (SOL) ion-scale modes are excited by density gradient and bad curvature. Collisions have weak effects on instabilities both in the core and SOL. Simulation results are consistent with density fluctuation measurements in the C-2 experiment using Doppler backscattering (DBS). The critical density gradients measured by the DBS qualitatively agree with the linear instability threshold calculated by GTC simulations.

One outstanding critical issue in the FRC is the interplay between turbulence in the FRC

core and SOL regions. While the magnetic flux coordinates used by GTC provide a number of computational advantages, they present unique challenges at the magnetic field separatrix. To address this limitation, a new code, capable of coupled core-SOL simulations, is formulated, implemented, and successfully verified.

Recent drastic improvement of plasma stability and confinement in the high performance C-2 advanced beam-driven field-reversed configuration (FRC) experiment at Tri Alpha Energy, Inc. (TAE) has led to consistently reproducible stable plasmas suitable for transport study. To understand and support the ongoing efforts towards an FRC-based reactor, the sources of the fluctuations and the mechanisms of the transport must first be identified such that a suitable transport scaling may be found and applied toward predicting confinement performance in larger, hotter, and denser FRC plasmas.

In the first half of this thesis, a mature, well-benchmarked turbulence simulation code, the Gyrokinetic Toroidal Code (GTC), has been extended and applied to a system with experimentally realistic C-2 parameters. Using GTC, local electrostatic drift-wave stabilities in the core and scrape-off layer (SOL) regions of C-2 have been characterized and compared to experimental findings. The drift-wave is found to be stable in the core. On the other hand, in the SOL, a class of ion-to-electron scale instabilities is observed. These simulation results are consistent with density fluctuation measurements in C-2.

Since experimental measurements show that fluctuations exist in the core, the discovery of the robust stability of the core suggests that the fluctuations may originate from the SOL. In the second half of this thesis, a new turbulence simulation code, A New Code (ANC), has been developed to study nonlocal phenomenon. Using ANC, the linear propagation and nonlinear spreading of a single-mode instability from the SOL to the core has been characterized. It is shown that nonlocal effects, due to the ion finite Larmor radius (FLR) effect and ion polarization drift, allows for the coupling of different drift-surfaces and for the instability in the SOL to spread into the core. The phase velocities of the instability is consistent with experimental measurements of radial propagation. The nonlinear saturation of the instability shows that the saturated mode amplitude in the SOL is higher than in the core, again, consistent with experimental measurements.

In addition, the first turbulent transport simulation in the FRC SOL has also been performed using gyrokinetic ions and adiabatic electrons. Self-consistent ion heat flux is calculated from these simulations to be ~6[kW/m^2] while an upper bound for the electron heat flux is calculated to be ~4[MW/m^2] through electron test particles, though the self-consistent electron heat flux is expected to be lower. An inverse spectral cascade is also observed, with unstable shorter wavelength modes feeding into stable or damped long wavelength modes.

Plasma wakefields, whether driven by laser or particle bunch, possess a stable, coherent, and robust structure that can accelerate particles to high energy. Wakefields derive these remarkably properties from a single physical principle: waves with a phase velocity much higher than the bulk speed of a population particles will not strongly couple to the particles. Instead, a small subset of particles are captured by the wake and coherently accelerated to high energy. In typical applications of wakefield acceleration, this property is harnessed to accelerate electrons, but extends widely into other applications. Notably, ion-cyclotron waves in fusion plasmas, when possessed of a fast phase velocity, can generate a fast-ion tail that can dramatically enhance fusion yield without increasing the bulk ion temperature, as has been observed in the C-2U experiment. The first part of this work explores this phenomenon, examining the physics of beam-driven ion-cyclotron waves in the context of the scrape-off-layer (SOL) of a field-reversed-configuration (FRC) plasma. In particular, the nonlinear mechanics of ion acceleration by these waves is examined. Interestingly, this principle of phase velocity can be just as useful when violated. In the field of laser-wakefield acceleration (LWFA), in the regime of near-critical density plasmas, the physics of wakefield acceleration transitions into a sheath acceleration, which is potentially capable of generating a large flux of low-energy electrons. The application of this principle to a novel method of internal cancer therapy is treated in the second part of this work.

The convective cells are observed in the auroral ionosphere and they could play an important role in the nonlinear interaction of Alfv {e}n waves and disrupt the kinetic Alfv {e}n wave (KAW) turbulence. Zonal fields, which are analogous to convective cells, are generated by microturbulence and regulate microturbulence inside toroidally confined plasmas. It is important to understand the role of convective cells in the nonlinear interaction of KAW leading to perpendicular cascade of spectral energy. A nonlinear gyrokinetic particle simulation has been developed to study the perpendicular spectral cascade of kinetic Alfv {e}n wave. However, convective cells were excluded in the study. In this thesis project, we have modified the formulation to implement the convective cells to study their role in the nonlinear interactions of KAW. This thesis contains detail description of the code formulation and convergence tests performed, and the simulation results on the role of convective cells in the nonlinear interactions of KAW. In the single KAW pump wave simulations, we observed the pump wave energy cascades to waves with shorter wavelengths, with three of them as dominant daughter waves. Convective cells are among those dominant daughter waves and they enhance the rate of energy transfer from pump to daughter waves. When zonal fields are present, the growth rates of the dominant daughter waves are doubled. The convective cell (zonal flow) of the zonal fields is shown to play a major role in the nonlinear wave interaction, while the linear zonal vector potential has little effects. The growth rates of the daughter waves linearly depends on the pump wave amplitude and the square of perpendicular wavenumber. On the other hand, the growth rates do not depend on the parallel wavenumber in the limit where the parallel wavenumber is much smaller than the perpendicular wavenumber. The nonlinear wave interactions with various perpendicular wavenumbers are also studied in this work. When convective cells are excluded, the nonlinear wave interactions show exponential growth on the daughter waves, but at a rate about half of that of the wave interactions with convective cells. In the two pump wave simulations, six daughter waves dominate in the energy cascade process, and three of them are convective cells. The growth rates of the daughter waves are doubled compared with the growth rates of the daughter waves generated in single KAW pump wave simulation. The relationship between the growth rates of the daughter waves and pump wave parameters are studied. The growth rates of the daughter waves have a linear relationship with both pump wave amplitudes and the square of perpendicular wavenumber of the pump waves. On the other hand, the growth rates do not depend on the parallel wavenumber of the pump waves in the limit where the parallel wavenumber is much smaller than the perpendicular wavenumber. The growth rate dependence on one of the two pump waves shows that the time variation on the pump wave amplitudes must be considered.

The gyrokinetic toroidal code(GTC) capability has been extended for simulating current- driven instabilities in magnetized plasmas such as kink and resistive tearing modes with kinetic effects. This new gyrokinetic capability enables first-principles, integrated simulations of macroscopic magnetohydrodynamic(MHD) modes, which limit the performance of burning plasmas and threaten the integrity of fusion devices. The excitation and evolution of macroscopic MHD modes often depend on the kinetic effects at microscopic scales and the nonlinear coupling of multiple physical processes.

GTC simulation in the fluid limit of the internal kink modes in cylindrical geometry has been verified by benchmarking with an MHD eigenvalue code. The global simulation domain covers the magnetic axis which is necessary for simulating the macroscopic MHD modes. Gyrokinetic simulations of the internal kink modes in the toroidal geometry find that ion kinetic effects significantly reduce the growth rate even when the banana orbit width is much smaller than the radial width of the perturbed current layer at the mode rational surface. This new GTC capability for current-driven instability has now been extended to simulate fishbone instabilities excited by energetic particles and resistive tearing modes.

GTC has also been applied to study the internal kink modes in astrophysical jets that are formed around supermassive black holes. Linear simulations find that the internal kink

modes in astrophysical jets are unstable with a broad eigenmode. Nonlinear saturation amplitude of these kink modes is observed to be small, suggesting that the jets can remain collimated even in the presence of the internal kink modes. Generation of a mean parallel electric field by the nonlinear dynamics of internal kink modes and the potential implication of this field on particle acceleration in jets has been examined.

Neutronics study to determine the validity and real world extendibility through Artificial Intelligence (AI) optimization of a transmutation concept with the aim of significantly reducing the radiotoxicity of Spent Nuclear Fuel (SNF) together with its required storage duration and volume. In this transmutation concept (the transmutator) utilizes a novel source providing laser-generated neutrons to transmute transuranic elements separated from SNF and dissolved in a molten salt within a subcritical core. The source neutrons are generated via beam-target fusion whereas the beam is created by laser irradiation of nanometric foils through the Coherent Acceleration of Ions by Laser (CAIL) process. This relatively low deuteron energy is catapulted by fusion and eventually by secondary fission processes. A significant factor in this study is that this can be accomplished using relatively cheap fiber lasers terminating onto small scale targets. Consequently, this makes possible the use of multiple tunable and distributable neutron sources. Such a source has not previously been considered and encourages an investigation with the aid of AI into new spatial arrangement and temporal control operation strategies as done here. This source is combined with a molten salt core whose liquid state allows and facilitates homogeneity by mixing, safety, laser irradiation, in-situ processing, and monitoring of chemical and physical properties. The combined use of molten salt and laser also allows for the introduction of rapid feedback or feedforward control of the system’s operation. This further extends the transmutator concept as this work demonstrates here by neutronics simulations showing: Efficient and continuous Minor Actinide (MA) waste only burning through AI optimized and balanced processing scheduling without the use of isotopic separation. As well as shaped thermal reactivity insertion for increased tank usage efficiency and active thermal management.