Effect of high plasma pressure on instabilities and turbulence in nuclear fusion devices with three-dimensional geometry

This dissertation aims to investigate the effect of high plasma pressure on instabilities and turbulence in nuclear fusion devices with three-dimensional geometry, i.e., in stellarator geometry. When referring to plasma pressure, we use the term “plasma β”, where β is the normalized plasma pressure, i.e., the ratio of plasma pressure to magnetic pressure. Finite-β studies of fusion plasma are of increasing interest and importance given that sustaining high β is crucial for optimal fusion-reactor performance (fusion-reaction rates scale with β^2). However, finite-β brings with it a series of challenges: it alters our current understanding of turbulence dynamics and energy transport; it gives rise to additional transport channels via magnetic perturbations; it leads to the destabilization of pressure-gradient driven instabilities such as kinetic ballooning modes (KBMs). Thus, in order to successfully achieve and sustain high β to exploit its benefits, enhancing our understanding of these potentially detrimental processes is of crucial importance for the successful operation of a future fusion power plant. To date, the vast majority of finite-β studies have focused exclusively on tokamaks (i.e., two-dimensional, axisymmetric geometries), and to a much lesser extent on stellarators (i.e., intrinsically three-dimensional geometries). Given the competitive performance and significant potential of the stellarator concept – granted by its unique versatility in adapting to newfound challenges via geometric optimization it is of interest to know how stellarators with different geometric characteristics (e.g., magnitude of background magnetic shear, Shafranov shift) perform in high-β scenarios, and to eventually see how we can utilize their many degrees of geometric freedom to overcome obstacles introduced by finite β. As such, enhancing our current understanding of high-β-plasma dynamics in stellarator geometry is a main goal of this dissertation. The research contributions resulting from this endeavor are as follows. Numerical studies are performed of finite-β gyrokinetic flux-tube simulations in the Wendelstein 7-X (W7-X) stellarator using the high-performance-computer code, Gene. This includes linear and nonlinear studies of plasma instabilities and the ensuing turbulence and transport at low and high β. These studies reveal the sub-threshold kinetic ballooning mode (stKBM), a new flavor of KBM characterized by its very broad eigenfunction that can be rendered unstable at much lower β than previously anticipated (i.e., far below the ideal MHD threshold), which is thought to indirectly catalyze an increase in turbulent transport with increasing β in W7-X. These studies have been published in two peer-reviewed journals. Following these numerical studies, analytical theory is developed to aid in explaining the existence of this newly discovered stKBM. This involves advancing linear gyrokinetic theory for KBMs in three-dimensional geometry (i.e., in stellarators) that accounts for the kinetic-physics mechanism of wave-particle resonances. A simplified KBM model is developed and numerically implemented – resulting in the KBM-eigenvalue-yielder (Key) code – which achieves qualitative agreement with high-fidelity gyrokinetic simulations using Gene; compared with the latter, the Key code produces its results in a fraction of the time and at virtually no cost. This simple model successfully shows that the existence of stKBMs is due to a combination of wave-particle resonances and specific geometric features manifest in the low-magnetic-shear stellarator W7-X, but which are absent in a circular tokamak. As such, the efficiency and fidelity of Key make it a promising candidate for aiding in transport model development and geometry-based turbulence optimization efforts going forward. An article pertaining to this work has been accepted for publication in a peer-reviewed journal. To further assess the influence of magnetic shear and Shafranov shift on instabilities and turbulence at finite β in stellarator geometry, additional numerical studies are performed using Gene. These comprise gyrokinetic flux-tube simulations in several configurations of W7-X and Heliotron-J (H-J) (another low-magnetic-shear stellarator). In W7-X, stKBMs are manifest and turbulent- transport levels increase with β. The thresholds for stKBM and conventional-KBM destabilization are found to increase with higher magnitude of background magnetic shear. Linear results from Gene show qualitative agreement with Key. The latter is used to show that both stKBMs and conventional KBMs can be stabilized by boosting the magnitude of magnetic shear and weakening bad magnetic-field-line curvature. Despite these linear results, turbulence studies in W7-X show that configurations with lower magnitude of magnetic shear produce lower levels of turbulent transport; this is owed to the generation of stronger zonal flows in those configurations, compared to those with higher magnitude of magnetic shear. In H-J, resonantly destabilized KBMs with broad eigenfunctions are found substantially below the ideal MHD threshold, i.e., KBMs that could be classified as stKBMs. Turbulent fluxes are found to decrease with increasing β, owed to the enhancement of zonal flows. These studies reveal the potential ubiquity of stKBM-like instabilities in low-magnetic-shear stellarators, and highlight challenges in predicting nonlinear performance based on the knowledge of linear physics alone. An article is currently in preparation pertaining to these results.