Modeling of Boundary Transport and Divertor Target Heat Flux - Implications for Advanced Divertor Concepts

Tokamaks are currently being designed and built to achieve net positive unharnessed fusion energy, an important milestone on the path to electricity production. Experimental trends predict an additional challenge in these upcoming devices: a decrease in the area of the metal wall on which the plasma deposits significant heat flux, increasing the likelihood of melting damage. The heat deposition area is proportional to a parameter called the heat flux width, which decreases with increasing poloidal magnetic field and average plasma pressure. In devices designed to achieve physics breakeven such as ITER and SPARC, the heat flux width is predicted by some estimates to be less than 1 millimeter. It is therefore crucial to develop methods to more accurately predict the heat flux width and to mitigate large heat fluxes. Data from the Alcator C-Mod tokamak are particularly relevant in the effort to predict conditions in SPARC, as both are designed to use a higher magnetic field than other major tokamak experiments. Before this work, the relationship between the heat flux width and edge profiles of plasma density and temperature in C-Mod was unknown. Studies with plasma edge simulation codes were limited to a small number of discharges at a time, with many model settings being ad-hoc and difficult to evaluate for general applicability. Simulations of C-Mod had a much shorter outer divertor leg compared to SPARC, making it difficult to use detachment studies in C-Mod to speculate on detachment in SPARC. Finally, there was only a rough idea of edge plasma conditions in SPARC, and it was not known whether detachment would even be feasible. This thesis uses data from Alcator C-Mod and simulations with the UEDGE code to investigate heat flux width scalings, detachment, and advanced divertor concepts to inform the design of next-generation tokamaks that can produce significant fusion energy while remaining safe against heat flux damage. This thesis begins by augmenting a C-Mod heat flux width database (containing ~300 discharges) with midplane density and temperature profile data. Detailed analysis finds that the outer target heat flux width depends on the edge plasma pressure, but fails to find a clear dependence on edge gradients. The scaling of the heat flux width with the edge pressure varies by confinement mode and is used to confirm predictions of the heat flux width of 0.2-0.4 mm in SPARC and 0.4-0.6 mm in ITER H-mode scenarios. The UEDGE code is then used to simulate the edge of Alcator C-Mod plasmas. 75 discharges from the heat flux width database are successfully modeled in UEDGE using a fully automated process that matches experimental midplane density and temperature profiles. The resulting heat flux width in UEDGE is then compared to experimental measurements, and it is found that the UEDGE and experimental values are correlated but that UEDGE overestimates the heat flux width by an average factor of 1.8. The UEDGE-modeled discharges are modified to include single-particle drift effects and (separately) to remove flux limits. These changes do not significantly improve the UEDGE heat flux width match to experiment but demonstrate the capability of this framework to evaluate which settings in the UEDGE model improve agreement with experiment over the large range of edge plasma conditions included in the C-Mod database. One particular C-Mod attached H-mode discharge is then simulated in UEDGE, and a good match is achieved to experimental data at the midplane and outer target simultaneously with full drift effects included in the model. This discharge is also simulated with a ~2x longer outer divertor leg, an important component of advanced divertor concepts that could enable better high heat flux handling. Detachment is found to occur when a nitrogen impurity is introduced at a fixed fraction of 3.5% of the main ion density in the real C-Mod geometry, while with the longer leg, detachment occurs at a significantly lower fraction of 2.4% nitrogen. This bodes well for the SPARC design, which features a long outer leg. Finally, a full-power SPARC H-mode scenario is directly simulated with UEDGE. It is found that detachment is possible at the high heat fluxes and small heat flux width predicted for SPARC and that the heat flux at the targets can remain significantly reduced with a carbon impurity fraction around 1%. This value is not a prediction of the detachment threshold in SPARC due to the use of bifurcated attached and detached solutions obtained at low power, but is encouraging when compared to the detachment thresholds in C-Mod UEDGE simulations. This study confirms that detachment is a promising solution to mitigate high heat fluxes in the SPARC full-power scenario.Ph.D