Prediction and control of the tokamak density limit
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maris_maris_phd_nse_2026_thesis.pdf
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Author(s)
Maris, Andrew D.
Advisor(s)
Rea, Cristina
Granetz, Robert
Marmar, Earl
Date Issued
February 2026
Publisher
Massachusetts Institute of Technology
Abstract
The "density limit'" is a key risk---or potential opportunity---for future tokamaks. After decades of research, the cause of the density limit (DL) remains contested. While the Greenwald limit has worked remarkably well for a simple empirical scaling, a growing body of evidence has shown that the full complexity of the L-mode density limit (LDL) and H-mode density limit (HDL) goes beyond $n^{\rm limit}_G = I_p/\pi a^2$. This creates a critical uncertainty for next-step devices and future fusion power plants. Given that their fusion power goals are highly sensitive to density ($P_{\rm fus} \sim n^2$), there is an urgent need to better understand the density limit and develop practical techniques for avoiding this constraint in experiments.
This PhD thesis advances the study of the tokamak density limit by (1) providing evidence that the LDL and HDL are both more accurately described as an\textit{ edge collisionality limit} and (2) demonstrating that collisionality-based scalings can be harnessed for real-time LDL and HDL avoidance at DIII-D. In two database studies, we find that scalings of effective collisionality in the edge of the plasma, along with $\beta_T$ and other secondary variables, are significantly more reliable predictors of the onset of the DL than the Greenwald limit across a multi-machine database. The first study focused on exploring a variety of data-driven methods to predict the LDL, with data spanning Alcator C-Mod, ASDEX-Upgrade, DIII-D, and TCV; the second added DIII-D negative triangularity and JET data, and analyzed the HDL as well. The databases used in this thesis are newly collated with hundreds of manually labeled LDLs and HDLs. Additionally, we include thousands of non-disruptive discharges to compute True Positive Rates (TPR) and False Positive Rates (FPR) of various predictive models, which is rare in a DL study. To identify an accurate and interpretable power law for the LDL and HDL, we developed a method of forward feature selection with Linear Support Vector Machines. For the case of the LDL, the scaling $\nu^{\rm limit}_{*,{\rm edge}} \sim \dfrac{1}{\sqrt{\beta_{T,{\rm edge}}}}$ reduces false positives by nearly 4x compared to the Greenwald fraction. For the case of the HDL, the scaling $\nu_{*,{\rm edge}}^{\rm limit} \sim \dfrac{\rho_{*,{\rm edge}}^{0.8}}{\beta_{T,{\rm edge}}^{0.9} q_*^{1.1}}$ reduces false positives by around 2x. Applied to edge plasma conditions expected in ARC, ITER, MANTA, and DEMO, these findings indicate that these reactors may have significant margin to the LDL and HDL, suggesting that even higher density operation is possible. We then implemented versions of these proximity-to-instability metrics into the DIII-D Plasma Control System to enable real-time LDL and HDL avoidance. By increasing neutral beam heating and reducing the density target in feedback with the instability metrics, we reliably suppressed the onset of the LDL; a similar strategy was successful in our proof-of-principle HDL avoidance experiment.
Finally, this thesis includes an analysis of the economic impact of transient events such as LDL disruptions and HDL-triggered H/L back-transitions on future magnetic fusion power plants. This brings into focus the practical benefits of improved instability prediction that this work advances, while also highlighting potential cost drivers and opportunities for impactful research directions.
Altogether, this thesis advances our knowledge of the density limit, presents a new tool for interpretable disruption prediction, demonstrates a control solution for the LDL and HDL at DIII-D, and models the impact plasma instabilities will have on the future fusion industry.
MIT Department
Massachusetts Institute of Technology. Department of Nuclear Science and Engineering
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