Dynamic exhaust modeling for fusion reactors

In a nuclear fusion reactor, the aim is to fuse together nuclei in a controlled way, releasing a lot of energy. This is the process that powers the Sun and the process that we want to mimic on Earth to provide dispatchable sustainable energy. To do this, the fusion community builds experimental reactors that trap the fuel and heat it for long enough times at a temperature of over 150 million degrees Celsius. In these reactor conditions, the gas fuel is ionized and forms a plasma, the fourth state of matter after solid, liquid, and gas. Energy and ashes produced in the fusion reactions are directed away from the core of the reactor towards dedicated target plate in the exhaust region, called the divertor. Unchallenged, the heat and particles incident on the target greatly exceed material limits and this is why the exhaust of particles and energy must be continuously operated in so-called detachment. Detachment can be achieved in a highly dissipative cold plasma regime where a large part of the exhausted heat and particles are redistributed (through impurity radiation and plasma neutral interactions) over the entire first wall before they reach the target plates, where sufficient pressure is required to pump the fusion ashes out of the reactor. However, such highly-dissipative regimes are also adjacent to radiative plasma limits, risking disruption events that threaten machine-integrity. In stark contrast to conventional experimental reactors, fusion power plants require a control system (not just for the exhaust) that promotes operation away from critical limits in presence of disturbances. Such operation can only be provided through validated dynamic models of the entire plasma that: 1) capture the time-dependent response to actuators and disturbances; 2) connect to reactor relevant sensors; 3) describe safety critical limits; 4) scale to reactors sized for energy production. Complex numerical exhaust models have been developed in the recent decades, but time-dependence has received little attention. In this dissertation, I focus on developing exhaust models that capture the time-dependent response to actuators and disturbances through a physics-basis that should scale to reactors sized for energy production. In a first article, Chapter 2 details the systematic development of density control on the Upgraded Mega Ampere Spherical Tokamak (MAST-U) and how to measure and quantify system dynamics that are relevant for the design of feedback controllers in order to provide guarantees for controller stability and performance. Then three articles, Chapters 3, 4, 5, detail extensions of a reduced numerical model (called DIV1D) that describes time-dependently the interaction between the reactor core and wall (in 1D) in response to gas valve actuators typically used for control. Stationary 2D results from a higher fidelity model (called SOLPS-ITER) are used in comparisons to show that DIV1D can describe the main features of a dynamic state and reactor exhaust. This is not obvious because DIV1D approximates the typical 2D solutions in 1D. Firstly, it is shown that mimicking transport in the second dimension of both neutrals and plasma is key to align 1D solutions to the higher-fidelity 2D ones (Chapter 3 and 4). Secondly, association of atoms into molecules at the wall is found as an important process for closing the global particle balance in which also the core plasma is simulated (Chapter 5). In a final article, Chapter 6, dynamics for multiple physics-based models are validated using a system-identification experiment in the Tokamak à Configuration Variable (TCV) tokamak. Three models are considered: 1) TCM a three chamber model simulating 0D reservoirs; 2) DIV1D using reservoirs combined with a 1D scrape-off layer; and 3) SOLEDGE3X-EIRENE as time-dependent 2D plasma-edge simulator. It is found that the coupling to a core reservoir and a realistic time-scale for neutrals to ionize allows each model to align with dynamic measurements within error bars. Taken together, by extending the DIV1D code, that simplifies the scrape-off layer in 1D and couples to neutral reservoirs outside the plasma, it is now possible simulate seconds of realistic exhaust plasma solutions responding to molecule gas injection in hours on a single CPU core. That is, compared to several weeks on multiple CPU cores with higher-fidelity models as SOLEDGE3X-EIRENE. The thesis ends with a discussion and perspective on future work in Chapter 7. Further development of DIV1D is discussed in view of modeling needs for exhaust control. I propose further validation of dynamic models on system-identification data on TCV and other devices that have data available. I present ingredients for a control-oriented exhaust model beyond DIV1D that may support fully model-based controller design and propose steps towards global tokamak simulation to test them. In Chapter 8, I conclude and reflect on the progress made in developing the physics basis necessary for knowledge-based design and optimization of exhaust control in future fusion reactors.