Fossil fuels (oil, gas, coal) currently represent about 85% of the world's primary energy sources, despite their expected depletion in a few decades and the CO2 greenhouse effect generated by their combustion. Controlled thermonuclear fusion by magnetic confinement, as achieved in tokamaks, is one of the potential options to provide a sustainable solution to our energy needs. Tokamak control issues are becoming increasingly important for the success of magnetic fusion and will be crucial for ITER, the world's largest tokamak under construction in the south of France. Feedback control of the plasma's main macroscopic parameters is now reasonably well Coils and magnetic ux in a tokamak mastered in various tokamaks worldwide, unlike the control of the plasma's internal radial profiles, crucial for ensuring both tokamak operation safety and the maintenance of high-performance plasma regimes. Our previous research, based on the stabilization of (quasi-)linear inhomogeneous partial differential equations (PDEs), provided key answers for controlling safety factor profiles (associated with magnetic ux) and temperature profiles for tokamak operation in "classical" mode (L mode). Operating the tokamak in "advanced" mode (H mode), as currently considered for ITER, requires regulating internal transport barriers (local magnetohydrodynamic phenomena) to allow a significant increase in the plasma core's energy and thus promote combustion. This optimization of combustion objective requires the explicit consideration (in the transport equations describing mass, momentum, and energy conservation) of ux terms, often described in a polynomial form.
Polynomial optimization (or Sum of Squares programming) has started to expand to the study of PDEs, around two approaches: (1) the moments-SoS hierarchy technique resorts to occupancy measures to represent generically the solutions of a PDE, at the cost of sometimes unrealistic assumptions. However, encouraging preliminary results have been published regarding the study of transport equations. (2) the certified computation of functional inequalities (Lyapunov, Wirtinger...) has proven crucial for stability analysis, with a strong potential for tokamak control applications. A weakness of this approach is that Lyapunov functionals are a problem data, and SoS programming is only used to verify their properties, whereas the moments-SoS hierarchy automates the search for Lyapunov functions.
Objectives of the Ph.D. thesis
From the perspective of controlled thermonuclear fusion research, combustion control has only been addressed for linearized PDEs or nonlinear ordinary differential equations, for operation in classical mode. Despite the difficulty in capturing the dynamics of internal transport barriers for advanced modes, our recent results have shown that plasma can be maintained in advanced mode by regulating 0D parameters with classical robust methods based on a model identified on a simulator. However, setting up this controller required an important work to associate a reference simulator with the studied tokamak (EAST, in China), and does not address an optimization objective for H-mode operation.
The central theme of the thesis will be the combustion control of a tokamak plasma in an "advanced" operation scenario, and will need to mobilize and improve knowledge on the control of PDEs, particularly nonlinear, possibly with constraints, and possibly with polynomial forms to describe internal transport phenomena (known as "blobs"). We aim to contribute to the state of the art in polynomial optimization, which consists of automating the search for Lyapunov functions, an essential tool for studying the stability of physical systems and thus controlling them.
This research is motivated by the need for tokamak control research to address the transition to sustainable energy sources. As such, this research will be part of the broader framework of sustainability and transitions, and will propose innovative control methods for future thermonuclear fusion reactors.
Thesis Organization
Research Team:
- Main Supervisor: Emmanuel Witrant, Professor UGA - GIPSA-lab, Infinity team, https://www.gipsa-lab.grenoble-inp.fr/~emmanuel.witrant
- Co-supervisor: Matteo Tacchi, CNRS Researcher - GIPSA-lab, MODUS team, https://matteotacchi.wordpress.com/
Partnerships and External Collaborations:
- implementation of control laws is envisioned on the TCV tokamak, with a stay at École Polytechnique Fédérale de Lausanne (Switzerland) within the Swiss Plasma Center (A. Fasolini, A. Mele, O. Sauter), with possible interactions with the Automatic Control Laboratory at EPFL (C.N. Jones, G. Ferrari- Trecate) and the Optimization and Risk Analysis Laboratory (D. Kuhn).
- collaborations are also foreseen with Università degli Studi della Tuscia and Consorzio CREATE, Italy.
Profile and skills required
A graduate degree (for example a master's degree) in control theory and/or mathematics with excellent academic results is required to apply to this position. During the selection process, candidates will be assessed upon their ability to: - independently pursue his or her work collaborate with others, - have a professional approach and analyse and work with complex issues. In the evaluation of candidates, great emphasis is placed on study results and completed courses. After the qualification requirements, great emphasis will be placed on personal competency.
How to apply / More information?
Send your transcripts, motivation letter and recommendations, following the procedure at
https://adum.fr/as/ed/voirproposition.pl?langue=&matricule_prop=56256&site=edeeats
