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Personne# Antoine Baillod

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Stellarator

Le stellarator (de stellar : stellaire, et generator : générateur) est un dispositif destiné à la production de réactions contrôlées de fusion nucléaire proche du tokamak. Le confinement du plasma e

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This thesis delves into the potential of magnetic fusion energy, and in particular focuses on the stellarator concept. Stellarators use external coils to produce 3-dimensional (3D) magnetic fields that confine a thermonuclear plasma in a topologically toroidal volume, and thus do not, in general, require an externally driven plasma current. This is one of the main advantages of the stellarator, as the absence of strong currents in the plasma makes it intrinsically more stable than his cousin, the tokamak. It also comes at a price, since the stellarator needs to break axisymmetry to provide confinement, which is a major engineering challenge.The fusion performance in stellarators increases with Î², i.e. the plasma pressure normalized by the magnetic pressure. At finite pressure however, the plasma generates additional currents, and therefore its own magnetic field, that adds up to the vacuum magnetic field generated by the external coils. The computation of the vacuum field produced by the external coils is thus not sufficient to design, optimize, operate, and interpret experimental results. Instead, it is crucial to compute the magnetohydrodynamical (MHD) equilibrium, which takes into account the non-linear contributions from the plasma. Of particular interest is the magnetic field line topology of 3D magnetic equilibria. These equilibria are in general composed of nested magnetic surfaces, magnetic islands and chaotic field lines, where the latter two topologies are, in general, detrimental to core confinement. Configurations with large regions filled with nested magnetic surfaces are thus usually sought. While it is possible to design stellarators with nested magnetic surfaces in vacuum, the plasma contribution to the total magnetic field can destroy the carefully designed magnetic surfaces at finite plasma Î², thereby setting the maximum achievable Î² in stellarators, and ultimately limiting their performance.This thesis investigates the effect of pressure and currents generated by the plasma on the topology of magnetic field lines in MHD equilibria. Tools to compute free-boundary 3D MHD equilibria with magnetic islands and chaotic field lines are presented and extended. In particular, the Stepped Pressure Equilibrium Code (SPEC) is expanded to allow the prescription of the net toroidal current profile, and is used to perform large parameter scans to identify the equilibrium Î²-limits in different stellarator geometries, taking into account the effect of the bootstrap current. New measures are developed to evaluate the amount of chaotic field lines in an equilibrium, and to calculate their impact on particle transport. An analytical model is then proposed to explain the numerical results and expose the underlying scaling laws. Finally, this thesis explores the use of SIMSOPT, a python optimization framework, to optimize a configuration equilibrium Î²-limit.Broadly, this thesis contributes to the ongoing research on magnetic fusion reactors and the potential of nuclear fusion as a clean, safe, and abundant energy source. Specifically, it provides a better understanding of the effect of pressure on the topology of magnetic field lines in MHD equilibria, and how it impacts the performance of the stellarator. Additionally, this thesis gives insight into how optimizations can improve the performance of the stellarator and increase the equilibrium Î²-limit.

Antoine Baillod, Ankit Kumar, Joaquim Loizu Cisquella

Over the last decade, a variational principle based on a generalisation of Taylor's relaxation, referred to as multi-region relaxed magnetohydrodynamics (MRxMHDs) has been developed. The numerical solutions of the MRxMHD equilibria have been constructed using the Stepped Pressure Equilibrium Code (SPEC) (Hudson et al 2012 Phys. Plasmas 19 112502). In principle, SPEC could also be established to describe the MRxMHD stability of an equilibrium. In this work, a theoretical framework is developed to relate the second variation of the energy functional to the so-called Hessian matrix, enabling the prediction of MHD linear instabilities of cylindrical plasmas, and is implemented in SPEC. The negative and positive eigenvalues of the Hessian matrix predict the stability of an equilibrium. Verification studies of SPEC stability results with the M3D-C1 code and the tearing mode $\Delta^{^{\prime}}$ criterion have been conducted for ideal and resistive MHD instabilities, respectively, in a pressureless cylindrical tokamak, and have shown good agreement. Our stability analysis is a critical step towards understanding the MHD stability of three-dimensional MHDs where nested flux surfaces, magnetic islands and stochastic regions co-exist.

2021Adnan Ali, Konstantinos Avramidis, Antoine Baillod, Attila Bencze, Alberto Bottino, Emiliano Fable, Jonathan Marc Philippe Faustin, Jonathan Graves, Michel Haas, Xiaoxue Han, Thomas Binderup Jensen, Ajay Kumar, Shuai Liu, Joaquim Loizu Cisquella, Mike Machielsen, Eduardo Sanchez, Nicola Vianello, Gregory Vogel, Frank Rüdiger Wagner, Hui Wang, Jieping Zhu, Hartmut Zohm

We present recent highlights from the most recent operation phases of Wendelstein 7-X, the most advanced stellarator in the world. Stable detachment with good particle exhaust, low impurity content, and energy confinement times exceeding 100 ms, have been maintained for tens of seconds. Pellet fueling allows for plasma phases with reduced ion-temperature-gradient turbulence, and during such phases, the overall confinement is so good (energy confinement times often exceeding 200 ms) that the attained density and temperature profiles would not have been possible in less optimized devices, since they would have had neoclassical transport losses exceeding the heating applied in W7-X. This provides proof that the reduction of neoclassical transport through magnetic field optimization is successful. W7-X plasmas generally show good impurity screening and high plasma purity, but there is evidence of longer impurity confinement times during turbulence-suppressed phases.