Modelling of power exhaust in fusion plasmas

This PhD thesis deals with the thorny problem of “Modelling of power exhaust in fusion plasmas”, a challenge concerning the development of a system able to withstand the large loads expected in the fusion power plant divertor. After an introduction to fusion and to the key concepts modelling the behaviour of the plasma during plasma-surface interactions and describing the power exhaust, an overview of the state-of-the-art in the research field on power exhaust is given. A brief introduction on theoretical basis of the plasma boundary reconstruction precedes the author first contribution in the design and vertical stability analysis of plasma alternative magnetic configurations for a demonstration fusion power plant (DEMO). The second contribution concerns an assessment of the DEMO divertor target tiles lifetime in case of strike-point sweeping. This technique is one of the most promising candidate solution to the power exhaust issue but its main drawback is related to the periodical heating and cooling of the plasma facing components inducing the thermal-fatigue phenomenon. To evaluate the lifetime of the DEMO divertor target tiles, different 2D and 3D thermo-mechanical models are presented. Finally, a preliminary analysis on the wobbling technique applied to a DEMO Double Null plasma magnetic configuration is illustrated

Model-based Control of the Current Density Profile in the Experimental Advanced Superconducting Tokamak (EAST)

As worldwide energy consumption increases, the world is facing the possibility of an energy shortage problem. While several approaches have been proposed to slow down this process, which include the improvement of the combustion efficiency of fossil fuels and the introduction of nuclear energy and renewable energy, such as solar, wind, and geothermal energy, a replacement for fossil fuels will eventually be needed. The energy that comes from a nuclear reaction, which includes nuclear fission and nuclear fusion, has a high energy production density (rate of energy produced divided by the area of the land needed to produce it) and produces no air pollution or greenhouse gases, which makes it a strong and attractive candidate. Compared with nuclear fission, the radioactive waste from nuclear fusion can be more easily disposed, the reactants in a nuclear fusion reaction are abundantly available in nature, and nuclear fusion poses no risk of a nuclear accident. For all these reasons, nuclear fusion is a potential solution for the energy shortage problem. However, there are many challenges that need to be conquered to achieve nuclear fusion. The primary challenge is to confine the hot reactants, whose temperatures are about one hundred million degrees Kelvin. At these temperatures, the reactants are in the plasma state and have enough kinetic energy to overcome the repelling electrostatic forces and fuse. One of the most promising approaches to confine the fusion plasma is magnetic confinement, where magnetic fields are used to confine the plasma through the Lorentz force. The tokamak is one of the fusion devices that exploit magnetic confinement. To demonstrate the viability of a nuclear fusion power plant, the International Thermonuclear Experimental Reactor (ITER) tokamak project is aimed at producing 500 megawatts power with 50 megawatts of input power, which will make it the first tokamak with net energy output. To be able to obtain the desired fusion gain, the ITER tokamak will need to operate at a temperature and a pressure so high that the plasma has a good chance of becoming unstable and difficult to confine. To address this issue, extensive research has been conducted on different fusion tokamaks around the world to find high performance operating scenarios characterized by a high fusion gain, good plasma confinement, plasma stability, and a dominant self-generated plasma current with the goal of developing candidate scenarios for ITER. The shape of the toroidal current density profile, or the safety factor profile ($q$-profile), impacts steady-state operation, magnetohydrodynamic (MHD) stability, and plasma performance. The plasma $\beta$, which is the ratio of the kinetic pressure of the plasma to the magnetic pressure (pressure exerted on plasma by the magnetic field), acts as an important economic factor in fusion power generation. Therefore, active control of the toroidal current density profile and plasma $\beta$ is one path towards advanced scenarios. This dissertation focuses on developing control solutions for regulating the current density profile, and to some extent the normalized plasma $\beta$ (denoted as $\beta_N$), on the Experimental Advanced Superconducting Tokamak (EAST) located at the Institute of Plasma Physics, Chinese Academy of Sciences (ASIPP), in Hefei, China. Towards this goal, a control-oriented, physics-based model has been developed for the current density profile evolution in EAST in response to available heating and current-drive (H\&CD) systems. The feasibility of reconstructing the internal plasma states, which may be crucial for feedback control, from measurements at the magnetic axis and at the plasma edge has been studied by using experimental data and exploiting the response model. Target scenarios (characterized by desired $q$-profile and $\beta_N$) have been developed by following a model-based finite-time optimization approach. Feedback controllers ranging from simpler Proportional-Integral-Derivative (PID) controllers to more complex model-based optimal controllers, derived from Linear-Quadratic-Regulator (LQR), $H_\infty$, and Model Predictive Control (MPC) theories, have been synthesized to counteract deviations from the desired target scenario. The overall control solution has been implemented in the Plasma Control System (PCS) and closed-loop $q$-profile regulation has been demonstrated for the first time ever in EAST in disturbance rejection and target tracking experiments

Contrôle et optimisation de systèmes physiques : application à la mécanique quantique et au confinement magnétique dans les stellarators.

This PhD manuscript deals with the optimization and control of several physical systems. It is divided into three parts.The first part is devoted to stellarators. This type of nuclear fusion reactor poses many challenges related to optimization. We focus on an inverse problem well known to physicists, modeling the optimal design of superconducting coils generating a given magnetic field. We conduct both a theoretical and a numerical study of an extension of this problem, involving shape optimization. Then, we develop a new method to prove the existence of optimal shapes in the case of hypersurface optimization problems. Finally, we study and optimize the Laplace forces acting on a current surface density. The second part of this manuscript deals with the control of finite dimensional quantum systems. We rigorously study the combination of the rotating wave approximation with the adiabatic approximation. First, we obtain the robustness of a population transfer method on qubits. The latter then allows to extend results of Li and Khaneja on the ensemble control of qubits by restricting to the use of a single control. We also present a second contribution, devoted to the analysis of a chattering phenomenon for an optimal control problem of a quantum system. Finally, the third part is dedicated to the proof of a small-time global null controllability result for generalized Burgers' equations using a boundary layer.Cette thèse porte sur l’optimisation et le contrôle de plusieurs systèmes physiques : elle est composée de trois parties.La première partie est consacrée aux stellarators. Ce type de réacteur à fusion nucléaire pose de nombreux défis reliés à l’optimisation. Nous nous sommes concentrés sur un problème inverse bien connu des physiciens, modélisant la conception optimale de bobines supraconductrices générant un champ magnétique donné. Nous avons conduit une étude théorique et numérique d’une extension de ce problème, portant sur une optimisation de forme. Nous avons ensuite développé une nouvelle méthode afin de prouver l’existence de formes optimales dans le cas de problèmes d’optimisation d’hypersurfaces. Nous avons enfin effectué l’étude et l’optimisation des forces de Laplace s’exerçant sur une densité surfaciquede courant.La deuxième partie porte ensuite sur l’étude du contrôle de systèmes quantiques de dimension finie. Nous avons étudié rigoureusement la combinaison de l’approximation de l’onde tournante avec l’approximation adiabatique. Dans un premier temps, nous avons obtenu la robustesse des méthodes de transfert de population sur les qubits. Cette dernière permet alors d’étendre des résultats de Li et Khaneja sur le contrôle d’ensemble des qubits en se restreignant à l’utilisation d’un seul contrôle. Nous présentons égallement une seconde contribution, consacrée à l’analyse d’un phénomène de chattering pour un problème de contrôle optimal d’un système quantique.Enfin, la troisième partie est dédiée à la preuve d’un résultat de contrôlabilité à zéro en temps petit pour des équations de Burgers généralisées grâce à l’utilisation d’une couche limite

Liquid metal flows in continuous casting molds: A numerical study of electromagnetic flow control, turbulence and multiphase phenomena

Der Effekt eines externen Magnetfeldes auf die mehrphasige und turbulente Strömung in Stranggußkokillen und deren Wechelspiel führt in den wissenschaftlichen Arbeiten zu widersprüchlichen Aussagen. Die verschiedenen Prozessparameter können innerhalb eines kleinen Varianzbereichs entscheidenden Einfluss auf die Aussage haben, ob ein Magnetfeld begünstigend oder schädigend auf die Qualität des Produkts wirkt. Um wichtige Einflussfaktoren zu identifizieren, werden daher numerische Strömungssimulationen des Prozesses durchgeführt. Dazu wird zunächst ein mehrphasiger und inkompressibler Mehrregionen-CFD-Löser für magnetohydrodynamische Strömungen entwickelt und validiert, um die komplexe Strömung in einer Stranggußkokille mit hoher Genauigkeit simulieren zu können. Darauf aufbauend wird das numerische Setup anhand einer Modellkokille mit aktuellen Messdaten validiert. Durch die neuartige Kombination Lagrange'scher Lösungsmethoden mit angepassten Termen für die Magnetohydrodynamik sowie der skalenaufgelösten magnetohydrodynamischen Turbulenz, können erstmals Aussagen zur optimalen Magnetfeldverteilung im Hinblick auf Strömungsstabilität, Turbulenzmodulation und Blasenverteilung getroffen werden. Mit Hilfe dieses Wissens können neuartige Konzepte elektromagnetischer Bremssysteme für den Stranggußprozess entwickelt werden

Integrated Application of Active Controls (IAAC) technology to an advanced subsonic transport project: Current and advanced act control system definition study. Volume 2: Appendices

The current status of the Active Controls Technology (ACT) for the advanced subsonic transport project is investigated through analysis of the systems technical data. Control systems technologies under examination include computerized reliability analysis, pitch axis fly by wire actuator, flaperon actuation system design trade study, control law synthesis and analysis, flutter mode control and gust load alleviation analysis, and implementation of alternative ACT systems. Extensive analysis of the computer techniques involved in each system is included

Aeroelastic and Aerothermoelastic Analysis in Hypersonic Flow: Past, Present, and Future

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90637/1/AIAA-54556-145.pd

Project Wish: The Emerald City, phase 3

Phase 3 of Project Wish saw the evolution of the Emerald City (E-City) from a collection of specialized independent analyses and ideas to a working structural design integrated with major support systems and analyses. Emphasis was placed on comparing and contrasting the closed and open cycle gas core nuclear rocket engines to further determine the optimum propulsive system for the C-City. Power and thermal control requirements were then defined and the question of how to meet these requirements was addressed. Software was developed to automate the mission/system/configuration analysis so changes dictated by various subsystems constraints could be managed efficiently and analyzed interactively. In addition, the liquid hydrogen propellant tank was statically designed for minimum mass and shape optimization using a finite element modeling package called SDRC I-DEAS while spoke and shaft cross-sectional areas were optimized on ASTROS (Automated Structural Optimization System). A structural dynamic analysis also conducted using ASTROS enabled a study of the displacements, accelerations, modes and frequencies of the C-City. Finally, the attitude control system design began with an initial mass moment of inertia analysis and was then designed and optimized using linear quadratic regulator control theory