The understanding and modelling of heat and radiation transport in tokamak plasmas is essential in order to progress in the development of thermonuclear fusion towards a practical energy source which meets all the future needs of environment, safety, and fuel inexhaustibility. This activity enables prospective studies and design to be carried out for next step tokamaks. Due to the complexity of the exact calculation, synchrotron losses are usually estimated in such studies, with expressions derived from a plasma description using simplifying assumptions on the geometry, radiation absorption, density and temperature profiles. In this thesis, a complete formulation of the transport of synchrotron radiation is performed for realistic conditions of toroidal plasma geometry with elongated cross-section, using a precise method for the calculation of the absorption coefficients, and for arbitrary shapes of density and temperature profiles. In particular, this formulation is able to describe plasmas with arbitrary aspect ratios and with temperature profiles obtained in internal transport barrier regimes, which cannot be described accurately with the present expressions. As an illustration, we show that in the case of an advanced high-temperature plasma envisaged for a steady state D-T commercial reactor, synchrotron losses represent approximately 20% of the total losses. Considering the quantitative importance of the above effects and the significant magnitude of synchrotron losses in the thermal power balance of a D-T tokamak reactor plasma, a new fit for the fast calculation of the synchrotron radiation loss is proposed. Using this improved model in the thermal balance, prospective and sensitivity studies are performed for future tokamak projects, and the key issues which limit the performance are isolated. It is shown that, the most restrictive constraint for achieving higher plasma performance is the peak heat flux on the divertor plates. In non-inductive steady-state operation, advanced tokamak regimes are required to achieve relevant thermonuclear plasma performance for next step tokamaks and for a commercial reactor. In the frame of a multi-step strategy towards a commercial reactor, a superconducting next step tokamak compatible with the European budget possibilities is optimized. Considering both the plasma physics and the magnetic system technology and for a given aspect ratio, the smallest machine meeting the physical and technological requirements is determined. In a steady state tokamak commercial reactor, we show that there is an optimal value for the confinement enhancement factor which maximizes the plasma performance, for a given and also for the highest electrical power into the network. This highest electrical power meeting the stability requirements steadily decreases with the confinement enhancement factor. This effect is crucial because both a high plasma performance and a high enough electrical power into the network are required to minimize the cost of electricity, and consequently to make fusion energy more competitive.

This thesis concerns modelling of Coulomb collisions in toroidal plasma with Monte Carlo operators, which is important for many applications such as heating, current drive and collisional transport in fusion plasmas. Collisions relax the distribution functions towards local isotropic ones and transfer power to the background species when they are perturbed e.g. by wave-particle interactions or injected beams. The evolution of the distribution function in phase space, due to the Coulomb scattering on background ions and electrons and the interaction with RF waves, can be obtained by solving a Fokker-Planck equation.The coupling between spatial and velocity coordinates in toroidal plasmas correlates the spatial diffusion with the pitch angle scattering by Coulomb collisions. In many applications the diffusion coefficients go to zero at the boundaries or in a part of the domain, which makes the SDE singular. To solve such SDEs or equivalent diffusion equations with Monte Carlo methods, we have proposed a new method, the hybrid method, as well as an adaptive method, which selects locally the faster method from the drift and diffusion coefficients. The proposed methods significantly reduce the computational efforts and improves the convergence. The radial diffusion changes rapidly when crossing the trapped-passing boundary creating a boundary layer. To solve this problem two methods are proposed. The first one is to use a non-standard drift term in the Monte Carlo equation. The second is to symmetrize the flux across the trapped passing boundary. Because of the coupling between the spatial and velocity coordinates drift terms associated with radial gradients in density, temperature and fraction of the trapped particles appear. In addition an extra drift term has been included to relax the density profile to a prescribed one. A simplified RF-operator in combination with the collision operator has been used to study the relaxation of a heated distribution function. Due to RF-heating the density of thermal ions is reduced by the formation of a high-energy tail in the distribution function. The Coulomb collisions tries to restore the density profile and thus generates an inward diffusion of thermal ions that results in a peaking of the total density profile of resonant ions. / <p>QC 20130415</p>

Le transport radial des particules dans les tokamaks constitue une des questions les plus cruciales pour la communauté de la fusion par con finement magnétique. En eff et, d'une part la puissance de fusion est proportionnelle au carré de la pression, d'autre part l'accumulation d'impuretés lourdes dans le coeur du plasma conduit à d'importantes pertes par rayonnement qui peuvent fi nir par causer un e ffondrement radiatif du plasma. Les dent de scie et la redistribution périodique de la température et de la densité de coeur qui lui est associée peuvent a ffecter signifi cativement le transport radial des électrons et des impuretés. Dans cette thèse, nous présentons des simulations numériques de dents de scie utilisant un code tridimensionnel non linéaire de magnétohydrodynamique appelé XTOR-2F, a n d'étudier le transport de particules pendant les dents de scie. Nous montrons que le code est capable de reproduire les structures fines de densité observées après le crash de la dent de scie avec le diagnostic de réfl ectométrie à balayage rapide sur les tokamaks Tore Supra et JET. La présence de ces structures implique la possibilité que le crash de dent de scie ne soit pas aussi effi cace que prévu pour évacuer les impuretés du coeur du plasma. Cependant, en appliquant le code aux impuretés, nous montrons que finalement le taux de redistribution est quantitativement similaire à ce qui est prévu par le modèle de Kadomtsev, un résultat inattendu a priori. Nous concluons que la dent de scie est e fficace pour évacuer les impuretés du coeur du plasma.

La description magnétohydrodynamique est utilisée pour étudier les plasmas de fusion par confinement magnétique dans deux configurations: tokamak et reversed field pinch. Une méthode de Fourier pseudo-spectrale et une technique de pénalisation en volume sont employées pour résoudre les équations. La méthode de pénalisation permet d'introduire des conditions aux limites de Dirichlet et donc de faire varier facilement la géométrie considérée. Les simulations dans des géométries toroïdales de type tokamak montrent l'apparition spontanée de vitesses. Une importante composante toroïdale se développe si le système est peu dissipatif. Il est aussi montré que la brisure de symétrie dans la forme de la section du tore fait apparaitre un moment angulaire toroïdal. Pour le Reversed Field Pinch on montre l'émergence de structures hélicoïdales. La forme de ces structures varie en fonction des coefficients de transport ainsi que du paramètre de pincement du champ magnétique imposé. Pour compléter l'étude on compare les résultats du tore aux calculs dans un cylindre périodique. Les différences dans la dynamique des deux cas sont mises en avant. Finalement les simulations sont confrontées à des expériences et un meilleur accord est observé entre simulation et expérience pour la géométrie toroïdale que pour la géométrie cylindrique.

In this thesis we mainly focus on the study of the turbulent transport of impurity particles in the plasma due to the electrostatic drift wave microinstabilities. In a fusion reactor, the helium produced as a result of the fusion process is an internal source of impurity. Moreover, impurities are released from the material surfaces surrounding the plasma by a variety of processes: by radiation from plasma, or as a result of sputtering, arcing and evaporation. Impurities in tokamak plasmas introduce a variety of problems. The most immediate effect is the radiated power loss (radiative cooling). Another effect is that the impurity ions produce many electrons and in view of the operating limits on density and pressure, this has the effect of replacing fuel ions. For example, at a given electron density, $n_{e}$, each fully ionized carbon ion (used in the wall materials in the form of graphite) replaces six fuel ions, so that a 7\\% concentration of fully ionized carbon in the plasma core, would reduce the fusion power to one half of the value in a pure plasma. Therefore, for all tokamaks it become an immediate and continuing task to reduce impurities to acceptably low concentrations. However, the presence of impurities, with control, can be beneficial for the plasma performance and reduction of strong plasma heat loads on the plasma facing walls. The radiative cooling effect which was mentioned above can be used at the edge of the plasma in order to distribute the plasma heat more evenly on the whole surface of the vessel walls and therefore, reduce significantly plasma heat bursts on the small regions on the divertor or limiter tiles. The experiments at TEXTOR show that the presence of the impurities at the plasma edge can also improve the performance and reduce the turbulent transport across the magnetic field lines. The observed behavior was explained trough the proposed mechanism of suppression of the most important plasma drift wave microinstability in this region, namely, the Ion Temperature Gradient mode (ITG mode) by the impurities. The impurity's positive impact on the plasma performance offered a possibility to better harness the fusion power, however, it is vital for a fusion reactor to have feedback controls in order to keep impurities at the plasma edge and limit their accumulation in the plasma core where the fusion reactions are happening. In order to have control over the impurity transport we first need to understand different mechanisms responsible for its transport. <p><p>One of the least understood areas of the impurity transport and indeed any plasma particle or heat transport in general, is the turbulent transport. Extensive efforts of the fusion plasma community are focused on the subject of turbulent transport. Motivated by the fact that impurity transport is an important issue for the whole community and it is an area which needs fundamental research, we focused our attention on the development of turbulent transport models for impurities and their examination against experiments. In a collaboration effort together with colleagues (theoreticians as well as experimentalist) from different research institutes, we tried to find, through our models, physical mechanisms responsible for experimental observations. Although our main focus in this thesis has been on the impurity transport, we also tried a fresh challenge, and started looking at the problem of drift wave turbulent transport in a different framework all together. Experimental observation of the edge turbulence in the fusion devices show that in the Scrape of Layer (SOL: the layer between last closed magnetic surface and machine walls) plasma is characterized with non-Gaussian statistics and non-Maxwellian Probability Distribution Function (PDF). It has been recognized that the nature of cross-field transport trough the SOL is dominated by turbulence with a significant ballistic or non-local component and it is not simply a diffusive process. There are studies of the SOL turbulent transport using the 2-D fluid descriptions or based on probabilistic models using the Levy statistics (fractional derivatives in space). However, these models are base on the fluid assumptions which is in contradiction with the non-Maxwellian plasmas observed. Therefore, we tried to make a more fundamental study by looking at the effect of the non-Maxwellian plasma on the turbulent transport using a gyro-kinetic formalism. We considered the application of fractional kinetics to plasma physics. This approach, classical indeed, is new in its application. Our aim was to study the effects of a non-Gaussian statistics on the characteristic of the drift waves in fusion plasmas.<p><p>Ce travail de thèse porte sur le transport turbulent d'impuretés dans les plasmas de fusion<p>par confinement magnétique. C'est une question de la plus haute importance pour le développement<p>de la fusion comme source d'énergie. En effet, une accumulation d'impuretés au coeur<p>du plasma impliquerait des pertes d'énergie par radiation, conduisant par refroidissement à<p>l'extinction des réactions de fusion. Il est par contre prévu d'injecter des impuretés dans le<p>bord du plasma, afin d'extraire la chaleur par rayonnement sans endommager les éléments de<p>la première paroi. Ces contraintes contradictoires nécessitent un contrôle précis du transport<p>d'impuretés, afin de minimiser la concentration d'impuretés au coeur du plasma tout en la<p>maximisant au bord. Une très bonne connaissance de la physique sous-jacente au transport<p>est donc indispensable. L'effet de la turbulence, principal mécanisme de transport, sur les impuretés<p>est alors une question centrale. Dans cette thèse, un code numérique, AFC-FL, a été développé sur la base d'une approche ``fluide' linéaire pour la turbulence d'ondes de dérive. Il calcule les taux de croissance qui caractérisent la rapidité de l'amorçage des instabilités. L'analyse de stabilité est complétée par l'évaluation des taux de croissance en présence d'un gradient de densité, un cisaillement magnétique ou un nombre arbitraire de différentes espèces d'impureté. Les formules complètes du flux turbulent d'impuretés pour ces taux de croissance calculés des instabilités des ondes de dérive ont été dérivées. Un modèle de transport anormal qui nous permet d'étudier la dépendence du transport en fonction de la charge d'impureté a été développé. Ce modèle prend en compte les effets collisionnels entre les ions, l'impureté et les particules principales de plasma. Une telle dépendence du transport anormal en fonction de la charge de l'impureté est observée dans les expériences et il a été montré que les résultats obtenus sont en bon accord avec les observations expérimentales. Nous avons également étudié l'effet des impuretés sur le confinement de l'énergie dans les plasmas du tokamak JET. La modélisation de transport a été exécutée pour des plasmas avec injection de néon dans la périphérie du tokamak. Cette technique est utilisée afin d'extraire la chaleur par rayonnement sans endommager la paroi et pour réduire certaines instabilités (ELM). Des simulations du code RITM ont été comparées à des mesures effectuées lors d'expériences au JET. Il a été montré que l'injection de néon mène toujours à une dégradation du confinement par rapport aux décharges sans néon. Cependant, l'augmentation de la charge effective, en raison du presence du néon peut diminuer le taux de croissance d'autres instabilité (ITG) et amèliorer le confinement du coeur du plasma. Ce confinement amélioré du coeur peut alors compenser la dégradation au bord et le confinement global du plasma peut s'améliorer. <p> / Doctorat en sciences, Spécialisation physique / info:eu-repo/semantics/nonPublished

The tearing mode (TM) is a resistive instability that can arise in magnetically confined plasmas. The TM can be driven unstable by the gradient of the plasma current. When the mode grows it destroys the magnetic field symmetry and reconnects the magnetic field in the form of a so-called magnetic island. The TMs are inherent to a type of device called the reversed-field pinch (RFP), which is a device for toroidal magnetic confinement of fusion plasmas. In the RFP, TMs arise at several resonant surfaces, i.e. where the field lines and the perturbation have the same pitch angle. These surfaces are closely spaced in the RFP and the neighboring TM islands can overlap. Due to the island overlap, the magnetic field lines become tangled resulting in a stochastic magnetic field, i.e. the field lines fill a volume instead of lying on toroidal surfaces. Consequently, a stochastic field results in an anomalously fast transport in the radial direction. Stochastic fields can also arise in other plasmas, for example, the tokamak edge when a resonant magnetic perturbation (RMP) is applied by external coils. This stochastization is intentional to mitigate the edge-localized modes. The RMPs are also used for control of other instabilities. Due to the finite number of RMP coils, however, the RMP fields can contain sidebands that decelerate and lock the TMs via electromagnetic torques. The locking causes an increased plasma-wall interaction. And in the tokamak, the TM locking can cause a plasma disruption which is disastrous for future high-energy devices like the ITER. In this thesis, the TM locking was studied in two RFPs (EXTRAP T2R and Madison Symmetric Torus) by applying RMPs. The experiments were compared with modern mode-locking theory. To determine the viscosity in different magnetic configurations where the field is stochastic, we perturbed the momentum via an RMP and an insertable biased electrode. In the TM locking experiments, we found qualitative agreement with the mode-locking theory. In the model, the kinematic viscosity was chosen to match the experimental locking instant. The model then predicts the braking curve, the short timescale dynamics, and the mode unlocking. To unlock a mode, the RMP amplitude had to decrease by a factor ten from the locking amplitude. These results show that mode-locking theory, including the relevant electromagnetic torques and the viscous plasma response, can explain the experimental features. The model required viscosity agreed with another independent estimation of the viscosity. This showed that the RMP technique can be utilized for estimations of the viscosity. In the momentum perturbation experiments, it was found that the viscosity increased 100-fold when the magnetic fluctuation amplitude increased 10-fold. Thus, the experimental viscosity exhibits the same scaling as predicted by transport in a stochastic magnetic field. The magnitude of the viscosity agreed with a model that assumes that transport occurs at the sound speed -- the first detailed test of this model. The result can, for example, lead to a clearer comparison between experiment and visco-resistive magnetohydrodynamics (MHD) modeling of plasmas with a stochastic magnetic field. These comparisons had been complicated due to the large uncertainty in the experimental viscosity. Now, the viscosity can be better constrained, improving the predictive capability of fusion science. / <p>QC 20171122</p>

No description available.

Un des dispositifs les plus prometteurs pour réaliser la fusion contrôlée est le réacteur de type tokamak. Dans ces réacteurs, un plasma chaud ionisé est confiné à l'aide d'un champ magnétique intense. Ce travail de thèse porte sur l'étude d'une classe particulière d'instabilités au sein d'un tokamak. Cette étude est menée par des simulations numériques magnétohydro-dynamiques (MHD). Le code JOREK-STARWALL est adapté et appliqué pour étudier les instabilités dites à frontière libre. Ce type d'instabilités nécessitent un traitement spécial concernant les conditions de bord du plasma, où l'interaction du plasma avec le vide et les structures conductrices environnantes doit être prise en compte. JOREK-STARWALL permet d'étudier la physique de deux instabilités particulières à frontière libre: les modes localisés au bord ("Edge Localized Modes", ELMs) déclenchés par des oscillations de la position verticale du plasma et les évènements de déplacement vertical (Vertical Displacement Events, VDEs). Deux résultats majeurs sont obtenus: 1. Le déclenchement des ELMs par des oscillations de la position verticale est pour la première fois reproduit avec des simulations auto-cohérentes. Celles-ci permettent d'étudier le mécanisme physique sous-jacent à ce phénomène. Les simulations révèlent que pour le projet international ITER, ces ELMs déclenchés sont principalement dus à une augmentation du courant au bord du plasma due au mouvement vertical. 2. Pour les VDEs, plusieurs comparaisons effectuées avec d'autres codes MHD existants montrent un bon accord avec JOREK-STARWALL et permettant ainsi de réaliser des simulations pour estimer la quantité attendue de courants de halo dans ITER / One of the most promising concepts for future fusion reactors is the tokamak. In these devices, a hot ionized plasma is confined with the use of large magnetic fields. The subject of this thesis is the study of a particular type of tokamak instabilities with MagnetoHydroDynamic (MHD) simulations. The code JOREK-STARWALL is adapted and applied to the simulation of the so-called free-boundary instabilities. The investigation of this type of instabilities requires a special treatment for the plasma boundary conditions, where the interaction of the plasma with the vacuum and the surrounding conducting structures needs to be taken into account. In this work, the modelling of the electromagnetic plasma-wall-vacuum interaction is reviewed and generalized for the so-called halo currents. The adapted JOREK-STARWALL code is applied in order to study the physics of two particular free-boundary instabilities: Edge Localized Modes (ELMs) triggered by vertical position oscillations and Vertical Displacement Events (VDEs). Two major results are obtained: 1. The triggering of ELMs during vertical position oscillations is for the first time reproduced with self-consistent simulations. These allow for the investigation of the physical mechanism underlying this phenomenon. The simulations reveal that for the international ITER project, a large-scale tokamak, these triggered ELMs are mainly due to an increase in the plasma edge current due to the vertical plasma motion. 2. For VDEs, several benchmarks are performed with other existing MHD codes showing a good agreement and therefore allowing the performance of ITER simulations to estimate the expected amount of halo currents in ITER

The study of dust dynamics in tokamaks has been carried out by means of the DDFTU numericalcode solving the coupled equations of motion, charging and heat balance for a dust grainimmersed in plasmas with given profiles. The code has been updated to include (i) a non-steadystate heat balance model and phase transitions, (ii) geometrical properties of the vessel suchas gaps, (iii) realistic boundary conditions for dust-wall collisions. The models for secondaryelectron emission (SEE), thermionic emission and black body radiation have also been refined,and sensitivity of the results to the SEE strength is demonstrated. The DDFTU code has been used for the first time to explore a large range of initial conditions(position, velocity and radius) for dust grains of various tokamak-relevant materials. This studyconfirmed the impact of the drag force as one of the main factors in dust dynamics and allowedto estimate average lifetimes, to locate preferred sites for dust deposition and to judge thesensitivity to initial conditions. This is a first step towards the use of the code as a predictivetool for devices of importance, such as JET and ITER. Preliminary simulations of scenarios relevant for dust injection experiments in TEXTOR haveyielded results in remarkable agreement with experimental data. These preliminary studies allowed to identify the most crucial issues affecting dust dynamics,lifetime, deposition rate and contribution to impurities, which are to be pursued in futurestudies.

Design and implementation of the plasma control system Mgr. Filip Janky The COMPASS tokamak was recommissioned in 2007 and it needed new digital controllers for its experimental research. This thesis presents the design and imple- mentation of control of main plasma parameters such as plasma current, plasma position, plasma shape and electron density. Improved plasma current control with resetting set points suppresses overshooting and thus increases the length of the flat top phase. A method for estimating the plasma position, gain tuning for the controller and decreasing latencies and delays to obtain robust position control are presented. Lower delays improve plasma stability and decrease the frequency of disruptions. The plasma shape controller is a feedforward controller with a method to suppress oscillations which are coming from mutual inductance between power supplies controlling plasma horizontal position, plasma shape and plasma current, which all use the same coil. Averaged electron density is corrected in real-time according to the interferometer line of sight and a non-linearity of measurement. Controllers and their improvements described here, played a major role in achiev- ing H-mode scenario and fulfilling the experimental program. Keywords: tokamak, plasma current control, plasma position...