Dissertations / Theses on the topic 'MHD tokamak'

Este trabalho descreve o estudo das instabilidades magneto-hidro-dinâmicas (MHD) comumente observadas nas descargas elétricas de plasma no tokamak TCABR, do Instituto de Física da USP. Dois diagnósticos principais foram empregados para observar essas instabilidades: um conjunto poloidal de 24 bobinas magnéticas (bobinas de Mirnov) colocadas próximas à borda do plasma e um medidor de emissões na faixa do Ultra Violeta e de raios X moles com 20 canais (sistema SXR), cujo circuito de condicionamento de sinais foi aprimorado como parte deste trabalho. Esses diagnósticos foram escolhidos porque fornecem informações complementares, uma vez que o sistema SXR observa a parte central da coluna de plasma, enquanto as bobinas de Mirnov detectam as instabilidades MHD na região mais externa da coluna. As informações coletadas por esses diagnósticos foram submetidas à análise espectral com resolução temporal e espacial, possibilitando determinar a evolução das características espectrais e espaciais das instabilidades MHD observadas. Essas análises revelaram que durante a etapa inicial da formação do plasma (quando a corrente de plasma ainda está aumentando) ilhas magnéticas com números de onda decrescente, identificadas como sendo modos kink de borda, são detectadas nas bobinas de Mirnov. Após a formação do plasma, quando os parâmetros de equilíbrio estão relativamente estáveis (platô), oscilações são detectadas tanto nas bobinas de Mirnov quanto no sistema de SXR, indicando a presença de instabilidades MHD em toda a coluna de plasma. Em geral as oscilações medidas nas bobinas de Mirnov tem baixa amplitude e correspondem a pequenas ilhas magnéticas que foram identificadas como sendo modos de ruptura (modos tearing). Por outro lado, as instabilidades na região central foram identificadas como dentes de serra, que correspondem a relaxações periódicas da região interna à superfície magnética com fator de segurança q=1 e que são acompanhadas de oscilações precursoras, cuja amplitude depende da fase do ciclo de relaxação. Devido à essa modulação de amplitude, aparecem picos de frequência satélite nos espectrogramas dos sinais do SXR. Além disso, devido ao fato dos ciclos de relaxação não serem sinusoidais, os harmônicos da frequência de relaxação também aparecem nesses espectrogramas. No entanto, em muitas descargas do TCABR, a intensidade das oscilações medidas nas bobinas de Mirnov aumentam significativamente durante o platô, com efeitos sobre a frequência de todas as instabilidades MHD, até mesmo sobre os dentes de serra localizados na região central da coluna. Em todos os casos, observou-se que durante o platô a frequência das ilhas magnéticas coincide com a frequência das oscilações precursoras do dente de serra, apesar de serem duas instabilidades distintas, localizadas em posições radiais muito diferentes. Essa coincidência de frequências possibilitou descrever a evolução em frequência de todas as oscilações detectadas em diversos diagnósticos com base em apenas duas frequências básicas: a dos ciclos de relaxação dente de serra e a das ilhas magnéticas.<br>This work describes the study of magneto-hydro-dynamic instabilities (MHD) commonly observed in plasma discharges in tokamak TCABR (at Instituto de Física da USP). Two main diagnostics were employed to observe these instabilities: a poloidal set of 24 magnetic coils (Mirnov coils) placed near the plasma border and a detector of emissions in the Ultra Violet and soft X-ray range with 20 channels (SXR system) which improvement of the signal conditioning circuit was done as part of this work. These diagnostics were chosen because they provide complementary information, since the SXR system measures the central part of the plasma column, while the Mirnov coils detect the MHD instabilities in the outer part of the column. The information collected by these diagnoses was submitted to spectral analysis with temporal and spatial resolution, making it possible to determine the evolution of the spectral and spatial characteristics of the observed MHD instabilities. These analyzes revealed that during the initial stage of the plasma formation (when the plasma current is still increasing) magnetic islands with decreasing wave numbers, identified as edge kink modes, are detected in the Mirnov coils. After the plasma formation, when the equilibrium parameters are relatively flat (plateau), oscillations are detected in both Mirnov coils and SXR system, indicating the presence of MHD instability in the whole plasma column. In general, the fluctuations measured by the Mirnov coils have low amplitude corresponding to small magnetic islands, which were identified as tearing modes. On the other hand, the instabilities at the central region were identified as sawteeth oscillations that correspond to periodic relaxations in the internal region of the magnetic surface with safety factor q = 1 and that are accompanied by precursor oscillations which amplitude depends on the phase of the relaxation cycles. Due to this amplitude modulation, frequency satellite peaks appear in the spectrograms of the SXR signals. Furthermore, due to the fact that relaxation cycles are not sinusoidal, harmonics of the relaxation frequency also appear in the spectrograms. However, in many TCABR discharges, the intensity of the oscillations measured by the Mirnov coils increase significantly during the plateau, with affects the frequency of all MHD instabilities, even over the sawteeth in the central region of the column. In all cases, it was observed that during the plateau the frequency of the magnetic islands coincides with the frequency of the sawtooth precursors, although they are two different instabilities located in separated radial positions. This coincidence of frequencies allowed describing the frequency evolution of all measured oscillations by considering only two basic frequencies: the cycles of sawtooth relaxation and the magnetic islands.

Neste trabalho foram estudadas instabilidades magnetohidrodinâmicas (MHD) utilizando um novo sistema bolométrico que foi instalado no tokamak TCABR para medidas da evolução temporal da potência irradiada. Este novo sistema conta com 24 cordas verticais, capazes de mapear toda uma secção poloidal da coluna de plasma com resolução espacial de aproximadamente 2 cm e uma resolução temporal de 20 µs. Como se sabe, as instabilidades MHD degradam o connamento do plasma e modicam a topologia das superfícies magnéticas, causando a perda da energia do plasma. Por conta disso, compreender essas instabilidades é fundamental para o sucesso dos futuros reatores de fusão nuclear. As perturbações (oscilações) causadas pelas instabilidades MHD modulam diversos parâmetros macroscópicos do plasma como a densidade, a temperatura e a potência irradiada. Então, utilizando o diagnóstico bolométrico, é possível medir as oscilações no perl de potência irradiada e, a partir deles, extrair informações importantes para determinar a origem e as características de tais instabilidades. No tokamak TCABR, as instabilidades foram caracterizadas através da análise espectral dos 24 sinais provenientes do novo sistema bolométrico. Para auxiliar a caracterização das instabilidades, um programa foi desenvolvido em Matlab para simular as medidas das perturbações no perl de potência irradiada. Através do mesmo procedimento de análise espectral, os resultados simulados foram comparados aos experimentais de forma que os parâmetros simulados, como largura e posição das ilhas magnéticas, fossem ajustados aos experimentais. Através dessa metodologia de análise, que combina simulação e experimento, foi possível caracterizar diversas instabilidades como o precursor dos dentes de serra e ilhas magnéticas de modos m = 2 e m = 3.<br>In this dissertation, magnetohydrodynamic (MHD) instabilities were investigated using a new bolometric system that was installed in the TCABR tokamak for radiation power measurements. This diagnostic is composed by 24 vertical chords that provide a full view of the poloidal cross section of the plasma column and provides spatial and temporal proles with approximately 2 cm space and 20 µs time resolution. As it is well known, the MHD instabilities degrade the plasma connement and modify the magnetic topology, leading to energy loss from the plasma. Therefore, the understanding of these instabilities is essential for the success of the controlled thermonuclear fusion reactors. The MHD instabilities also cause perturbations (oscillations) in various macroscopic parameters, such as plasma density, temperature, and radiated power. Therefore, the oscillations in the radiated power prole measured by the bolometric diagnostic system provide a possibility to investigate the origin and features of the instabilities. In the TCABR tokamak, the instabilities were characterized by spectral analysis of the 24 vertical chords of the bolometric signals. In addition, a Matlab program was developed to simulate the integral characteristic of the oscillations in the radiated power measured by the bolometric system. The spectral analysis of the simulated signals is then compared with the spectral analysis of the bolometric signals. The simulated parameters, island width and radial position, were then adjusted to t the experimental spectrum results. Using this method of analysis, which combines experiment and simulation, it was possible to characterize various instabilities, such as sawtooth precursor and m = 2 and m = 3 magnetic islands.

Um sistema de bobinas de Mirnov foi construído, calibrado e utilizado para a análise das descargas de plasma no tokamak TCABR. Este sistema é composto de 22 bobinas magnéticas que foram instaladas ao redor de uma seção transversal no interior da câmara de vácuo do TCABR, tendo-se em conta os efeitos produzidos pela geometria toroidal do sistema. Cuidados especiais foram tomados para proteger os enrolamentos das bobinas com relação a ação do plasma, e também para evitar que correntes de Foucault viessem a comprometer o funcionamento do sistema. Para este diagnóstico também foi construído um sistema eletrônico específico para a filtragem e amplificação dos sinais das bobinas, para serem, depois, digitalizadas pelo sistema VME e gravados através do sistema de aquisição de dados do TCABR. Foi desenvolvido, também, um programa para a análise destes dados, baseados no processo da análise de Fourier, de forma a permitir a identificação dos modos de perturbação MHD presentes nas descargas do TCABR. Com esse sistema de deteção colocado em operação, foi então possível investigar as descargas de plasma do TCABR para dois regimes de operação: descargas de 'run-away' e plasma resistivo. Nas descargas com elétrons fugitivos 'run-away', foram observadas estruturas nos sinais de tensão de enlace, H alfa, raios-X duros e bobinas de Mirnov, bastante correlacionados entre si. Nas descargas com plasma resistivo, foi observado que as oscilações de Mirnov no tokamak TCABR possuem freqüências no intervalo de 10 kHz - 15 kHz. Em algumas das descargas também foram observadas correlações entre os sinais de emissão de raios-X duros e as oscilações de Mirnov, bem como correlações entre as flutuações da densidade de partículas e as oscilações de Mirnov. Experimentos com deslocamento horizontal da coluna de plasma permitiram observar como variava o comportamento das amplitudes dos sinais das bobinas de Mirnov. Também foram estudadas algumas descargas disruptivas com plasma resistivo no limite de altas densidades. Pode-se analisar as oscilações de Mirnov e os modos de perturbação antes da ocorrência de disrupturas. Observou-se, por exemplo, que o modo precursor m = 3 é predominante ao longo da descarga mas, antes da disruptura, os modos m = 1, 2, 3 e 4 passam a ser dominantes. Nesta situação a velocidade angular das ilhas magnéticas foi determinada como sendo de 5000 rad/s. Finalmente, utilizaram-se os sinais do sistema de bobinas de Mirnov para algumas análises preliminares envolvendo descargas resistivas com ondas de Alfvèn. Foi observado, por exemplo, que depois de 3 ms de serem ligadas as antenas de Alfvèn, as oscilações de Mirnov geralmente crescem em amplitude enquanto diminuem em freqüência, mantendo-se assim até o final da descarga.

Le code XTOR-2F simule la dynamique 3D des instabilités MHD bi-fluides de plasmas de tokamaks.La première partie de la thèse a été consacrée à la parallélisation du code XTOR-2F. Le code a été parallélisé significativement malgré la représentation pseudo-spectrale pour les deux directions angulaires, la raideur des équations résolues et l’utilisation d’une décomposition LU exacte afin d’inverser le préconditionneur physique. Le temps d’exécution de la version parallèle est un ordre de grandeur plus petit que la version séquentielle sur un maillage basse résolution. L’accélération croît ensuite avec la taille du maillage. La parallélisation permet également de réaliser des simulations avec des maillages plus grands, autrefois non réalisables par la limitation du stockage en RAM.La seconde partie de la thèse a été consacrée au développement d’une version du code permettant de réaliser des simulations en géométrie à frontière libre, s’approchant de la géométrie des tokamaks expérimentaux de grandes tailles. Les conditions initiales sont fournies par le code d’équilibre CHEASE à l’intérieur du plasma. A l’extérieur du plasma, la solution a été étendue en ajustant le potentiel magnétique avec un ensemble de bobines magnétiques poloïdales externes. Les conditions de bord utilisent des fonctions de Green afin de calculer une matrice de transfert permettant de relier les composantes tangentes et normales du champ magnétique externe à la coque avec la solution interne. Ceci permet de modéliser une coque résistive fine. Cette nouvelle version élargie le domaine d’investigation de XTOR-2F, autrefois restreint aux instabilités internes, aux instabilités externes. Le comportement linéaire du code est validé sur deux familles d’instabilités, les modes axisymétriques n = 0 et les kinks externes n = 1 / m = 2. Afin de valider le comportement non linéaire, des simulations en MHD résistive de modes tearing à bêta nul évoluant vers un état stationnaire ont été réalisées<br>The XTOR-2F code simulates the 3D dynamics of full bi-fluid MHD instabilities in tokamak plasmas.The first part of the thesis was dedicated to the parallelisation of XTOR-2F code. The code has been parallelised significantly despite the numerical profile of the problem solved, i.e. a discretisation with pseudo-spectral representations in all angular directions, the stiffness of the two-fluid stability problem in tokamaks, and the use of a direct LU decomposition to invert the physical pre-conditioner. The execution time of the parallelised version is an order of magnitude smaller than the sequential one for low-resolution cases, with an increasing speedup when the discretisation mesh is refined. Moreover, it allows to perform simulations with higher resolutions, previously forbidden because of memory limitations.The second part of the thesis was dedicated to the development of free boundary condition. The original fixed boundary computational domain of the code was generalised to a free-boundary one, thus approaching closely the geometry of today’s and future large experimental devices. The initial conditions are given by the CHEASE equilibrium code inside the plasma. Outside the plasma, fitting the magnetic potential at the CHEASE computation domain boundary with a set of external poloidal magnetic coils extends the solution. The boundary conditions use Green functions to construct a response matrix matching the normal and tangential components of the outside magnetic field with the inside solution. A thin resistive wall can be added to the computational domain. This new numerical setup generalises the investigation field from internal MHD instabilities towards external instabilities. The code linear behaviour is validated with two families of instabilities, n = 0 axisymmetric modes and n = 1/m = 2 external kinks. In order to validate the nonlinear behaviour, nonlinear resistive MHD simulations of tearing modes at zero beta evolving to a stationary state have been performed

Resumo O conhecimento dos parâmetros macroscópicos do plasma, tais como a densidade e temperatura, bem como sua evolução e dependência espacial são fundamentais para a compreensão e controle do plasma. Esses parâmetros são essenciais para descrição dos eventos associados a fenômenos de transporte, atividade MHD, estudos de regime de confinamento melhorado (modo H), entre outros. O perfil de temperatura e densidade de íons e elétrons caracteriza um parâmetro extremamente importante em plasmas termonucleares que é o perfil de pressão. Para obter esses perfis foram utilizados os principais diagnósticos disponíveis no tokamak TCABR: espalhamento Thomson, interferometria, reflectometria, ECE e diagnósticos espectroscópicos. O espalhamento Thomson é capaz de determinar o perfil de temperatura e densidade eletrônica durante o disparo; já o diagnóstico ECE é capaz de medir a temperatura eletrônica sob certas condições de descargas. Já os diagnósticos de interferometria e reflectometria medem a densidade eletrônica integrada e a densidade eletrônica local, respectivamente. Por fim, o perfil de temperatura iônica pode ser estimado através do alargamento Doppler das linhas de emissão de impurezas. Tais dados são usados para reconstrução do perfil de pressão, em diferentes tipos de descargas no tokamak, bem como possibilitar a reconstrução do equilíbrio. Não obstante, esses diagnósticos podem fornecer informações como estimativa do Z efetivo do plasma, da velocidade de rotação, e das condições que promovem disrupção no TCABR<br>The knowledge of the plasma macroscopic parameters such as density and temperature as well as their temporal and spatial evolution are fundamental to the understanding and control of the plasma. These parameters are essential for description of events associated with transport phenomena, magnetohydrodynamics (MHD) activity, improved confinement studies (H mode), among others. The temperature and density profiles of electrons and ions define an extremely important parameter in thermonuclear plasmas that is the pressure profile. To measure these profiles we used all the main diagnostics available in the TCABR tokamak: Thomson scattering, interferometry, reflectometry, ECE and spectroscopic diagnostics. The Thomson scattering is able to determine the local electron temperature and density in the plasma discharge; ECE diagnostic is also able to measure the local electron temperature under certain plasma discharge conditions. And the interferometric and reflectometric diagnostics measure the line-integrated electronic density and the local electronic density, respectively. Finally, the ion temperature profile can be estimated by the Doppler broadening of the impurity line emissions. These data are used to reconstruct the pressure profile in different types of discharges in tokamak, and to enable the MHD equilibrium reconstruction. Nevertheless, these analyzes can provide information to estimate the plasma Z effective, plasma rotation velocity, and the conditions that promote the disruption in the TCABR.

Dans les plasmas de tokamak peuvent se développer des instabilités MHD (Magneto-Hydro-Dynamiques) se manifestant sous la forme d’îlots magnétiques qui réduisent le confinement. Ces îlots peuvent être contrôlés par la génération localisée de courant dans le plasma. Dans cette thèse, nous nous intéressons à la modélisation des îlots magnétiques et de leur contrôle en utilisant une description fluide (MHD) du plasma, à l’aide du code XTOR. Nous détaillons l'inclusion d'une source de courant au sein du modèle MHD, ce qui nécessite l'ajout d'une équation supplémentaire pour modéliser la propagation de la densité de courant le long des lignes de champ magnétique. Cette implémentation est ensuite vérifiée sur la base de modèles analytiques, nous permettant de retrouver l'influence de paramètres tels que la largeur du dépôt ou son désalignement. Nous avons mis en évidence des effets non-décrits par les modèles asymptotiques, liés à la nature de la localisation spatiale de la source de courant. Nous nous sommes ensuite intéressés aux stratégies de contrôle envisageable pour la suppression des îlots. Nous avons ajouté au sein du code XTOR un système de contrôle qui ajuste le dépôt de courant selon les stratégies choisies. Des simulations MHD non-linéaires des différents schémas de contrôle ont été effectuées, et les différentes stratégies comparées, permettant de préciser pour chacune une gamme d’intérêt<br>Magneto-Hydro-Dynamic (MHD) instabilities are susceptible to develop within a tokamak plasma. These instabilities manifest themselves as magnetic islands which reduce the plasma confinement. The islands can however be controlled by driving current inside them. In this thesis, we consider the modeling of the magnetic islands and their control using first principle approaches, which rely on a global MHD description of the plasma. We have detailed the inclusion a RF-driven current like source term in an MHD code, which requires special care to be given to the modeling of the current density evolution. The implementation has been benchmarked against the asymptotic models, allowing us to retrieve the influence of parameters such as deposition width or misalignment with respect to the island width and position. Beyond these aspects, we have evidenced new effects, linked to the 3D nature of the current deposition. We have observed a flip instability in which an island, reduced by the ECCD, brutally inverse its phase so that its X-Point faces the current deposition, allowing the mode the grow further. We then moved on to the topic of the best suitable control strategies for the control of the island. We have implemented in XTOR a control system that mimics the experimental ones and adapt the current deposition in function of a preset strategy. Nonlinear MHD simulations have been carried out using different control schemes, allowing us to quantify the gain to expect from each of these methods depending on the characteristics of the current deposition

Dans ce travail de thèse, l’excitation de modes magnétohydrodynamique (MHD) spécifiques appelés les Toroidal Alfvèn Eigenmodes sont étudiés. Ces modes peuvent être facilement déstabilisés par plusieurs populations de particules rapides. L’excitation de modes TAE par une antenne externe en 3D est simulée pour la première fois dans les configurations point X et limiteur. Les simulations présentent une bonne concordance avec la difficulté d’exciter des modes TAE en géométrie X observée expérimentalement. L’utilisation du code Castor a permis de montrer que pour certains profils de densité, l’atténuation provenant d’une région de la séparatrice dont la limite est proche de la séparatrice peut être une source d’amplification de l’atténuation. Les résultats obtenus avec le code Jorek montrent que la région où les lignes de champ sont ouvertes est la principale source d’atténuation. Le code purement fluide Jorek a été modifié afin d’inclure les termes cinétiques fournis par son extension cinétique. Afin de confirmer l’implémentation du schéma, les taux de croissance linéaires de TAE sont calculés pour le cas de référence ITPA. Un pas supplémentaire a été fait à travers l’étude de l’évolution des modes TAE excités par une antenne externe en présence de particules rapides. L’intérêt principal de cette approche est d’investiguer la possibilité d’extraction d’information sur l’excitation des particules rapides depuis la réponse plasma à une excitation TAE. Une méthode permettant l’estimation de l’excitation de particules rapides à travers la mesure de la différence de réponse fréquentielle entre les deux directions des ondes progressives TAE est développé<br>In this thesis, the excitation of a specific types of the MHD modes called the Toroidal Alfven Eigenmodes is studied. These global modes can be easily destabilized by one of the several populations of the fast particles present in tokamaks. For the first time the modelling of the excitation of the TAE modes by a 3D external antenna is performed in case of limiter and X-point geometries. With the use of the code CASTOR it has been shown that the damping from the region inside the separatrix with plasma boundary approaching the separatrix can be a source of an increased damping for certain density profile shapes. The results obtained with the JOREK code identifies the region of the open-field lines as the main source of damping. Firther, the purely fluid code JOREK was modified to include the kinetic terms provided by the code's kinetic extension. Between the two commonly used hybrid schemes, pressure and current coupling schemes. In order to confirm the implementation of the scheme, the TAE linear growth rates are obtained for the ITPA benchmark case. A further step that was taken is to combine the previously used approaches by examining the evolution of the TAE modes excited by an external antenna now in the presence of fast particles. The principal interest in this approach is to investigate the possibility of extracting information on the fast particle drive from the plasma response on the TAE excitation. A method allowing an estimate of the fast particle drive by measuring the difference in the frequency response of the two directions of the traveling TAE waves was developed

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 2000.<br>Includes bibliographical references (p. 175-181).<br>Magnetohydrodynamic (MHD) activity has been analyzed primarily using electron cyclotron emission (ECE) diagnostics on Alcator C-Mod tokamak. The main results are that i) two MHD instabilities have been identified during current ramp-up discharges (resistive 'multiple' tearing mode and ideal interchange mode) and ii) a new approach to diagnose edge localized modes (ELMs) using ECE diagnostics was explored. Both MHD modes were accompanied by hollow pressure and current profiles. The associated q-profiles were also hollow with q0 >> 1, where q0 is the safety factor on the magnetic axis. In both cases, the electron temperature fluctuations observed on ECE diagnostics agreed reasonably well with the perturbed pressure fluctuations predicted in a resistive linear stability code (MARS). For the resistive 'multiple' tearing mode , the MHD fluctuations were peaked near the outer q=3 rational surface but had several other resonant layers, which affected the plasma globally. The predicted growth time was ~0.44 msec, which is within the typical range of tearing mode evolution times. For the ideal interchange mode, the MHD fluctuations were highly localized near the inner q=5 rational surface. According to ideal MHD stability theory, the q = 5 surface was found to be ideally unstable because of the reversed pressure gradient (dp/dr > 0) and q > 1 with moderate shear. When kinetic effects were added, the ideally unstable mode was finite ion Larmor radius (FLR) stabilized. However, considering that 1) electrons are collisional, 2) ions are collisionless, and 3) the thermal ion transit frequency is comparable to the ion diamagnetic drift frequency, ion Landau damping was found to be strong enough to drive a kinetic Mercier instability. As a result, a FLR modified kinetic Mercier instability has been identified, possibly for the first time since the Mercier criterion was formulated forty years ago. During 'Type III' ELMs, rather unusual signal changes were observed on two ECE diagnostics; signal drops of second harmonic X-mode on one diagnostic and signal spikes of fundamental harmonic 0-mode on another. These were explained in terms of refraction effects and found to be useful to infer the associated geometrical dimensions. For this investigation, a new ray tracing code, which can accommodate poloidal variations, has been developed. As a result, an ELM has been modeled successfully as a poloidally elongated density loss. Observations are consistent with the following dimensions; radial width of the affected region ([delta] r) ~ 1 - 3 cm, poloidal elongation ~1.5 (equivalent to a poloidal wave number ... minimum density 0.5 x I020m-3 at the mid plane ~~ 1cm inside the last closed flux surface (LCFS). This knowledge helps to assess the influence of the particle loss on the main plasma. Considering that ELMs challenge present diagnostic capabilities in terms of spatiotemporal resolution, such indirect measurement opens the door to improved physical understanding of ELMs. In particular, it is the first to reveal the poloidal structure of an ELM.<br>by Yongkyoon In.<br>Ph.D.

Les performances des plasmas de fusion confinés magnétiquement peuvent être dégradées par l'accumulation d'impuretés. Plus particulièrement, les impuretés lourdes accumulées au centre du plasma diluent les réactifs, et peuvent aussi conduire à un collapse radiatif du plasma par de fortes pertes par rayonnement. La compréhension du transport des impuretés lourdes produites lors de l'interaction plasma-paroi est donc devenue cruciale.Le coeur du plasma est sujet à une instabilité magnétohydrodynamique (MHD) appelée ‘kink interne’, conduisant à des oscillations de relaxation nommées ‘dents de scie’. Les dents de scie entraînent une relaxation périodique de densité et de température dans le coeur du plasma, et affectent significativement le transport radial. Notamment, les particules et la chaleur sont redistribuées pendant un crash dont la durée est très courte par rapport au temps de confinement.En l'absence des instabilités MHD, le transport des impuretés est porté par les collisions (transport néoclassique) et la turbulence. Il est établi que le transport néoclassique est important pour les impuretés lourdes dans la région centrale du plasma de tokamak. Cependant, des mesures expérimentales du tokamak ASDEX-Upgrade montrent que la dynamique des impuretés en présence des dents de scie est différente des prédictions faites par les codes de transport.Dans cette thèse, l'outil numérique utilisé pour simuler les dents de scie est le code XTOR-2F, qui est un code non-linéaire tridimensionnel résolvant les équations de la MHD. Les équations fluides modélisant le transport des impuretés dans un régime de collisionalité élevée (Pfirsch-Schlüter) ont été implémentées et couplées avec l'ensemble des équations de la MHD bi-fluide.Les simulations montrent que les profils de densité d'impuretés sont affectés par les dents de scie, en accord avec les observations expérimentales. Ceci résulte d'une compétition entre processus néoclassiques et relaxations dues aux dents de scie<br>Impurity accumulation can degrade the performance of magnetically confined fusion plasmas. In particular, heavy impurities accumulated in the core plasma dilute fusion reactants and may also lead to a radiative collapse of the plasma due to excessive cooling by radiation. Therefore, understanding the transport of heavy impurities produced by plasma-wall interaction has become a subject of utmost importance.The plasma core is likely to be affected by a magnetohydrodynamic (MHD) instability called 'internal kink' that induces relaxation oscillations named 'sawteeth'. Sawteeth are responsible for periodic relaxations of the core density and temperature and affect significantly the radial transport. Especially, particles and heat are redistributed during the crash phase the duration of which is short compared to the confinement time.In absence of MHD instabilities, impurity transport is governed by collisions (neoclassical transport) and turbulence. It is shown that neoclassical transport is important for heavy impurities in the core region of tokamak plasmas. Meanwhile, experimental measurements in the ASDEX-Upgrade tokamak show that the impurity dynamics in presence of sawteeth differs from the predictions made by transport codes.In this thesis, the numerical tool used to simulate sawteeth is the XTOR-2F code, which is a non-linear tridimensional code solving MHD equations. Fluid equations that model the transport of impurities in a highly collisional (Pfirsch-Schlüter) regime have been implemented and coupled to the set of two-fluid MHD equations.The simulations show a difference between the impurity profiles with and without sawteeth, which is consistent with experimental observations. This results from a competition between neoclassical processes and sawtooth relaxations

Dans les tokamaks, les instabilités nommées ELMs (pour ``Edge Localized Modes'') génèrent des relaxations quasi-périodiques du plasma, potentiellement néfastes pour le divertor d'ITER. Une méthode de contrôle des ELMs prévue pour ITER est l'application de Perturbations Magnétiques Résonantes (RMPs), capables de mitiger ou supprimer les ELMs dans les tokamaks existants. Afin d'améliorer la compréhension de l'interaction entre les ELMs, les RMPs et les écoulements du plasma et de réaliser des prédictions fiables pour ITER, la simulation non-linéaire des ELMs et des RMPs est réalisée avec le code de MHD réduite JOREK, en géométrie réaliste. Les effets bi-fluides diamagnétiques, la friction poloidale néoclassique, une source de rotation parallèle et les RMPs ont été ajoutés dans JOREK pour simuler la pénétration des RMP en prenant en compte la réponse cohérente du plasma. Dans un premier temps, la réponse du plasma aux RMPs (sans ELMs) est étudiée dans le cas des tokamaks JET, MAST et ITER, pour des paramètres réalistes. Ensuite, la dynamique cyclique des ELMs (sans RMPs) est modélisée pour la première fois en géométrie réaliste. La compétition entre la stabilisation du plasma par la rotation diamagnétique et sa déstabilisation par la source de chaleur induit la reconstruction cyclique du piédestal. Enfin la mitigation et la suppression des ELMs sont obtenues pour la première fois dans nos simulations. Le couplage non-linéaire des RMPs avec des modes instables du plasma induit une activité MHD continue à la place des violentes relaxations d'ELMs. Au-delà d'un seuil de perturbation magnétique, la suppression totale des ELMs est également observée<br>The growth of plasma instabilities called Edge Localized Modes (ELMs) in tokamaks results in the quasi-periodic relaxations of the edge plasma, potentially harmful for the divertor in ITER. One of the promising ELM control methods planned in ITER is the application of external resonant magnetic perturbations (RMPs), already efficient for ELM mitigation/suppression in current tokamak experiments. However a better understanding of the interaction between ELMs, RMPs and plasma flows is needed to make reliable predictions for ITER. In this perspective, non-linear modeling of ELMs and RMPs is done with the reduced MHD code JOREK, in realisitic geometry including the X-point and the Scrape-Off Layer. The two-fluid diamagnetic drifts, the neoclassical friction, a source of parallel rotation and RMPs have been implemented to simulate the RMP penetration consistently with the plasma response. As a first step, the plasma response to RMPs (without ELMs) is studied for JET, MAST and ITER realistic plasma parameters and geometry. Then the cyclic dynamics of the ELMs (without RMPs) is modeled for the first time in realistic geometry. After an ELM crash, the diamagnetic rotation is found to be instrumental to stabilize the plasma and to model the cyclic reconstruction and collapse of the plasma pressure profile. Last the ELM mitigation and suppression by RMPs is observed for the first time in modeling. The non-linear coupling of the RMPs with unstable modes is found to induce a continuous MHD activity in place of a large ELM crash, resulting in the mitigation of the ELMs. Over a threshold in magnetic perturbation, the full ELM suppression is also observed

In this work we study the magnetic field modeling of realistic non-axisymmetric plasma equilibrium configurations and the heat flux patterns on the plasma facing components of tokamak divertor discharges. We start by establishing the relation between generic magnetic configurations and Hamiltonian dynamical systems. We apply the concept of magnetic helicity, used to establish topological bounds for the magnetic field lines in ideal plasmas, and to understand the self-consistency of reconnected magnetic surfaces in non-axisymmetric configurations. After this theoretical discussion, we present some results on magnetohydrodynamic equilibrium and the use of analytical solutions to the Grad-Shafranov equation for describing real tokamak discharges based on the experimental diagnostics and realistic boundary conditions. We also compare the equilibrium reconstruction of a DIII-D discharge obtained with a numerical reconstruction routine, developed as part of this research, and the EFIT code used by several tokamak laboratories around the world. The magnetic topology and plasma profiles obtained with our method are in considerable agreement with the numerical reconstruction performed with the other code. Then, we introduce a simplified description of the generic non-axisymmetric magnetic field created by known sources and implement it numerically for describing the magnetic field due to external coils in tokamak devices. After that, we use this routines to develop a numerical procedure to adjust a suitable set of non-linear parameters of internal filamentary currents, which are intended to model the plasma response based on the magnetic field measurements outside the plasma. Finally, these methods are used to model the magnetic field created by a slowly rotating plasma instability in a real DIII-D discharge. The plasma response modeling is based on the magnetic probe measurements and allow us to calculate the magnetic field in arbitrary locations near the plasma edge. Using this information we determine the non-axisymmetric plasma edge through the magnetic invariant manifolds routine developed during this work. The intersection of the calculated invariant manifold with the tokamak chamber agrees considerably well with the heat flux measurements for the same discharge at the divertor plates, indicating the development of a rotating manifold due to the internal asymmetric plasma currents, giving quantitative support to our simplified description of the magnetic field and the plasma edge definition through the invariant manifolds.<br>Neste trabalho estuda-se a modelagem do campo magnético em configurações realistas de plasmas em equilíbrio não-axissimétrico e o fluxo de calor nos componentes em contato com o plasma em descargas de tokamaks com desviadores poloidais. Começa-se estabelecendo a relação entre configurações magnéticas arbitrárias e sistemas dinâmicos Hamiltonianos. Então aplicamos o conceito de helicidade magnética, que é usado para estabelecer limitações topológicas sobre as linhas de campo magnético em plasmas ideais, assim como para compreender a auto-consistência das superfícies magnéticas reconectadas em configurações não-axissimétricas. Após esta discussão teórica, apresentam-se alguns resultados sobre o equilíbrio magnetohidrodinâmico e o uso de soluções analíticas à equação de Grad-Shafranov para descrever descargas reais em tokamaks, com base em diagnósticos experimentais e condições de contorno realistas. Também realiza-se uma comparação entre a reconstrução do equilíbrio de uma descarga do DIII-D, obtida mediante uma rotina numérica desenvolvida para esta pesquisa, com a obtida mediante o código EFIT, usado amplamente em diversos tokamaks. Após isso, apresenta-se uma descrição simplificada do campo magnético não-axissimétrico, criado por fontes determinadas, e a sua implementação para descrever o campo magnético devido às correntes externas em tokamaks. Então, usam-se estas rotinas para desenvolver um procedimento numérico que ajusta um conjunto adequado de parâmetros não-lineares de correntes filamentares internas, com as quais pretende-se modelar a resposta do plasma com base nas medidas de campo magnético fora do plasma. Finalmente, estes métodos são utilizados para modelar o campo magnético criado por uma instabilidade com rotação lenta numa descarga do DIII-D. Com base nas medidas das sondas magnéticas é possível modelar os campos criados em regiões arbitrárias próximas da borda do plasma. Usando esta informação é possível determinar a borda não-axissimétrica do plasma mediante as invariantes magnéticas calculadas com a utilização de uma rotina desenvolvida durante este trabalho. A intersecção da superfície invariante com a câmara do tokamak coincide satisfatoriamente com as medidas de fluxo de calor nas placas do divertor para a mesma descarga, indicando o desenvolvimento de uma variedade giratória criada pelas correntes de plasma não-axissimétricas, e sustentando quantitativamente a nossa descrição simplificada do campo magnético, assim como a definição da borda do plasma mediante as invariantes magnéticas.

La stabilité des modes magnéto-hydrodynamiques dans les plasmas de tokamaks est modifiée par la présence de particules rapides. Dans un tokamak tel qu'ITER ces particules rapides peuvent être soit les particules alpha créées par les réactions de fusion, soit les ions et électrons accélérés par les dispositifs de chauffage additionnel et de génération de courant. Les modes appelés fishbones électroniques correspondent à la déstabilisation du mode de kink interne due à la résonance avec le lent mouvement de précession toroidale des électrons rapides. Ces modes sont fréquemment observés dans les plasmas des tokamaks actuels en présence de chauffage par onde cyclotronique électronique (ECRH) ou de génération de courant par onde hybride basse (LHCD). La stabilité de ces modes est particulièrement sensible aux détails de la fonction de distribution électronique et du facteur de sécurité, ce qui fait des fishbones électroniques un excellent candidat pour tester la théorie linéaire des instabilités liées aux particules rapides. Dans le tokamak Tore Supra, des fishbones électroniques sont couramment observés lors de décharges où l'utilisation de l'onde hybride basse crée une importante queue de particules rapides dans la fonction de distribution électronique. Bien que ces modes soit clairement liés à la présence de particules rapides, la fréquence observée de ces modes est plus basse que celle prévue par la théorie. En effet, si on estime l'énergie des électrons résonants en faisant correspondre la fréquence du mode avec la fréquence de précession toroidale des électrons faiblement piégés, on obtient une valeur comparable à celle des électrons thermiques. L'objet principal de cette thèse est l'analyse linéaire de la stabilité des fishbones électroniques. La relation de dispersion de ces modes est dérivée et la forme obtenue prend en compte, dans la condition de résonance, la contribution du mouvement parallèle des particules passantes. Cette relation de dispersion est implémentée dans le code MIKE qui est ensuite testé avec succès en utilisant des fonctions de distributions analytiques. En le couplant au code Fokker-Planck relativiste LUKE et à la plate-forme de simulation intégrée CRONOS, MIKE peut estimer la stabilité des fishbones électroniques en utilisant les données reconstruites de l'expérience. En utilisant des fonctions de distributions et des équilibres analytiques dans le code MIKE nous montrons que les électrons faiblement piégés ou faiblement passants peuvent déstabiliser le mode de kink interne en résonant avec lui. Si l'on s'éloigne de la frontière entre électrons passants et piégés, les effets résonants s'affaiblissent. Cependant les électrons passants conservent une influence déstabilisante alors que les électrons piégées tendent à stabiliser le mode. D'autres simulations avec MIKE, utilisant cette fois des distributions complètes similaires à celles obtenues en présence de chauffage de type ECRH, montrent que l'interaction avec les électrons faiblement passants peut entraîner une déstabilisation du mode à une fréquence relativement basse ce qui pourrait permettre d'expliquer les observations sur le tokamak Tore Supra.

Le contrôle des instabilités de bord connues sous le nom d' "Edge Localized Modes" (ELMs) est une question capitale pour le futur tokamak ITER. Ce travail est consacré à l'une des plus prometteuses méthodes de contrôle des ELMs, basée sur un système de bobines produisant des Perturbations Magnétiques Résonantes (PMRs), dont le fonctionnement a été démontré en premier lieu dans le tokamak DIII-D en 2003. Nos objectifs principaux sont, d'une part, d'éclaircir la compréhension physique des mécanismes en jeu, et d'autre part, de proposer un design concret de bobines de contrôle des ELMs pour ITER. Afin de calculer et d'analyser les perturbations magnétiques créées par un ensemble de bobines donné, nous avons développé le code ERGOS. Le premier calcul ERGOS a été consacré aux bobines de contrôle des ELMs de DIII-D, les I-coils. Il montre que celles-ci créent des chaines d'îlots magnétiques se recouvrant au bord du plasma, engendrant ainsi une ergodisation du champ magnétique. Nous avons par la suite utilisé ERGOS pour la modélisation des expériences de contrôle des ELMs à l'aide des bobines de correction de champ d'erreur sur JET et MAST, auxquelles nous participons depuis 2006. Dans le cas de JET, nous avons montré l'existence d'une corrélation entre la mitigation des ELMs et l'ergodisation du champ magnétique au bord, en accord avec le résultat pour DIII-D. Le design des bobines de contrôle des ELMs pour ITER s'est fait principalement dans le cadre d'un contrat EFDA (European Fusion Development Agreement)-CEA, en collaboration avec des ingénieurs et physiciens de l'EFDA et d'ITER. Nous avons utilisé ERGOS intensivement, le cas des I-coils de DIII-D nous servant de référence. Trois designs candidats sont ressortis, que nous avons présentés au cours de la revue de design d'ITER, en 2007. La direction d'ITER a décidé récemment d'attribuer un budget pour les bobines de contrôle des ELMs, dont le design reste à choisir entre deux des trois options que nous avons proposées (ou proches de celles que nous avons proposées). Enfin, dans le but de mieux comprendre les phénomènes de magnétohydrodynamique non-linéaires liés au contrôle des ELMs par PMRs, nous avons recouru à la simulation numérique, notamment avec le code JOREK pour un cas DIII-D. Les simulations révèlent l'existence de cellules de convection induites au bord du plasma par les perturbations magnétiques et le possible "écrantage" des PMRs par le plasma en présence de rotation. La modélisation adéquate de l'écrantage, qui demande la prise en compte de plusieurs phénomènes physiques supplémentaires dans JOREK, a été entamée.

This Thesis presents a series of results on the development of advanced magnetic feedback schemes for the active control of magnetohydrodynamic (MHD) instabilities and error elds obtained in two magnetically conned toroidal experiments: the RFX-mod reversed-eld pinch (RFP) in Padova, Italy, and the DIII-D tokamak at General Atomics, San Diego, CA, USA. In the last years, these two devices have explored dierent types of highperformance regimes, also thanks to their sophisticated active control systems. In RFX-mod, high-plasma current experiments, up to 2MA, were performed for the rst time in a RFP. These experiments allowed for the discovery of a new self-organized helical equilibrium with good connement properties [40]. Instead, in DIII-D, steady-state, high-performance tokamak operations are being explored. The scientic programs of these experiments, in particular on error eld and MHD mode control, can give precious contributions to the International Thermonuclear Experimental Reactor (ITER) and to magnetic fusion research in general. The RFP and the tokamak are toroidal devices for the magnetic connement of thermonuclear plasmas. An introduction to thermonuclear fusion, the main requests to exploit fusion as a future energy source, the magnetic connement of the plasma, and the MHD model which describes the plasma behavior in many cases of interest will be given in Chapter 1. The role of magnetic feedback control for the development of advanced operational regimes in RFX-mod and in DIII-D will be also discussed in this Chapter. Chapter 2 describes the two experiments above mentioned and their magnetic feedback control systems. They are in fact equipped with very exible systems devoted to the control of MHD instabilities and error elds. In particular the feedback control strategies that are crucial for the work discussed in this Thesis will be presented. The rst important result of this Thesis is reported in Chapter 3 and regards the optimization of multi-mode control of tearing instabilities in RFX-mod. Tearing modes, which sustain the reversed-eld conguration typical of RFP experiments through a dynamo mechanism, can not be completely suppressed by magnetic feedback control. Nonetheless, it is important to reduce their edge radial magnetic eld amplitude to the lowest possible value, since it produces a deformation of the last closed ux surface, enhancing the plasma-wall interaction. In this work, the control of tearing modes has been optimized by using a non-linear model of the tearing mode dynamics in presence of the multiple-shell layout of RFX-mod and of the magnetic feedback system. This model of tearing modes has been implemented in a code named RFXlocking and previously described in [84]. Given the good match between the model predictions and the experimental mode behavior, the RFXlocking code has been used as a tool to identify a new set of mode control parameters (i.e. feedback gains), which allow to reduce the radial magnetic eld of multiple tearing modes at the plasma edge, maintaing at the same time the modes into rotation and avoiding coil current saturations. The optimization approach consisted in simulating the mode dynamics varying the feedback gains and identifying the gain set, which fullls the requirements above described. Once the "model-based" gain set was identied, an extensive experimental campaign was performed on RFX-mod, obtaining satisfactory results in terms of edge radial magnetic eld reduction and also conrming the code predictions. The magnetic feedback optimization performed during this Thesis work concerned not only tearing modes, but also the main magnetic eld errors present in RFX-mod. The presence of poloidal gaps in the RFX-mod wall modies the pattern of eddy-currents induced in it by the vertical magnetic eld during the plasma current ramp-up, thus forming toroidally-localized error elds to which tearing modes are phase-locked. Two advanced feedback control strategies have been applied to correct these error elds: a multi-mode control scheme and a dynamic decoupling scheme. Regarding the rst feedback control strategy, a Simulink model of the RFXmod magnetic feedback system has been used to identify the feedback gains, which allow a signicant reduction of the error eld amplitude, avoiding coil current saturations. A dynamic decoupler has also been used to compute oine the feedback currents needed to cancel the error elds. As will be described in Chapter 4, these two techniques have been tested during a dedicated experimental campaign. The best result in terms of error eld reduction has been obtained when both multimode control and the decoupler are used. With error eld correction during the plasma current ramp-up, the phase-locking among tearing modes is no more localized near the poloidal gaps of the wall, thus reducing the plasma-wall interaction at these positions. As mentioned above, the high-current RFX-mod experiments have disclosed a promising physics regime, where the RFP spontaneously evolves towards an Ohmic helical equilibrium. This new magnetic equilibrium is characterized by a single helical magnetic axis and helical magnetic surfaces in the plasma core. This leads to a signicant decrease in the stochastic transport and to the formation of core electron temperature barriers. During the last experimental campaign, it has been demonstrated that a (1;-7) helical equilibrium can be sustained and controlled by applying helical boundary conditions at the plasma edge through magnetic feedback. In this Thesis work, Chapter 5 and Chapter 6 deal with the optimization of the helical boundary conditions used to control the helical equilibrium. The optimization procedure uses control strategies analogous to those described above and adopted to improve the control of tearing modes and error elds. The RFXlocking code has been modied by adding the possibility to apply a helical boundary conditions. In this way, the mode dynamics has been simulated with this new helical boundary, by varying the feedback gains and the amplitude and phase of the helical magnetic eld perturbations imposed at the plasma edge. A model-based optimization approach similar to the one described in Chapter 3 has been adopted here to identify the feedback gains that allow to produce the requested radial eld pattern at the edge with the lowest possible coil current. A partial gain scan has been performed in the experiment and the results conrm the model predictions. The main outcomes of the model-based optimization and an analysis of the effects on the plasma performance of the applied helical boundary conditions are described in Chapter 5. Vacuum eld analyses described in Chapter 6 reveal that, when rotating magnetic eld perturbations are applied through magnetic feedback, as in the case of the helical equilibria above described, error elds are induced by the frequency response of the wall to external magnetic elds varying in time. These error elds, that are mainly introduced by the presence of the toroidal and poloidal gaps in the wall structure, may somehow aect the good connement properties of the helical equilibrium. For this reason, a dynamic decoupler similar to the one used to correct the error elds in the current ramp-up phase of the plasma discharges has been applied. Encouraging results in terms of error eld reduction are obtained. The frequency-response of the wall to any external time-varying magnetic eld has been investigated also in the DIII-D tokamak, in the framework of a collaboration between the RFX-mod and DIII-D teams. In the DIII-D control algorithm, the magnetic feedback measurements are usually real-time compensated for spurious magnetic elds, due for instance to the feedback and axi-symmentric coils. These contributions are calculated from the zero-frequency coupling coecients between each actuator and sensor. In this way the eects of eddy-currents induced in the wall are neglected. The relevance of these frequency-dependent, or AC eects, on RWM and error eld control has been evaluated by analyzing past experiments. The analyses suggested that, if the wall frequency response is not taken into account in the feedback compensation scheme, error elds can be introduced when doing magnetic feedback. These can be important especially at high β, where uncorrected error elds can be strongly amplied by the plasma. An AC compensation algorithm has been implemented and tested in real-time in dry-shots and Ohmic plasmas. More tests of this algorithm at high β have been proposed for the next experimental campaign to assess its relevance on plasma performance in scenarios where the plasma is less resilient to error elds. The main outcomes of this Thesis work is reported in Chapter 7. Chapter 8 summarizes the main conclusions of this work and describes a series of experiments that could be made both in RFX-mod and DIII-D in the near future, to further develop the studies started with this Thesis.<br>Questa Tesi presenta una serie di risultati sullo sviluppo di avanzati schemi di feedback per il controllo di instabilità magnetoidrodinamiche (MHD) e di campi errori ottenuti in due esperimenti toroidali a connamento magnetico: il reversed-eld pinch (RFP) RFX-mod, a Padova, Italia, e il tokamak DIII-D, presso la General Atomics, San Diego, CA, USA. Negli ultimi anni, questi due esperimenti hanno esplorato differenti tipi di regimi ad alte prestazioni, anche grazie ai loro sofisticati sistemi di controllo attivo. Ad RFX-mod, esperimenti ad alta corrente di plasma, sino a 2MA, sono stati realizzati per la prima volta in un RFP. Questi esperimenti hanno permesso la scoperta di un nuovo equilibrio elicoidale, auto-organizzato e con buone proprietà di connamento [40]. Invece, a DIII-D scenari stazionari ed operazioni ad alte prestazioni vengono investigati. I programmi scientifici di questi esperimenti, in particolar modo il controllo di campi errori e di instabilità MHD, possono dare preziosi contributi all'International Thermonuclear Experimental Reactor (ITER) e, più in generale, alla ricerca nel campo della fusione. Il RFP e il tokamak sono esperimenti toroidali per il connamento magnetico di plasmi termonucleari. Un'introduzione alla fusione termonucleare, i principali requisiti per sfruttare la fusione come una sorgente di energia per il futuro, il connamento magnetico del plasma, e il modello MHD che descrive il comportamento del plasma in molti casi di interesse, verranno descritti nel Capitolo 1. Il ruolo del controllo dei campi magnetici in feedback per lo sviluppo di regimi operazionali avanzati in RFX-mod e a DIII-D verrà anche discusso in questo Capitolo. Il Capitolo 2 descrive gli esperimenti sopra citati e i relativi sistemi di controllo dei campi magnetici in feedback. Questi infatti sono muniti di sistemi molto essibili per il controllo di instabilita MHD e di campi errori. In particolar modo, verranno presentate le strategie di controllo in feedback che sono cruciali per il lavoro discusso in questa Tesi. Il primo risultato importante di questa Tesi è riportato nel Capitolo 3 e riguarda l'ottimizzazione del controllore a multi-modo delle instabilita tearing di RFX-mod. I modi tearing, che sostengono la congurazione a campo rovesciato tipica degli esperimenti RFP attraverso un meccanismo di dinamo, non possono essere completamente soppressi dal controllo dei campi magnetici in feeedback. Ciò nonostante, è importante ridurre la loro ampiezza di campo magnetico radiale al bordo del plasma al più piccolo valore possibile, dal momento che questa produce una deformazione dell'ultima superficie chiusa di flusso, aumentando l'interazione plasmaparete. In questo lavoro, il controllo dei modi tearing è stato ottimizzato utilizzando un modello non lineare che simula la dinamica dei modi tearing in presenza del layout a multipla shell di RFX-mod e del sistema per il controllo di campi magnetici in feedback. Questo modello dei modi tearing è stato sviluppato in un codice chiamato RFXlocking che è stato descritto in [84]. Dato il buon accordo tra le predizioni del modello e il comportamento dei modi nell'esperimento, il codice RFXlocking è stato usato per identicare un nuovo set di parametri di controllo (i.e. i guadagni del feedback), che permetta di ridurre l'ampiezza radiale dei modi tearing al bordo del plasma, mantenendo allo stesso tempo i modi in rotazione ed evitando saturazioni di corrente nelle bobine di controllo. L'approccio per l'ottimizzazione prevede di simulare la dinamica dei modi tearing al variare dei guadagni del feedback, e di identicare un set di guadagni che soddisfa le richieste sopra descritte. Una volta trovato il set di guadagni ispirato dal modello, una lunga campagna sperimentale è stata fatta ottenendo soddisfacenti risultati in termine di riduzione di campo magnetico radiale al bordo del plasma e confermando così le previsioni del codice. L'ottimizzazione del controllo dei campi magnetici in feedback svolta in questo lavoro di Tesi non ha solo riguardato i modi tearing ma anche i principali campi errori in RFX-mod. La presenza di tagli in direzione poloidale nella struttura conduttiva di RFX-mod modica il pattern delle correnti immagine indotte dal campo magnetico verticale durante la fase di salita di corrente di plasma, inducendo campi errori localizzati dove i modi tearing hanno un'inteferenza costruttiva. Due tecniche di controllo in feedback sono state utilizzate per sopprimere questi campi errori: uno schema di controllo a multi modo e il disaccoppiatore dinamico. Per quanto riguarda la prima strategia di controllo, un modello di Simulink del sistema magnetico di feedback di RFX-mod è stato usato per identicare i guadagni del feedback, che permettono di ridurre signicativamente l'ampiezza del campo errore, evitando saturazioni di corrente nelle bobine di controllo. Un disaccopiatore dinamico è stato usato per calcolare le correnti nelle bobine di controllo necessarie a cancellare i campi errore. Come verrà descritto nel Capitolo 4, durante una campagna sperimentale dedicata, queste due tecniche sono state testate. Il miglior risultato in termini di riduzione dei campi errore è stato ottenuto quando il controllore a multi-modo e il disaccopiatore sono stati usati contemporaneamente. Quando la correzione del campi errori è applicata durante la fase di salita di corrente di plasma, l'interferenza costruttiva tra i modi tearing non è piu localizzata vicino ai tagli in direzione poloidale della struttura conduttrice, in questo modo viene ridotta l'interazione plasma-parete in queste zone. Come accennato precedentemente, gli esperimenti ad alta corrente in RFX-mod hanno rivelato un nuovo regime promettente, in cui l'RFP evolve spontaneamente in uno stato elicoidale Ohmico. Questo nuovo equilibrio magnetico è caratterizzato da un singolo asse magnetico elicoidale e da superci magnetiche elicoidali all'interno del plasma. Questo produce una diminuzione del trasporto stocastico e la formazione di proli di temperatura elettronica molto ripidi. Nell'ultima campagnia sperimentale è stato dimostrato che un equilibrio elicoidale con elicità (1,-7) può essere indotto e controllato applicando condizioni elicoidali al bordo del plasma per mezzo del sistema magnetico di feedback. In questo lavoro di Tesi, il Capitolo 5 e il Capitolo 6 descrivono l'ottimizzazione delle perturbazioni magnetiche elicoidali usate per controllare l'equilibrio elicoidale. La procedura di ottimizzazione usa le stesse strategie di controllo che sono state adottate per migliorare il controllo dei modi tearing e dei campi errori. Il codice RFXlocking è stato modificato permettendo di applicare condizioni elicoidali al bordo del plasma. In questo modo, la dinamica dei modi può essere simulata con questo nuovo boundary elicoidale, al variare dei guadagni di feedback, dell'ampiezza e della fase delle perturbazioni elicoidali imposte al bordo del plasma. Un approccio di ottimizzazione ispirato dal modello, simile a quello descritto nel Capitolo 3, è stato adottato in questo caso per identicare i guadagni di feedback che permettono di produrre il richiesto pattern di campo radiale al bordo del plasma con la minor richiesta di corrente nelle bobine di controllo. Uno scan parziale dei guadagni è stato svolto nell'esperimento e i risultati confermano le predizioni del modello. I risultati salienti dell'ottimizzazione ispirata dal modello e le prestazioni del plasma negli stati elicoidali sostenuti imponendo condizioni elicoidali al bordo plasma sono descritti nel Capitolo 5. Analisi di esperimenti a vuoto, descritte nel Capitolo 6, rivelano che, quando una perturbazione rotante di campo magnetico viene applicata dal sistema di feedback, come nel caso degli stati elicoidali descritti sopra, campi errori vengono indotti dalla risposta in frequenza della struttura conduttrice ai campi magnetici esterni che variano nel tempo. Questi campi errori, che sono indotti principalmente dalla presenza di tagli in direzione toroidale e poloidale nella struttura conduttrice, possono in qualche modo influenzare le proprietà di buon connamento degli stati elicoidali. Per questo motivo un disaccoppiatore dinamico, simile a quello usato per correggere i campi errori durante la fase di salita delle corrente, è stato utilizzato. Esperimenti a vuoto mostrano risultati incoraggianti in termini di riduzione dell'ampiezza del campo errore. La risposta in frequenza della struttura conduttiva ad un campo magnetico variabile nel tempo è stata esaminata anche nell'esperimento DIII-D, durante una collaborazione tra i gruppi di ricerca di RFX-mod e di DIII-D. Nell'algoritmo di controllo di DIII-D, le misure di campo magnetico sono compensate in tempo reale dai campi magnetici spuri, che possono essere indotti dalle bobine di controllo o dalle bobine assialsimmetriche. Questi contributi esterni sono calcolati dai coefficienti di accoppiamento tra ciascun attuatore e sensore, a frequenza nulla. In questo approccio, gli effetti delle correnti immagine indotte nella struttura conduttiva vengono trascurati. L'importanza di questi effetti che dipendono dalla frequenza, o effetti AC, per il controllo di RWM e di campi errori è stata valutata analizzando esperimenti precedenti. Le analisi suggeriscono che campi errori possono essere indotti quando viene applicato il controllo in feedback se la risposta in frequenza delle strutture conduttive non è inclusa nell'algoritmo di feedback di compensazione. Questi possono risultare importanti specialmente ad alto β regime in cui i campi errori residui possono essere amplicati dal plasma. Un algoritmo di compensazione AC e stato implementato e testato in tempo reale in spari a vuoto e in spari Ohmici. Un maggior numero di test di questo algoritmo ad alto β è stato proposto per la prossima campagna sperimentale per testare la sua rilevanza nella performance del plasma quando questo è più soggetto ai campi errori. I risultati più salienti di questo lavoro di Tesi sono discussi nel Capitolo 7. Il Capitolo 8 riassume le conclusioni principali di questo lavoro e presenta degli esperimenti che posso essere eseguiti ad RFX-mod e a DIII-D nel futuro prossimo che possono indagare ulteriormente gli studi iniziati in questo lavoro di Tesi.

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<br>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

Les disruptions sont des pertes violentes et très rapides (environ 20 ms) du confinement des plasmas de tokamak qui peuvent conduire à des endommagements de la structure du tokamak. Elles génèrent des charges thermiques sur les composants face au plasma, des forces électromagnétiques dans les structures de la machine et produisent des électrons découplés relativistes pouvant perforer l'enceinte à vide. Pour des futurs réacteurs, il sera indispensable d'amortir ces effets. L'injection massive de gaz est une des méthodes proposées dans ce but. Son étude expérimentale et numérique est l'objet de la thèse. Des expériences menées sur les tokamaks Tore Supra et JET ont montré que l'injection de gaz légers comme l'hélium empêchaient la production d'électrons découplés, au contraire des gaz plus lourds. Les gaz légers sont en effet capables d'accroître suffisamment la densité du plasma pour empêcher la création de ces électrons. En revanche, les gaz lourds permettent de dissiper par rayonnement et de façon plus bénigne une partie de l'énergie thermique du plasma. Tous les gaz diminuent les forces électromagnétiques. Des mélanges de gaz ont également été testés avec succès pour profiter des avantages des deux types de gaz. La pénétration du gaz dans le plasma semble liée à des instabilités MHD augmentant le transport radial du gaz ionisé vers le centre, mais empêchant la propagation des neutres au-delà d'une surface critique. Des simulations d'injections massives ont été réalisées avec le code 3D MHD Jorek, en y ajoutant un modèle de fluide neutre. Les résultats montrent que la croissance des instabilités MHD est plus rapide lorsque de grandes quantités de gaz sont injectées et que les surfaces rationnelles sont successivement ergodisées lors de la pénétration du front de densité dans le plasma, conformément aux observations expérimentales.

Neste trabalho apresentamos o estudo da possivilidade de melhores regimes para o uso dos experimentos de aquecimento e geracao de corrente e fluxo de plasma no tokamak TCABR. Apresentamos um estudo dos efeitos de rotacao de plasma em baixa frequencia (low-frequency (LF)), penetração de campo eletromagnético, absorção e forças ponderomotoras no “Tokamak Chauffage Alfvén Brésilien” (TCABR) com ênfase na faixa de frequências de 0, 5–10, 0kHz. Os campos de LF são dirigidos pelo limitador magnético ergódico (ergodic magnetic limiter (EML)) no TCABR. Foi feito um estudo analítico das ondas de Alfvén e ressonância usando modelos simples. Um estudo num´erico tembém foi realizado utilizando três códigos, quais sejam, o código cinético toroidal, o código cilíndrico e o código ALTOK.<br>In this work we present the study of the determination the best regimes and parameters¶for the heating experiments and current generation and plasma flow in the tokamak TCABR. Study of effects of plasma rotation in low frequency (LF), field penetration, absorption and ponderomotive forces in “Tokamak Chauffage Alfvén Brésilien” (TCABR)is investigated with emphasis in the frequency range of 0, 5–10, 0kHz. The fields of LF are driven by the ergodic magnetic limiter (EML) in TCABR. A qualitative analytical study of the Alfvén waves and their resonances is performed using simple models. A numeric study was carried out using through three codes, called the kinetic totoidal code, the cylindrical code and the ALTOK code.

Sistemas de confinamentos magnéticos de plasmas quentes, têm há muito despontado como uma das melhores alternativas para estudar plasmas de fusão. Dentre estes sistemas os tokamaks apresentam-se como os mais viáveis. Entretanto, a compreensão dos mecanismos físicos que regem a dinâmica e o equilibro da coluna de plasma no interior destas máquinas ainda tem diversos tópicos em aberto. A equação básica que descreve o equilíbrio Magneto Hidrodinâmico (MHD) neste tipo de sistema é a equação de Grad-Shafranov, uma equação auto consistente que depende do perfil de densidade de corrente toroidal da coluna de plasma. Condições de equilíbrio MHD quando um perfil de densidade de corrente toroidal com inversão é aplicado à equação de Grad-Shafranov têm sido foco de estudos recentes. Esse tipo de perfil de densidade de corrente está relacionado ao modo alternado de operação dos tokamaks. Este modo de operação por sua vez está relacionado ao aparecimento de barreiras de transporte e de correntes de retroalimentação do plasma, chamadas correntes "Bootstrap". Mesmo sob condições de equilíbrio, esse tipo de configuração de densidade de corrente toroidal tem apresentado a formação de ilhas magnéticas. A análise desse tipo de equilíbrio tem sido feita na literatura usando métodos numéricos, dada a complexidade e não linearidade da equação envolvida. Há alguns modelos analíticos que abordam perfis de corrente toroidal simplificados. Neste trabalho desenvolvemos um tratamento analítico para tratar o equilíbrio MHD com perfil de corrente invertida, através do método das aproximações sucessivas, determinando o fluxo poloidal magnético para esse equilíbrio aplicado às configurações do tokamak TCABR do Instituto de Física da Universidade de São Paulo. Foi possível caracterizar a formação de ilhas magnéticas através da determinação do fator de segurança desse novo equilíbrio além do cálculo do número e da largura das ilhas encontradas.

Il est essentiel pour rendre performants les futurs réacteurs à fusion par confinement magnétique de maximiser le confinement du plasma. Jouer sur la vitesse du plasma peut être un moyen de stabiliser d’éventuelles instabilités et de contrôler la turbulence avec des effets très bénéfiques sur les performances fusion. Il est donc crucial de comprendre comment on peut mettre en rotation un plasma de tokamak.Idéalement on souhaite que le tokamak, en tant que réacteur à fusion, travaille en régime permanent. Il est donc raisonnable de déterminer les états stationnaires d’un plasma de tokamak en toute généralité, sans imposer la nullité du champ de vitesse du plasma. Dans le cadre de la magnétohydrodynamique (MHD) visco-résistive, cela revient à conserver notamment le terme non-linéaire (v.grad)v dans l’équation stationnaire de Navier-Stokes.En utilisant le logiciel open-source FreeFem++ de résolution des équations aux dérivées partielles par la méthode des éléments finis, nous avons pu déterminer numériquement les états stationnaires axisymmétriques d’un plasma de tokamak dans des géométries réalistes de type JET.Cette thèse étudie le comportement du plasma incompressible d'un tokamak en régime permanent en utilisant un modèle magnétohydrodynamique (MHD) visco-résistif, avec une résistivité eta et une viscosité u constantes. On montre que la vitesse moyenne quadratique du plasma se comporte comme eta f(H) tant que le terme inertiel reste négligeable, où H représente le nombre de Hartmann Hequiv (etau)^{-1/2}, et que f(H) présente des comportements de loi de puissance dans les limites H ll 1 et H gg 1. Dans cette dernière limite, nous établissons que f(H) s'échelonne comme H^{1/4}, ce qui est cohérent avec les résultats numériques.De plus, ce travail établit l'équation de Poisson régissant le profil de pression. Il est démontré que l'hypothèse simplificatrice d'une composante de densité de courant toroïdale découlant uniquement de la loi d'Ohm en réponse à un champ électrique toroïdal sans courbure et indépendant du temps ne permet pas de produire des niveaux de pression réalistes. Pour y remédier, nous introduisons des entraînements de courant non inductifs supplémentaires, comparables à ceux de l'injection d'un faisceau neutre, modélisés comme des modifications du courant toroïdal. Le nouveau modèle est validé par des simulations numériques, qui montrent des améliorations significatives du profil de pression. Pour les exemples considérés, l'effet de ces entraînements de courant sur les profils de vitesse est modéré, sauf dans le cas où les entraînements induisent des inversions dans la densité totale du courant toroïdal, produisant des surfaces de flux non imbriquées avec des séparatrices internes.Enfin, l'effet de profils de densité de courant fixes est examiné, révélant un nouveau second régime, où les vitesses toroïdales et poloïdales s'échelonnent avec le nombre de Hartmann comme H^2<br>Maximizing plasma confinement is essential to the performance of future magnetic fusion reactors. Playing with plasma speed can be a way to stabilize possible instabilities and control turbulence with a very beneficial impact on fusion yield. It is, therefore, essential to understand how a tokamak plasma can be rotated.Ideally, the tokamak should work in a stationary state as a fusion reactor. It is, therefore, reasonable to determine the steady states of a tokamak plasma in full generality without imposing the nullity of the plasma velocity field. In the visco-resistive magnetohydrodynamics (MHD) framework, this amounts in particular to retaining the non-linear term (v.grad)v in the stationary Navier-Stokes equation.Using the FreeFem++ open-source software for solving partial differential equations using the finite element method, we numerically determined the axisymmetric stationary states of a tokamak plasma in realistic JET.This thesis shows that the plasma velocity root-mean-square behaves as eta f(H) as long as the inertial term remains negligible, where H stands for the Hartmann number Hequiv (etau)^{-1/2}, and that f(H) exhibits power-law behaviours in the limits H ll 1 and H gg 1. In the latter limit, we establish that f(H) scales as H^{1/4}, which is consistent with numerical results.Additionally, this work establishes Poisson's equation governing the pressure profile. It is shown that the simplifying assumption of a toroidal current density component arising solely from Ohm's law in response to a time-independent, curl-free toroidal electric field fails to produce realistic pressure levels. To overcome this, we introduce additional non-inductive current drives, comparable to those from neutral beam injection, modeled as modifications to the toroidal current. The new model is validated using numerical simulations, showing significant pressure profile improvements. For the examples considered, the effect of these current drives on the velocity profiles is moderate except in the case where the drives induce some reversals in the total toroidal current density, producing non-nested flux surfaces with internal separatrices.Finally, the effect of fixed current density profiles is examined, revealing a new second regime, where toroidal and poloidal velocities scale with Hartmann number as H^2

An almost universal instability in high pressure plasmas is the Neoclassical Tearing Mode (NTM). NTMs are driven by local perturbations in the current density and result in magnetic island like deformations of the magnetic topology. They can be stabilized by compensating the current perturbations with local electron cyclotron resonance heating (ECRH) or with non-inductive current drive (ECCD). The modified Rutherford equation describes the nonlinear evolution of tearing modes as determined by various contributions to the local current density pertubation. An extensive investigation of the two terms representing the stabilizing effects from ECRH and ECCD have been made resulting in accurate description of both terms. The results of this model can now be compared to the experimental observations. For this purpose, an extensive data set exists from the past experiments on tearing mode stabilization by ECRH and ECCD on TEXTOR. The properly benchmarked model can then be used to predict the effectiveness of ECRH and ECCD for NTM stabilization on International Thermonuclear Experimental Reactor (ITER). In addition, a number of predictions on the effects of ECRH and ECCD on the growth of the NTM have been made on the basis of crude approximations to the ECRH and ECCD tems in the modified Rutherford equation. These predictions can now be checked against the more accurate expressions obtained.

03etude de la stabilite de l'etat d'equilibre d'un plasma confine par des champs magnetiques a l'interieur d'un tokamak et represente par les equations de la mhd. Pour deux des principaux types d'instabilite, la convection et l'instabilite de dechirement des surfaces magnetiques, on fait une etude non lineaire des solutions, en considerant le probleme mathematique comme un probleme de bifurcation

Nous présentons une étude numérique des dents de scie dans un plasma de tokamak ohmique avec le code XTOR-2F. Cette étude est à notre connaissance la première à explorer la dynamique au long terme du kink interne. La MHD résistive prévoit deux régimes distincts : oscillations stables ou régime saturé hélicoïdal. Les dérives diamagnétiques stabilisantes permettent de retrouver des dents de scie pour des paramètres expérimentaux pertinents. On détaille aussi les contributions faites à la transition du code vers le code hybride MHD-cinétique XTOR-K, pour coupler effets cinétiques et fluides. On a choisi un modèle cinétique full-f, full-orbit couplé à la partie fluide par un algorithme Newton-Krylov/Picard stable vis-à-vis des modes MHD fondamentaux. L'avancée des particules est faite par l'algorithme de Boris, adapté en géométrie torique. Les invariants du mouvement ne dérivent pas numériquement. Différentes méthodes, entre autres un filtrage temporel numérique, sont envisagées pour réduire le bruit sur le tenseur de pression particulaire.

The tokamak is so far the most promising magnetic configuration for achieving a net production of fusion energy. The D-T fusion reactions result in 3.5 MeV alpha-particles, which may destabilize Alfvén eigenmodes through wave-particle interaction. These instabilities redistribute the alpha-particles from the central region of the plasma towards the edge, where they are thermalized, and hence result in a reduced heating efficiency. The high-energy alpha-particles may even be thrown out of the plasma and may damage the wall. To investigate the destabilization of Alfvén eigenmodes by high-energy ions, ion cyclotron resonance heating (ICRH) and neutral beam injection (NBI) are often used to create a high-energy tail on the distribution function. The ICRH does not only produce high-energy anisotropic tails, it also decorrelates the wave-particle interaction with the Alfvén eigenmodes. Without decorrelation of the wave-particle interaction an ion will undergo a superadiabatic oscillation in phase space and there will be no net transfer of energy to the mode. For the thermal ions the decorrelation from collisions dominates while for the high-energy ions the decorrelation from ICRH dominates. As the unstable modes grow up, the gradients in phase space, which drive the mode, are reduced, resulting in a weaker drive. The dynamics of the system becomes non-linear due to a continuous restoration of the gradients by D-T reactions and ICRH. In this thesis the non-linear dynamics of toroidal Alfvén eigenmodes (TAEs) during ICRH has been investigated using the SELFO code. The SELFO code, which calculates the distribution function during ICRH self-consistently using a Monte-Carlo metod, has been upgraded to include interactions with TAEs. The fast decay of the mode amplitude as the ICRH is switched off, which is seen in experiments, as well as the oscillation of the mode amplitude as the distribution function is repetetively built up by the ICRH and flattened by the TAE has been reproduced using numerical simulations. In the presence of several unstable modes the dynamics become more complicated. The redistribution of an alpha-particle slowing down distribution function as well as the reduced heating efficiency in the presence of several modes has also been investigated.<br>QC 20100628

Dans les plasmas de tokamak peuvent se développer des instabilités MHD (Magneto-Hydro-Dynamiques) se manifestant sous la forme d’îlots magnétiques qui réduisent le confinement. Ces îlots peuvent être contrôlés par la génération localisée de courant dans le plasma. Dans cette thèse, nous nous intéressons à la modélisation des îlots magnétiques et de leur contrôle en utilisant une description fluide (MHD) du plasma, à l’aide du code XTOR. Nous détaillons l'inclusion d'une source de courant au sein du modèle MHD, ce qui nécessite l'ajout d'une équation supplémentaire pour modéliser la propagation de la densité de courant le long des lignes de champ magnétique. Cette implémentation est ensuite vérifiée sur la base de modèles analytiques, nous permettant de retrouver l'influence de paramètres tels que la largeur du dépôt ou son désalignement. Nous avons mis en évidence des effets non-décrits par les modèles asymptotiques, liés à la nature de la localisation spatiale de la source de courant. Nous nous sommes ensuite intéressés aux stratégies de contrôle envisageable pour la suppression des îlots. Nous avons ajouté au sein du code XTOR un système de contrôle qui ajuste le dépôt de courant selon les stratégies choisies. Des simulations MHD non-linéaires des différents schémas de contrôle ont été effectuées, et les différentes stratégies comparées, permettant de préciser pour chacune une gamme d’intérêt<br>Magneto-Hydro-Dynamic (MHD) instabilities are susceptible to develop within a tokamak plasma. These instabilities manifest themselves as magnetic islands which reduce the plasma confinement. The islands can however be controlled by driving current inside them. In this thesis, we consider the modeling of the magnetic islands and their control using first principle approaches, which rely on a global MHD description of the plasma. We have detailed the inclusion a RF-driven current like source term in an MHD code, which requires special care to be given to the modeling of the current density evolution. The implementation has been benchmarked against the asymptotic models, allowing us to retrieve the influence of parameters such as deposition width or misalignment with respect to the island width and position. Beyond these aspects, we have evidenced new effects, linked to the 3D nature of the current deposition. We have observed a flip instability in which an island, reduced by the ECCD, brutally inverse its phase so that its X-Point faces the current deposition, allowing the mode the grow further. We then moved on to the topic of the best suitable control strategies for the control of the island. We have implemented in XTOR a control system that mimics the experimental ones and adapt the current deposition in function of a preset strategy. Nonlinear MHD simulations have been carried out using different control schemes, allowing us to quantify the gain to expect from each of these methods depending on the characteristics of the current deposition

This thesis represents the summary of the research activities carried out during a three-years Ph.D. project. The work is divided into two parts, with the common feature of investigating the physical properties related to stability and control of Magneto-Hydro-Dynamic modes in fusion relevant plasmas. One of the aims of the work is to better understand the interaction between such plasmas and a wide range of 3-dimensional electro-magnetic boundary conditions. This part of the research has been carried out on the RFX-mod device, where advanced control strategies have been developed thanks to its state-of-the-art magnetic feedback system. A variety of interlaced problems have been addressed, starting with the improvement of the vacuum magnetic field spectrum through actuator-sensor decoupling, compensation of broken or deactivated coils with simple and real-time applicable strategies and multi-modal Resistive Wall Mode control with varying coil number and geometry. This has allowed to develop relevant control optimization techniques and knowledge for both the Reversed Field Pinch and Tokamak configurations. The former is an excellent playground for RWM studies, given the instability spectrum that is naturally developing. For the latter configuration instead, RWM stability is considered to be one major milestone to be achieved along the road to a commercial fusion reactor. The second part of the work is dedicated to this issue, and deals with the stability properties of Advanced Tokamak scenarios, with reference to the JT-60SA experiment in particular. Studies to understand RWM physics in high beta plasmas, where fluid rotation profiles and hot ions populations from Neutral Beams can play an important role, have been carried out with the MARS-F/K linear MHD codes. If detailed physics such as kinetic effects is coupled to a simplified description of the passive/active structures on one side, on the other hand a simplified plasma can be coupled to a complex 3-D model of the structures to assess realistic active control capabilities of a given system. Different tools are used and described for studying RWM damping physics, and to five a proof-of-principle for feedback control of such instabilities in Advanced Tokamak plasmas operating beyond the no-wall pressure limit.<br>Questa tesi rappresenta la raccolta delle attività svolte durante i tre anni di un progetto di Dottorato di Ricerca. Il lavoro è stato diviso principalmente in due parti, con il comune denominatore di investigare le problematiche relative alla stabilità e al controllo di instabilità Magneto-Idro-Dinamiche in plasmi di interesse fusionistico. Uno dei principali obiettivi di questo lavoro è lo studio di come questi plasmi interagiscano con diverse condizioni al contorno, strutturali ed elettro-magnetiche, con caratteristiche tridimensionali. Questa parte della ricerca è stata svolta sull'esperimento RFX-mod, dove è stato possibile sviluppare peculiari strategie di controllo grazie all'avanzato sistema di controllo attivo. Sono state affrontate varie problematiche tra loro interconnesse, a partire dallo sviluppo di tecniche per il miglioramento del contenuto armonico dei campi magnetici di vuoto tramite disaccoppiamento attuatori-sensori. Da ciò è stato sviluppato un metodo semplificato e applicabile in tempo reale per la compensazione di attuatori rotti o disattivati, con il medesimo obiettivo di migliorare il contenuto armonico dei campi magnetici prodotti dal sistema di controllo reale. A conclusione di questa parte il controllo multi-modale di modi di parete resistiva (RWM) è stato affrontato, dal punto di vista modellistico e sperimentale. Le strategie sviluppate e gli studi effettuati sono rilevanti sia per la configurazione Reversed Field Pinch sia per il Tokamak. Il primo è un ottimo terreno di prova per studiare i modi RWM, per via dello spettro di instabilità che naturalmente sviluppa. Per la seconda configurazione invece, la stabilizzazione dei modi RWM è considerato uno dei principali obiettivi da raggiungere sulla strada verso un reattore a fusione commerciale. La seconda parte del lavoro è relativa proprio alla problematica della stabilità RWM nella configurazione Tokamak, in particolar modo negli scenari avanzati in fase di sviluppo per l'esperimento JT-60SA. Una serie di studi è stata portata avanti con i codici MARS-F/K per determinare le proprietà dei modi RWM in plasmi ad alto beta, nei quali i profili di rotazione e le popolazioni di ioni sovra termici provenienti dagli iniettori di neutri possono giocare un ruolo importante. Da un lato una descrizione dettagliata del plasma, includendo gli effetti cinetici, è stata accoppiata a un modello semplificato e bidimensionale delle strutture passive. D'altra parte una più semplice descrizione del plasma è stata considerata per l'accoppiamento con un modello dettagliato e tridimensionale delle strutture attive e passive, in quest'ultimo caso è stato possibile sviluppare un modello di controllo attivo in catena chiusa dei modi RWM.

Thèse no 882 sciences EPF Lausanne.<br>siehe auch: Stabilité MHD d'un tokamak quasi circulaire. Optimisation des profils de courant et de pression et influence d'un point de rebroussement à la surface du plasma. Bibliogr.

Les resultats experimentaux obtenus sur le tokamak petula-b constituent une phenomenologie originale des instabilites mhd en regime non inductif. Ils mettent en evidence les differences qui existent entre les profils de densite de courant dans les deux regimes de fonctionnement. La generation de courant par l'onde hybride peut permettre de s'affranchir des instabilites en dents de scie, qui actuellement sur les machines de grandes dimensions, sont impliquees dans le processus de degradation du temps de confinement de l'energie en presence de chauffages additionnels. Le controle du profil de densite de courant par l'onde hybride peut donc avoir un role capital a jouer dans l'amelioration des performances des machines concues pour atteindre l'ignition

Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(エネルギー科学)<br>甲第10333号<br>エネ博第69号<br>新制||エネ||20(附属図書館)<br>UT51-2003-H754<br>京都大学大学院エネルギー科学研究科エネルギー基礎科学専攻<br>(主査)教授 前川 孝, 教授 近藤 克己, 助教授 浜口 智志<br>学位規則第4条第1項該当

In the present work, Current Reversal Equilibrium Configurations (CRECs) in the context of Magnetohydrodinamic (MHD) equilibrium are considered. The hamiltonian nature of the magnetic field lines is used to introduce the concept of magnetic surfaces and their relation to the Grad-Shafranov (G-S) equation. From a geometrical perspective and the Maxwell equations, it is shown that current reversal configurations in two-dimensional equilibrium do not generate the usual nested topology of the equilibrium magnetic surfaces. The concept of intersecting critical curves is introduced to describe the CRECs and recently published equilibria are shown to be compatible with such description. The equilibrium with a single magnetic island is constructed analytically, through a local successive approximations method, valid for any choice of the source functions of the G-S equation. From the local solution, an estimate of the island width in terms of simple quantities is deduced and verified to a good accuracy with recently published CRECs; the accuracy of this simple model suggests the existence of strong topological constraints in the formation of the equilibria. Lastly, an instability mechanism is conjectured to explain the lack of conclusive experimental evidence of reversed currents, in favor of the current clamp hypothesis.<br>No presente trabalho, as configurações de equilíbrio com corrente reversa (CRECs), são consideradas no contexto de Equilíbrio Magnetoidrodinâmico. A natureza hamiltoniana das linhas de campo magnético é usada para introduzir o conceito de superfícies magnéticas, e sua relação com a equação de Grad-Shafranov (G-S). Desde uma perspectiva geométrica e usando as equações de Maxwell, é demonstrado que as configurações de corrente reversa em equilíbrios bidimensionais não é compativel com as topologias aninhadas usuais para as superfícies magnéticas de equilíbrio. O conceito de curvas críticas é introduzido para descrever as CRECs e é observado que os equilíbrios recentemente publicados satisfazem esta descrição. O equilíbrio com uma única ilha magnética é construído analiticamente, por meio de aproximações sucessivas locais, este é válido para qualquer escolha das funções arbitrárias da equação G-S. A partir da solução local, se desenvolve uma estimativa do tamanho da ilha magnética em termos de quantidades simples. Esta estimativa concorda bem com as CRECs da literatura recente, sugerindo pela simplicidade do modelo, que existem fortes restrições topológicas no estabelecimento do equilíbrio. Finalmente, na forma de conjectura, introduzimos um mecanismo para instabilidades que tenta dar conta da falta de evidência experimental conclusiva em relação às CRECs em favor da hipótese de corrente unidirecional (current clamp).

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Physics, 1999.<br>Includes bibliographical references.<br>A visible continuum array diagnostic has been constructed to perform experiments on the Alcator C-Mod tokamak. It views plasma Bremsstrahlung in a narrow spectral region free from atomic lines. Signals from thirty chordal views on the midplane are digitized and then Abel inverted to obtain emissivity as a function of minor radius. A procedure based on Green's functions was developed to deal with the problem of noise inherent to Abel inversion. It has a demonstrated ability to pick out the original signal from among noise of equal magnitude. Bremsstrahlung intensity is proportional to the square of electron density times "Z effective", which is a measure of impurities. In conjunction with an independent density diagnostic, the continuum array gives time-resolved impurity density profiles. Alternatively, when it is known that Z~1, the array gives electron density profiles with excellent time and space resolution and coverage of the plasma. An eigenfunction expansion method was used to obtain highly accurate solutions to the transport equation, using posited values of diffusion and convection coefficients and matching the data at the initial time and at the edge of the analysis region. The method assumes the simplest model of constant diffusion and convection linear in r, both constant in time. Possible values of coefficients are systematically scanned to find the best fit to the data. The fits are excellent, which justifies the model. A formal error analysis is done. Impurity injections are analyzed. It is shown that the transport of light elements can be analyzed in the core without the need for diagnostic beams. The elemental composition need not be known. A new electron transport regime was investigated. It is sometimes entered into at the ends of shots when the current is being ramped down. It features a small core plasma and greatly enhanced inward transport, producing very high density. Its potential as a tokamak operational scenario is unclear.<br>by Cindy R. Christensen.<br>Ph.D.

The subject that concerns this thesis is the modelling and control of plasma equilibria in the RFX-mod device operating as shaped tokamak. The aim was to develop an overall model of the plasma-conductors-controller system of RFX-mod shaped tokamak configuration for electromagnetic control purposes, with particular focus on vertical stability. Thus, the RFX-mod device is described by models of increasing complexity and involving both theoretical and experimental data. The CREATE-L code is used to develop 2D linearized plasma response models, with simplifying assumptions on the conducting structures (axisymmetric approximations). Such models, thanks to their simplicity, have been used for feedback controller design. The CarMa0 code is used to develop linearized plasma response models, but considering a detailed 3D description of the conducting structures. These models provide useful hints on the accuracy of the simplified models and on the importance of 3D structures in the plasma dynamics. The CarMa0NL code is used to model the time evolution of plasma equilibria, by taking into account also nonlinear effects which can come into play during specific phases (e.g. disruptions, limiter-to-divertor transitions, L-H transition etc.). The activity can be divided into two main parts: the first one involves the modelling of numerically generated low-β plasmas, which are used as a reference for the design and implementation of the plasma shape and position control system; the second part is related to the results of the experimental campaigns on shaped plasmas from low-β to H-mode regime, with particular efforts on the development of a novel plasma response model for the new equilibrium regimes achieved. Several challenges and peculiarities characterize the project in both the modelling and control frameworks. Strong plasma shape and different plasma regimes (i.e. low-β to H-mode plasmas), deeply affect the modelling activity and require the development of several numerical tools and methods of analysis. From the control system point of view, non-totally observable dynamic and model order reduction requirements allowed a full application of the model based approach in order to successfully design the plasma shape and vertical stability control system. The first part is based on theoretical data generated by the MAXFEA equilibrium code and used to derive the linearized model through the CREATE-L code. Two reference models have been produced for the magnetic configurations interested in shaped operations: the lower single null (LSN) and the upper single null (USN). The CREATE-L models are the most simple in terms of modelling complexity, because the conducting structures are described within the axisymmetric approximation. On the other hand, the simple but reliable properties of the CREATE-L model led to the successful design of the RFX-mod plasma shape and control system, which has been successfully tested and used to increase plasma performances involved in the second part of the thesis. Then, an investigation on the possible 3D effects of the conducting structures on these numerically generated plasma configurations has been carried out by producing plasma linearized models with an increased level of complexity. A detailed 3D volumetric description of the conducting structures of RFX-mod has been carried out and included in the plasma linearized models through the CarMa0 code. A comparison between the accuracy of this model and the previous 2D one has been performed. The different assumptions and approximations of the various models allow a clear identification of the key phenomena ruling the evolution of the n=0 vertical instability in RFX-mod tokamak discharges, and hence, provide fundamental information in the planning and the execution of related experiments and in refining the control system design. Finally, the nonlinear evolutionary equilibrium model including 3D volumetric structures CarMa0NL has been used to model nonlinear effects by simulating a "fictitious" linear current quench. The second part involves a modelling activity strictly related to the results of the experimental campaigns. In particular, new linearized models for the experimental plasmas in USN configuration have been carried out for all the plasma regimes involved in the experimental campaign, i.e. from low-β to H-mode. An iterative procedure for the production of accurate linearized plasma response models has been realized in order to handle the experimental data. The new plasma linearized models allowed further investigations on vertical stability, including 3D wall effects, in the three different plasma regimes (i.e. low-β, intermediate-β, H-mode). Furthermore, the axisymmetric plasma linearized models (CREATE-L) have been analyzed in the framework of the control theory revealing peculiar features in terms of associated SISO transfer function for vertical stability control and in terms of full MIMO model for shaping control. The MIMO model has been used to investigate the plasma wall-gaps oscillations experimentally observed in some intermediate-β plasma shots. A non-linear time evolution of the plasma discharge for a low-β plasma has been carried out by using the evolutionary equilibrium code CarMa0NL. Finally, it was investigated the vertical instability for the experimental plasmas in terms of a possible relation between plasma parameters and the occurrence of it; for these purposes, the solution of the inverse plasma equilibrium problem for the production of numerically generated plasma equilibria with variations on the plasma parameters observed experimentally was performed. This involves a wide class of numerical methods that will be described in details. Then, statistical hypothesis test has been adopted to compare the mean values of the parameters of both experimental and numerically generated plasmas showing different behaviours in terms of vertical stability.<br>La presente tesi tratta la modellazione e il controllo di plasmi in equilibrio, a sezione non circolare e relativi all’esperimento RFX-mod operante come tokamak. L’obiettivo è di sviluppare un modello complessivo di RFX-mod (includendo plasmaconduttori- controllore) con finalità di controllo elettromagnetico del plasma. L’esperimento RFX-mod è stato descritto con modelli caratterizzati da un crescente livello di complessità, coinvolgendo sia dati teorici che sperimentali. Il codice CREATE-L è stato usato per lo sviluppo di modelli linearizzati di risposta di plasma, con ipotesi semplificative sulla rappresentazione delle strutture conduttrici (approssimazione assialsimmetrica). Questi modelli, grazie alla loro semplicità, sono stati utilizzati per la progettazione del sistema di controllo. Il codice CarMa0 è stato usato per sviluppare modelli analoghi ma con una rappresentazione tridimensionale delle strutture conduttrici; questi permettono di verificare l’accuratezza dei modelli semplificati e indagare l’importanza delle strutture tridimensionali sulla dinamica del sistema. Il codice CarMa0NL ha permesso la trattazione di fenomeni evolutivi nel tempo e nonlineari (e.g. disruzioni, transizioni limiter-divertor, transizioni L-H etc.). L’attività può essere suddivisa in due parti: la prima riguarda la modellizzazione di plasmi a basso β teorici, non ottenuti sperimentalmente, usati come riferimento per la progettazione e l’implementazione del sistema di controllo della forma e della posizione verticale del plasma; la seconda parte, è legata ai risultati delle campagne sperimentali sui plasmi a sezione non circolari in diversi regimi, dal basso β al modo H, con particolare attenzione allo sviluppo di un nuovo modello linearizzato di risposta di plasma per i nuovi regimi di equilibrio raggiunti. L’attività di ricerca è caratterizzata da molteplici problematiche e peculiarità sia in termini di modellazione che di controllo. La pronunciata non circolarità della forma di plasma e i diversi regimi coinvolti hanno influenzato fortemente l’attività di modellazione che ha richiesto, infatti, lo sviluppo di molteplici strumenti computazionali e di analisi dati. Per quanto concerne il controllo, la non completa osservabilità della dinamica del sistema e la necessità di ridurre l’ordine del modello sono solo alcuni degli aspetti che hanno determinato la progettazione del sistema di controllo di forma e di posizione verticale. La prima parte è basata su dati teorici generati dal codice di equilibrio MAXFEA e poi utilizzati per derivare il modello linearizzato attraverso il codice CREATE-L. In questo contesto, sono stati prodotti due modelli di riferimento per le configurazioni magnetiche relative a plasmi non circolari: il singolo nullo inferiore (LSN) e il singolo nullo superiore (USN). I modelli CREATE-L sono i più semplici in termini di complessità di modellazione, in quanto le strutture conduttive della macchina sono descritte nell’approssimazione assialsimmetrica. D’altro canto, le proprietà semplici ma affidabili del modello CREATE-L hanno portato alla progettazione del sistema di controllo di forma e posizione verticale del plasma di RFX-mod, che è stato in seguito testato e utilizzato con successo per aumentare le prestazioni del plasma. Successivamente, è stata condotta un’analisi sui possibili effetti 3D delle strutture conduttrici sulle due configurazioni di plasma di riferimento, producendo dunque modelli linearizzati caratterizzati da un sempre maggiore livello di complessità. Una dettagliata descrizione volumetrica (3D) delle strutture conduttrici di RFX-mod è stata eseguita e inclusa nei modelli linearizzati di plasma attraverso il codice CarMa0. Successivamente, è stato eseguito un confronto tra l’accuratezza di questo modello e quello precedente 2D. Le diverse ipotesi e approssimazioni dei vari modelli consentono una chiara identificazione dei fenomeni chiave che governano l’evoluzione dell’instabilità verticale n = 0 in scariche RFX-mod tokamak e quindi forniscono informazioni fondamentali nella pianificazione ed esecuzione di esperimenti correlati oltre che nella raffinazione del progetto del sistema di controllo. Infine, il modello di equilibrio evolutivo non lineare CarMa0NL, che comprende le strutture volumetriche 3D, è stato utilizzato per modellare gli effetti non lineari simulando una variazione di corrente lineare "fittizia". La seconda parte è costituita da un’attività di modellazione strettamente correlata ai risultati delle campagne sperimentali. In particolare, sono stati eseguiti nuovi modelli linearizzati per i plasmi sperimentali nella configurazione USN per tutti i regimi di plasma coinvolti, cioè dal basso β fino al modo H. È stata ideata e sviluppata una procedura iterativa per la produzione di modelli linearizzati di risposta di plasma estremamente accurati, al fine di riprodurre al meglio i dati sperimentali. I nuovi modelli hanno consentito ulteriori studi sulla stabilità verticale, inclusi gli effetti della parete 3D, nei tre diversi regimi studiati (basso β, β intermedio, modo H). I modelli linearizzati assialsimmetrici (CREATE-L) sono stati analizzati dal punto di vista della teoria dei controlli, rilevando caratteristiche peculiari in termini di funzione di trasferimento SISO associata al controllo della stabilità verticale e in termini di modello completo MIMO relativo al controllo di forma. Il modello MIMO è stato utilizzato per indagare le oscillazioni nella forma del plasma osservate sperimentalmente in alcune scariche a β intermedio. L’evoluzione temporale non lineare della scarica di plasma, per plasmi sperimentali a regimi a basso β, è stata effettuata usando il codice di equilibrio evolutivo CarMa0NL. Infine, è stata studiata l’instabilità verticale per i plasmi sperimentali in termini di un possibile rapporto tra i parametri del plasma e il suo verificarsi; a tal fine è stata eseguita la soluzione del problema inverso per la produzione di equilibri di plasma teorici di riferimento, prodotti come variazioni sui parametri dei plasmi osservati sperimentalmente, il che comporta una vasta gamma di metodi numerici descritti in dettaglio. Successivamente, è stato adottato un test di ipotesi statistica per confrontare i valori medi dei parametri di plasma, sia sperimentali che teorici, associati a due diversi comportamenti in termini di stabilità verticale.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 2003.<br>Includes bibliographical references (p. 155-161).<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>This dissertation reports on the development of a diagnostic visible imaging system on the Alcator C-Mod tokamak and the results from that system. The dissertation asserts the value of this system as a qualitative and quantitative diagnostic for magnetically confined plasmas. The visible imaging system consists of six CCD cameras, absolutely calibrated and filtered for specific spectral ranges. Two of these cameras view the divertor region tangentially, two view RF antenna structures and two are used for a wide-angle survey of the vacuum vessel. The divertor viewing cameras are used to generate two-dimensional emissivity profiles using tomography. Three physics issues have been addressed using the visible imaging system: 1) Using two-dimensional emissivity profiles of Da, volumetric recombination rate profiles have been measured and found to have a structure that depends on a poloidal temperature gradient in the outer scrape-off-layer. 2) A camera viewing the inner wall tangentially was used to measure Da emission profiles. A sharp break in slope of the radial density profile was found at the location of the secondary separatrix near the inner wall by using these profiles and a kinetic model of the neutrals. 3) Two-dimensional emissivity profiles of visible continuum (420-430nm) have been measured and found to be an order of magnitude too large when compared to expected levels from electron-ion bremsstrahlung and radiative recombination. Several atomic and molecular processes have been considered to explain the enhanced continuum. However, none of the considered processes could explain the continuum level without particle densities inconsistent with current modeling efforts.<br>(cont.) The visible imaging system was also used in identifying the causes of impurity injections during discharges, in identifying the failure of invessel components, and as a monitor of vessel and plasma conditions. Both the physics results and the operational benefits of the visible imaging system show that the system is a valuable quantitative and qualitative diagnostic.<br>by Christopher James Boswell.<br>Ph.D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1997.<br>Includes bibliographical references (p. 329-338).<br>Two complementary approaches were used to characterize transport on the Alcator C­Mod tokamak. The first was an empirical analysis of the scaling of transport with P*, the ion Larmor radius normalized to the plasma size. The second was a comparison of the transport predictions from the IFS-PPPL model of ion temperature gradient (ITG) driven turbulence to observations on C-Mod. The P* scaling experiments on C-Mod extend the range of plasma parameters over which the dimensionless scaling approach has been tested in both magnetic field ( to 8 T) and density (to (ne ) = 3.8 x 1020 /m3) ...<br>by Jeffrey Marc Schachter.<br>Ph.D.

Kyoto University (京都大学)<br>0048<br>新制・課程博士<br>博士(エネルギー科学)<br>甲第9045号<br>エネ博第32号<br>新制||エネ||9(附属図書館)<br>UT51-2001-F375<br>京都大学大学院エネルギー科学研究科エネルギー基礎科学専攻<br>(主査)教授 若谷 誠宏, 教授 近藤 克己, 教授 佐野 史道<br>学位規則第4条第1項該当

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 2005.<br>Includes bibliographical references (p. 211-226).<br>Edge transport barriers (ETBs) in tokamak plasmas accompany transitions from low confinement (L-mode) to high confinement (H-mode) and exhibit large density and temperature gradients in a narrow pedestal region near the last closed flux surface (LCFS). Because tokamak energy confinement depends strongly on the boundary condition imposed by the edge plasma pressure, one desires a predictive capability for the pedestal on a future tokamak. On Alcator C-Mod, significant contributions to ETB studies were made possible with edge Thomson scattering (ETS), which measures profiles of electron temperature (20 Te[eV] 800) and density (0.3 ne[1020m-3] ' 5) with 1.3-mm spatial resolution near the LCFS. Profiles of Te, ne, and Pe = neTe are fitted with a parameterized function, revealing typical pedestal widths A of 2-6mm, with ATe Ane, on average. Pedestals are examined to determine existence criteria for the enhanced D, (EDA) H-mode. A feature that distinguishes this regime is a quasi-coherent mode (QCM) near the LCFS. The presence or absence of the QCM is related to edge conditions, in particular density, temperature and safety factor q. Results are consistent with higher values of both q and collisionality v* giving the EDA regime. Further evidence suggests that increased Vpel may favor the QCM; thus EDA may have relevance to low-v* reactor regimes, should sufficient edge pressure gradient exist.<br>(cont.) Scaling studies of pedestal parameters and plasma confinement in EDA H-modes varied operational parameters such as current Ip and L-mode target density ne,L. At fixed plasma shape, widths show little systematic variation with plasma parameters. Scalings are however determined for pedestal heights and gradients. The Pe pedestal height and gradient both scale as I, similar to scalings found on other tokamaks, though with differing pedestal-limiting physics. It is seen that the density pedestal value ne,PED scales linearly with Ip, and more weakly with h,L, indicating that neutral fueling plays a relatively limited role in setting H-mode density. Plasma stored energy scales in a linear fashion with the Pe pedestal, such that empirical confinement scalings are affected by edge pedestal scalings. Empirical determination of neutral density and ionization source was made across the pedestal region, enabling inference of neutral gradient scale length Lo and effective diffusivity Def. The Def well is comparable in width to the pedestal, and Lo tends to be less than Ane. Computation of Lo in discharges with varying ne,L yields a similar result, suggesting that A,, is generally set by the ETB extent and not neutral penetration length. Puffing gas into an existing H-mode edge yields no significant change in the values of ne,PED, Vne, which is qualitatively consistent with simulations using a coupled fluid-kinetic neutral model. Experiment and modeling indicate the importance of thermal equilibration of neutrals with ions, particularly in high density collisional) plasmas.<br>by Jerry W. Hugues, Jr.<br>Ph.D.

In tokamaks, the stability of magneto-hydrodynamic modes can be modified by populations of energetic particles. In ITER-type fusion reactors, such populations can be generated by fusion reactions or auxiliary heating. The electron-driven fishbone mode belongs to this category of instabilities. It results from the resonant interaction of the internal kink mode with the slow toroidal precessional motion of energetic electrons and is frequently observed in present-day tokamaks with Electron Cyclotron Resonance Heating or Lower Hybrid Current Drive. These modes provide a good test bed for the linear theory of fast-particle driven instabilities as they exhibit a very high sensitivity to the details of both the equilibrium and the electronic distribution function. In Tore Supra, electron-driven fishbones are observed during LHCD-powered discharges in which a high-energy tail of the electronic distribution function is created. Although the destabilization of those modes is related to the existence of a fast particle population, the modes are observed at a frequency that is lower than expected. Indeed, the corresponding energy assuming resonance with the toroidal precession frequency of barely trapped electrons falls in the thermal range. The linear stability analysis of electron-driven fishbone modes is the main focus of this thesis. The fishbone dispersion relation is derived in a form that accounts for the contribution of the parallel motion of passing particles to the resonance condition. The MIKE code is developed to compute and solve the dispersion relation of electron-driven fishbones. The code is successfully benchmarked against theory using simple analytical distributions. When coupled to the relativistic Fokker-Planck code LUKE and to the integrated modeling platform CRONOS, it is used to compute the stability of electron-driven fishbones using reconstructed data from tokamak experiments. Using the code MIKE with parametric distributions and equilibria, we show that both barely trapped and barely passing electrons resonate with the mode and can drive it unstable. More deeply trapped and passing electrons have a non-resonant effect on the mode that is, respectively, stabilizing and destabilizing. MIKE simulations using complete ECRH-like distribution functions show that energetic barely passing electrons can contribute to drive a mode unstable at a relatively low frequency. This observation could provide some insight to the understanding of Tore Supra experiments<br>La stabilité des modes magnéto-hydrodynamiques dans les plasmas de tokamaks est modifiée par la présence de particules rapides. Dans un tokamak tel qu'ITER ces particules rapides peuvent être soit les particules alpha créées par les réactions de fusion, soit les ions et électrons accélérés par les dispositifs de chauffage additionnel et de génération de courant. Les modes appelés fishbones électroniques correspondent à la déstabilisation du mode de kink interne due à la résonance avec le lent mouvement de précession toroidale des électrons rapides. Ces modes sont fréquemment observés dans les plasmas des tokamaks actuels en présence de chauffage par onde cyclotronique électronique (ECRH) ou de génération de courant par onde hybride basse (LHCD). La stabilité de ces modes est particulièrement sensible aux détails de la fonction de distribution électronique et du facteur de sécurité, ce qui fait des fishbones électroniques un excellent candidat pour tester la théorie linéaire des instabilités liées aux particules rapides. Dans le tokamak Tore Supra, des fishbones électroniques sont couramment observés lors de décharges où l'utilisation de l'onde hybride basse crée une importante queue de particules rapides dans la fonction de distribution électronique. Bien que ces modes soit clairement liés à la présence de particules rapides, la fréquence observée de ces modes est plus basse que celle prévue par la théorie. En effet, si on estime l'énergie des électrons résonants en faisant correspondre la fréquence du mode avec la fréquence de précession toroidale des électrons faiblement piégés, on obtient une valeur comparable à celle des électrons thermiques. L'objet principal de cette thèse est l'analyse linéaire de la stabilité des fishbones électroniques. La relation de dispersion de ces modes est dérivée et la forme obtenue prend en compte, dans la condition de résonance, la contribution du mouvement parallèle des particules passantes. Cette relation de dispersion est implémentée dans le code MIKE qui est ensuite testé avec succès en utilisant des fonctions de distributions analytiques. En le couplant au code Fokker-Planck relativiste LUKE et à la plate-forme de simulation intégrée CRONOS, MIKE peut estimer la stabilité des fishbones électroniques en utilisant les données reconstruites de l'expérience. En utilisant des fonctions de distributions et des équilibres analytiques dans le code MIKE nous montrons que les électrons faiblement piégés ou faiblement passants peuvent déstabiliser le mode de kink interne en résonant avec lui. Si l'on s'éloigne de la frontière entre électrons passants et piégés, les effets résonants s'affaiblissent. Cependant les électrons passants conservent une influence déstabilisante alors que les électrons piégées tendent à stabiliser le mode. D'autres simulations avec MIKE, utilisant cette fois des distributions complètes similaires à celles obtenues en présence de chauffage de type ECRH, montrent que l'interaction avec les électrons faiblement passants peut entraîner une déstabilisation du mode à une fréquence relativement basse ce qui pourrait permettre d'expliquer les observations sur le tokamak Tore Supra

Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 2000.<br>Includes bibliographical references (p. 187-191).<br>In this thesis a study of molybdenum sources and screening in Alcator C-Mod is presented. This work contributes in characterizing the performance of molybdenum, a high Z material, as a tokamak first wall surface. Understanding the molybdenum production mechanism is crucial if one wants to minimize it. A simple physical sputtering model has been developed that calculates the molybdenum source at the divertor, providing satisfactory agreement with the spectroscopic results. The effect of deuterons, boron ions, and redeposited molybdenum incident on the target is included in the calculation which shows that the boron ions dominate the sputtering. It is also found that the probability of molybdenum being "promptly" redeposited (within a gyration after having been sputtered) can be as high as 80%. High probability of redeposition is favorable because it reduces the net erosion. Specifically, it has been found that although the molybdenum gross erosion peaks close to the separatrix, the net erosion peaks further away in the target plate. Three surfaces have been identified spectroscopically in C-Mod to be significant sources of molybdenum: the inner wall, the outer divertor and the antenna protection tiles. The inner wall is the only important source during limited plasma operation, while, in diverted discharges, the molybdenum generated there is very well screened by the plasma. In RF-heated diverted plasmas, it is believed that the antenna protection tiles are the source of most of the molybdenum that ends up in the core. The outer divertor can not be excluded as a contributor to the core molybdenum density but there are indications that it is often not the dominant source during RF heating. This result is significant since it is expected that the divertor target in the next generation fusion devices will be made primarily with a high-Z material. The study of boronization as a surface conditioning method which reduces the molybdenum source rates and core concentration has shown a varying effectiveness dependent on first wall surface location. The beneficial effects of boronization disappear rather fast for the outer divertor, last longer for the inner wall, with the antennas and plasma core benefiting the most.<br>by Dimitrios Pappas.<br>Ph.D.

Thesis: Ph. D., Massachusetts Institute of Technology, Department of Nuclear Science and Engineering, 2014.<br>Cataloged from PDF version of thesis.<br>Includes bibliographical references (pages 209-216).<br>In an effort to illuminate the effects of the strong plasma gradients in the pedestal region on impurity transport, research was conducted to measure complete sets of impurity density, poloidal and parallel velocity, and temperature at two separate poloidal locations in the pedestal region of the Alcator C-Mod tokamak. To this end, the diagnostic technique gas puff-CXRS was refined and expanded on, allowing for the first time in a tokamak complete measurements of impurities at the high-field side (HFS). Large in-out B5+ impurity density asymmetries were measured in H-mode plasmas with strong boundary electron density gradients, with a build-up of impurity density at the HFS. Impurity temperatures were also found to be asymmetric in the pedestal region, with larger temperatures at the low-field side (LFS). Such temperature asymmetries suggest a significant asymmetry in electron density near the separatrix. In contrast to these H-mode results, plasmas with low boundary electron density gradients, such as L-mode and I-mode, exhibit constant impurity density on a flux surface, even if strong electron temperature gradients are present. Mechanisms which could drive such poloidal asymmetries are explored. Experiments provide evidence against localized impurity sources and fluctuation-induced transport as primary causes. Particle transport timescales are compared, showing that the radial transport becomes comparable to or faster than the parallel transport in the pedestal region. Additionally, modelling of impurity transport using conventional, one-dimensional neoclassical physics fails to correctly reproduce the measured flux-surface averaged impurity density, suggesting along with the timescale estimates that a more complete two-dimensional treatment of impurity particle transport is required. The measured impurity velocities at the LFS and HFS are compared to the canonical form for particle flow velocity within the flux surface of a tokamak. Within the error bars of the measurement, agreement is found with the canonical form. The implications of exact matches to the canonical form are low radial transport, and the E x B drift dominating the perpendicular impurity flow. Further work is motivated into more precise velocity measurements to determine if the velocities exactly match this canonical form.<br>by Randy Michael Churchill.<br>Ph. D.

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Physics, 2013.<br>This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.<br>Cataloged from student-submitted PDF version of thesis.<br>Includes bibliographical references (p. 201-210).<br>Usually when sufficient heating power is injected, tokamak plasma will make an abrupt transition into a state with improved confinement, known as the high-confinement mode, or H-mode. Given the greatly enhanced fusion yield, H-mode is foreseen as the baseline scenario for the future plasma operation of the International Thermonuclear Experimental Reactor (ITER). Many research efforts have been given to understand the criteria for H-mode access. To further contribute to this research, a primary focus of this thesis is characterizing the H-mode access conditions in the Alcator C-Mod tokamak, across a broad range of plasma density, magnetic field, and plasma current. In addition, dedicated experiments were designed and executed on C-Mod, to explore the effects of divertor geometry, ICRF resonance location, and main ion species on H-mode access conditions. Results from these experiments will be included in this thesis. The underlying physics of H-mode access is very complex, and the critical mechanisms remain largely unresolved. To promote our understanding, some models proposed for the H-mode transition are tested, using well documented local plasma conditions, obtained in C-Mod experiments. In particular, this thesis pioneers the test of a recently developed model for H-mode threshold power predictions.<br>by Yunxing Ma.<br>Ph.D.

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1998.<br>Includes bibliographical references (leaves 89-90).<br>This thesis investigates alternate methods of controlling the vertical position of the plasma in the ALCATOR C-Mod Tokamak. The purpose of this work is to examine alternative methods of controlling the plasma position that can be adopted to improve performance over the current system, which uses a proportional-derivative (PD) control system actuated through a pair of outboard equilibrium field coils (EFC). The first part of this investigation examines the possibility of using inboard ohmic heating coils (OH2) as the controlling coils. A coupling transformer was designed to connect a large amperage/low bandwidth power supply to a small amperage/high bandwidth power supply, removing the need for an expensive large and fast power supply. Both PD control laws and full state feedback laws were also compared for performance. A rigid displacement model of the plasma motion was developed that took into account a model of induced currents in the vacuum vessel and coils. The results of the analysis concluded that there were moderate speed advantages to using state feedback on The OH2 coils, but these were outweighed by the robust operation of EFC PD control. No design achieved a decisive margin of improvement over the current control system.<br>by ENS George Hugh Miller, USN.<br>S.M.