Thesis: Ph. D., Massachusetts Institute of Technology, Department of Nuclear Engineering, 1977 / Vita. / Includes bibliographical references. / Ph. D. / Ph. D. Massachusetts Institute of Technology, Department of Nuclear Engineering

The physics of the biasing induced L-H transition and the mechanism for E×B shear flow suppression of turbulence are investigated on HBT-EP. Detailed measurements of the transverse length scales, behavior, and propagation direction of the edge turbulence match what is expected for the ion temperature gradient (ITG) mode. In the scrape-off layer (SOL), radially propagating blob-filament turbulence is identified and characterized, with velocities, sizes, and distributions comparable to measurements on other devices. Through systematic studies of the effect of applied shear flow on the turbulence, it is found that the E×B suppression of turbulence matches what is expected by the spectral shift model [Staebler et al. 2013 Phys. Rev. Lett. 110 055003]. Namely, the application of shear flow tilts the turbulent eddies and shifts the mean radial wavenumber ⟨kr⟩ of the turbulence spectrum from near zero to finite values, leading to a reduction in the turbulence intensity. The investigation also shows that both the decorrelation model and quench rule are able to reproduce the measured reduction of the turbulence intensity with applied shear flow when appropriate parameters are chosen. However, the decorrelation model fails to explain the increase in the shear-wise correlation length measured with increasing applied shear, and the quench rule fails to capture the suppression of the turbulence to a finite intensity at high shear. It is found that the same shearing effect that tilts the eddy structures and shifts ⟨kr⟩, enhances the gradient in the Reynolds stress at the edge and suppresses the blob-filament turbulence in the SOL. Although the biasing levels leading up to the transition are shown to enhance the Reynolds stress in a radially varying manner, it is found that the high flow shear in the H-mode state completely quenches the Reynolds stress. A careful examination of the spatial structure and temporal dynamics of the forcing terms in both dithering and one-step transitions reveals that the biasing induced L-H transition is caused by a reduction in poloidal viscosity at high flow velocity, in agreement with neoclassical theory. Nevertheless, the Reynolds force is measured to be comparable to the force from the electrode current, allowing the turbulence driven stress to work synergistically (or antagonistically) with forces from the probe to achieve the critical poloidal flow velocities. The similarities between the transition criteria on HBT-EP and other devices indicate that reduction of poloidal viscosity leading to the transition to improved confinement regimes may be a universal trait among toroidal confinement devices. The application of resonant magnetic perturbations (RMPs) is shown to both reduce the Reynolds stress and increase the biasing threshold for the transition. The observed reduction in the Reynolds stress stems from a reduction in the intensity of the underlying turbulence; namely, a decrease in the amplitude of velocity fluctuations in regions where the Reynolds stress is high without an applied RMP. This study has therefore expanded the current understanding of transport barrier formation in magnetic confinement devices.

The first experimental demonstration of feedback suppression of rotating external kink modes near the ideal wall limit in a tokamak using Kalman filtering to discriminate the n = 1 kink mode from background noise is reported. In order to achieve the highest plasma pressure limits in tokamak fusion experiments, feedback stabilization of long-wavelength, external instabilities will be required, and feedback algorithms will need to distinguish the unstable mode from noise due to other magnetohydrodynamic activity. When noise is present in measurements of a system, a Kalman filter can be used to compare the measurements with an internal model, producing a realtime, optimal estimate for the system's state. For the work described here, the Kalman filter contains an internal model that captures the dynamics of a rotating, growing instability and produces an estimate for the instability's amplitude and spatial phase. On the High Beta Tokamak-Extended Pulse (HBT-EP) experiment, the Kalman filter algorithm is implemented using a set of digital, field-programmable gate array controllers with 10 microsecond latencies. The feedback system with the Kalman filter is able to suppress the external kink mode over a broad range of spatial phase angles between the sensed mode and applied control field, and performance is robust at noise levels that render feedback with a classical, proportional gain algorithm ineffective. Scans of filter parameters show good agreement between simulation and experiment, and feedback suppression and excitation of the kink mode are enhanced in experiments when a filter made using optimal parameters from the experimental scans is used.

This thesis presents a comprehensive investigation into the observations and suppression of sawtooth instabilities on the High Beta Tokamak-Extended Pulse (HBT-EP) device. The principle and design of a new tangential multi-energy extreme ultraviolet and soft x-ray (ME-EUV/SXR) diagnostic system is presented. This system enables the clear detection of sawtooth events for the first time on HBT-EP. It is the first multi-energy tangential-view system designed to work in a temperature range below 200 eV in a tokamak, which enables measurements of the electron temperature and the examination of mode dynamics. By employing a combination of 0.1 um aluminum and 0.2 um titanium filters, the system allows measurements of electron temperature profiles through reconstruction of the emission profile using the standard ``double-foil'' technique. Using the tangential ME-EUV/SXR diagnostic system, the thesis reports on the first detailed observations of sawtooth events on HBT-EP, analyzing their features and comparing the findings with results from other devices. It investigates the phenomenon of discharge scenario bifurcation, where plasma exhibits distinct behaviors under similar parameters. The study examines the correlation between the amplitude of the edge mode and the strength of sawtooth events, along with the role of the conducting wall system in this context. It was found that when the normalized wall radius 𝒃/𝒂 is within a critical value, the edge mode can be stabilized and strong sawtooth events occur. In-depth analysis is performed on the modes present during sawtooth-suppressed stages, with a particular focus on the coupling between the 1/1 helical core (HC), 2/1 tearing mode (TM) and the 3/1 external kink mode (𝐗𝐊). Evidence is provided to support the effectiveness of magnetic flux pumping in suppressing sawtooth instabilities when the 3/1 𝐗𝐊 exhibits a significant amplitude. Conversely, the suppression of the 3/1 𝐗𝐊 due to stabilization by the conducting wall leads to the weakening of magnetic flux pumping, resulting in the occurrence of strong sawtooth events. In conclusion, this thesis contributes to the understanding of sawtooth instabilities on the HBT-EP tokamak and highlights the role of magnetic flux pumping as a mechanism for sawtooth suppression. It broadens the understanding of flux pumping across various tokamak operational regimes and demonstrates the potential of sawtooth suppression through external mode manipulation. This contributes to the future development of sawtooth control strategies, improving plasma stability and advancing fusion energy research.

Experiments on the DIII-D device in the negative triangularity (NT) regime of tokamak operation demonstrate core conditions that offer advantageous stability properties. Long duration, stationary discharges in this scenario maintain performance metrics that scale to viable reactor gain. Deleterious global modes of toroidal mode number n=1 are infrequent in these plasmas, which operate free of core instability cycles that can kick off global instabilities. These plasmas operate free of edge instability cycles that would damage reactor components, as do all strongly shaped NT plasmas. Reproducible access to high-power stationary states was developed at two values of q95, the edge magnetic winding number or “safety factor”. Core MHD instabilities manifest in one form of internal ideal mode, the quasi-interchange mode (QI), found to be consistent with modeling of the profiles and parameter space in which NT operates. The GATO and DCON ideal MHD codes are used to characterize the limits to normalized pressure in NT, finding global kink modes with strong poloidal harmonic m=1,2 components at normalized plasma pressure βN=3-3.5. Limits to β_N are predicted to be mostly insensitive to plasma boundary shape in NT and similar at both q95 values obtained in experiments. Average triangularity is shown to affect ideal limits, when modified at the outer midplane. A similar result is obtained with the RDCON resistive MHD code, which is used to characterize the stability to resistive “tearing modes”. Experimental NT equilibria and equilibria across shape scans were investigated. Only outer midplane modifications affected tearing calculations. Ideal kink modeling and experimental observations of sporadic QI mode provide an explanation for current diffusion not predicted by neoclassical theory. This effect is found in experiments at q95=3, analyzed with the ONETWO transport code’s facility to evolve magnetic flux over a discharge consistently with measured profiles and reconstructed magnetic flux surfaces. This result is compared with GATO calculations and ONETWO flux diffusion analysis of a conventional shape, ITER baseline demonstration discharge that is shown to have an intrinsically 3D core. Radiation from accumulated plasma impurities seems to alter the core q profile. This makes unstable a QI mode that spurs formation of a helical core, sustained by anomalous magnetic flux diffusion. NT experiments at q95=4 are limited in energy confinement by poor fast ion confinement, as a result of nondisruptive core 3/2 tearing modes. Analysis with ONETWO shows agreement with neoclassical flux diffusion predictions in these cases, corresponding to a removal of core instabilities and elevation of minimum safety factor values qmin to unity. This understanding of the core MHD, performance, and operational limits of NT scenarios in DIII-D advances the development of negative triangularity scenarios and informs the core phenomena observed in experiments spanning the regime.

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. / 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.

Ce travail porte sur le développement et la vérification d’une nouvelle approche de coordonnées alignées FCI (Flux-Coordinate Independent), qui tire partie de l’anisotropie du transport dans un plasma immergé dans un fort champ magnétique. Sa prise en compte dans les codes numériques permet de réduire grandement le coût de calcul nécessaire pour une précision donnée. Une particularité de l’approche nouvellement développée dans ce manuscrit est en particulier sa capacité à traiter, pour la première fois, des configurations avec point X. Toutes ces analyses ont été conduites avec FENICIA, code modulaire entièrement développé dans le cadre de cette thèse, et permettant la résolution d’une classe de modèles génériques. En résumé, la méthode développée dans ce travail est validée. Elle peut s’avérer pertinente pour un large champ d’application dans le contexte de la fusion magnétique. Il est montré dans cette thèse que cette technique devrait pouvoir s’appliquer aussi bien aux modèles fluides que gyrocinétiques de turbulence, et qu’elle permet notamment de surmonter un des problèmes fondamentaux des techniques actuelles, qui peinent à traiter de manière précise la traversée de la séparatrice. / The primary thrust of this work is the development and implementation of a new approach to the problem of field-aligned coordinates in magnetized plasma turbulence simulations called the FCI approach (Flux-Coordinate Independent). The method exploits the elongated nature of micro-instability driven turbulence which typically has perpendicular scales on the order of a few ion gyro-radii, and parallel scales on the order of the machine size. Mathematically speaking, it relies on local transformations that align a suitable coordinate to the magnetic field to allow efficient computation of the parallel derivative. However, it does not rely on flux coordinates, which permits discretizing any given field on a regular grid in the natural coordinates such as (x, y, z) in the cylindrical limit. The new method has a number of advantages over methods constructed starting from flux coordinates, allowing for more flexible coding in a variety of situations including X-point configurations. In light of these findings, a plasma simulation code FENICIA has been developed based on the FCI approach with the ability to tackle a wide class of physical models. The code has been verified on several 3D test models. The accuracy of the approach is tested in particular with respect to the question of spurious radial transport. Tests on 3D models of the drift wave propagation and of the Ion Temperature Gradient (ITG) instability in cylindrical geometry in the linear regime demonstrate again the high quality of the numerical method. Finally, the FCI approach is shown to be able to deal with an X-point configuration such as one with a magnetic island with good convergence and conservation properties.

As tentativas de se conseguir um funcionamento contínuo para o tokamak e as perspectivas de estabilização de oscilações MHD através do controle do perfil de corrente, motivaram pesquisas que levassem a uma forma de geração de corrente não indutiva. Uma das possíveis alternativas para atingir esta meta é a injeção de ondas de alta freqüência como, por exemplo, ondas na freqüência híbrida inferior ou Lower Hybrid (LH), que impulsionam elétrons através do amortecimento de Landau na direção paralela ao campo magnético toroidal, tomando-os capazes de transportar corrente. Nos futuros reatores, entretanto, a absorção da onda pelas partículas de 3.5 MeV, conforme o que é previsto, e que ocorre através do amortecimento de Landau na direção perpendicular ao campo magnético, pode diminuir a eficiência do método descrito acima. Nosso objetivo, neste trabalho, é simular a interação LH-partículas com a interação entre a onda LHe os íons rápidos do plasma, que atingem até alguns MeV de energia e que são provenientes do aquecimento de íons de minoria pela onda ciclotrônica de íons (IC). Estes fenômenos podem ser descritos através de uma equação de Fokker-Planck uni-dimensional, no espaço de velocidades, onde os termos de difusão quase-linear, correspondentes à injeção das ondas IC e LH, estão presentes juntamente com os termos colisionais, que representam a termalização dos íons rápidos sobre um plasma maxwelliano. Apresentamos, aqui, as primeiras evidências experimentais da interação LH-íons rápidos no tokamak JET. A análise de dados foi baseada na observação do conteúdo energético dos íons de minoria e das taxas de emissão de raios e de nêutrons no plasma, toda vez que a onda LH estava presente simultaneamente ao aquecimento com ondas IC. Observamos, nesta situação, que há um aumento de cerca de 20% do conteúdo energético dos íons rápidos, que corresponde a uma potência da onda absorvida de até, aproximadamente, 25%, dependendo dos parâmetros do plasma. O aumento de emissão de raios e de nêutrons, provenientes das reações de fusão, também confrrmou o aumento de energia dos íons rápidos quando a onda LH estava presente. Análises com FFT em experimentos onde a potência da onda estava 100% modulada, propiciaram o estudo da absorção de potência da onda LH de acordo com os níveis de superposição dos dois perfis de deposição sobre o plasma (ICe LH). / Attempts to achieve a steady-state operation in a reactor regime and the possibilities of stabilising MHD oscillations by controlling the plasma current density profile motivated studies of different methods of generating non-inductive current in reactor scenarios. The injection of Lower Hybrid waves (LH) in tokamak plasmas is considered as a possible route to reach this goal and has been successfully employed to generate plasma current by transferring momentum to the electrons in the direction parallel to the magnetic field through Electron Landau Damping (ELD). However, in a reactor operation regime, LHCD (Lower Hybrid Current Drive) efficiency can be affected, as it is predicted, by the damping of the wave on the 3.5 MeV particles, produced during fusion reactions. This interaction occurs through perpendicular Landau Damping since the particles can be considered as unmagnetized. In this work, the interaction of LH waves with particles is simulated through the interaction between the LH wave and ICRH driven minority íons, that can reach energies up to few MeV. Both phenomena can be described by a 1-D Fokker-Planck equation in velocity space that includes both quasi-linear diffusion coefficients due to ICRH and LH waves and collision terms which represent the fast ions slowing-down over a maxwellian plasma Once this Fokker-Planck equation is solved, the fast ion distribution function can be obtained in order to provide information on the fast minority íons. The first experimental evidence of the interaction of LH waves with ICRH minority íons in the MeV energy range is presented in this work. This interaction was detected in JET through measurements of the fast ion energy, ray and neutron ernission rates and by means of Fast Fourier Transform (FFT) analysis in experiments with 100% LH power modulation. An increase has been observed of approximately 20% in the fast ion energy content which corresponds about to 25% of LH power absorbed by the fast minority ions, depending on the plasma parameters. The increase of ray and neutron rates ernitted in the plasma and the FFT analysis confirm, respectively, the fast ion energy increase and a better damping of the wave when the overlap between IC and LH deposition profiles is maxirnized.

As tentativas de se conseguir um funcionamento contínuo para o tokamak e as perspectivas de estabilização de oscilações MHD através do controle do perfil de corrente, motivaram pesquisas que levassem a uma forma de geração de corrente não indutiva. Uma das possíveis alternativas para atingir esta meta é a injeção de ondas de alta freqüência como, por exemplo, ondas na freqüência híbrida inferior ou Lower Hybrid (LH), que impulsionam elétrons através do amortecimento de Landau na direção paralela ao campo magnético toroidal, tomando-os capazes de transportar corrente. Nos futuros reatores, entretanto, a absorção da onda pelas partículas de 3.5 MeV, conforme o que é previsto, e que ocorre através do amortecimento de Landau na direção perpendicular ao campo magnético, pode diminuir a eficiência do método descrito acima. Nosso objetivo, neste trabalho, é simular a interação LH-partículas com a interação entre a onda LHe os íons rápidos do plasma, que atingem até alguns MeV de energia e que são provenientes do aquecimento de íons de minoria pela onda ciclotrônica de íons (IC). Estes fenômenos podem ser descritos através de uma equação de Fokker-Planck uni-dimensional, no espaço de velocidades, onde os termos de difusão quase-linear, correspondentes à injeção das ondas IC e LH, estão presentes juntamente com os termos colisionais, que representam a termalização dos íons rápidos sobre um plasma maxwelliano. Apresentamos, aqui, as primeiras evidências experimentais da interação LH-íons rápidos no tokamak JET. A análise de dados foi baseada na observação do conteúdo energético dos íons de minoria e das taxas de emissão de raios e de nêutrons no plasma, toda vez que a onda LH estava presente simultaneamente ao aquecimento com ondas IC. Observamos, nesta situação, que há um aumento de cerca de 20% do conteúdo energético dos íons rápidos, que corresponde a uma potência da onda absorvida de até, aproximadamente, 25%, dependendo dos parâmetros do plasma. O aumento de emissão de raios e de nêutrons, provenientes das reações de fusão, também confrrmou o aumento de energia dos íons rápidos quando a onda LH estava presente. Análises com FFT em experimentos onde a potência da onda estava 100% modulada, propiciaram o estudo da absorção de potência da onda LH de acordo com os níveis de superposição dos dois perfis de deposição sobre o plasma (ICe LH). / Attempts to achieve a steady-state operation in a reactor regime and the possibilities of stabilising MHD oscillations by controlling the plasma current density profile motivated studies of different methods of generating non-inductive current in reactor scenarios. The injection of Lower Hybrid waves (LH) in tokamak plasmas is considered as a possible route to reach this goal and has been successfully employed to generate plasma current by transferring momentum to the electrons in the direction parallel to the magnetic field through Electron Landau Damping (ELD). However, in a reactor operation regime, LHCD (Lower Hybrid Current Drive) efficiency can be affected, as it is predicted, by the damping of the wave on the 3.5 MeV particles, produced during fusion reactions. This interaction occurs through perpendicular Landau Damping since the particles can be considered as unmagnetized. In this work, the interaction of LH waves with particles is simulated through the interaction between the LH wave and ICRH driven minority íons, that can reach energies up to few MeV. Both phenomena can be described by a 1-D Fokker-Planck equation in velocity space that includes both quasi-linear diffusion coefficients due to ICRH and LH waves and collision terms which represent the fast ions slowing-down over a maxwellian plasma Once this Fokker-Planck equation is solved, the fast ion distribution function can be obtained in order to provide information on the fast minority íons. The first experimental evidence of the interaction of LH waves with ICRH minority íons in the MeV energy range is presented in this work. This interaction was detected in JET through measurements of the fast ion energy, ray and neutron ernission rates and by means of Fast Fourier Transform (FFT) analysis in experiments with 100% LH power modulation. An increase has been observed of approximately 20% in the fast ion energy content which corresponds about to 25% of LH power absorbed by the fast minority ions, depending on the plasma parameters. The increase of ray and neutron rates ernitted in the plasma and the FFT analysis confirm, respectively, the fast ion energy increase and a better damping of the wave when the overlap between IC and LH deposition profiles is maxirnized.

L'interaction onde-particule dans les plasma est un sujet de recherche important, pour la compréhension des phénomènes physiques fondamentaux comme pour l'opération de réacteurs à fusion tels que les tokamaks. Cette intéraction peut être responsable de l'existence de modes instables, comme l'instabilité "fishbone" dans les plasmas de tokamak. Celle-ci est causée par l'interaction résonante entre un mode vivant dans la plasma et une population de particules supra-thermiques. Cette instabilité cause l'éjection d'une partie de ces particules énergétiques. Elle est par ailleurs caractérisée par une diminution de sa fréquence durant son évolution. Dans cette thèse, un modèle pour l'instabilité "fishbone", décrivant le plasma thérmique avec un traitement fluide et les particlules énergétiques avec un traitement cinétique, est développé. Ce modèle est simplifié de manière à permettre la compréhension des mécanismes les plus basiques qui causent la destabilisation du mode, sa diminution en fréquence durant son évolution ainsi que l'éjection de particules qu'il engendre. La théorie linéaire de ce modèle est faite, montrant les conditions qui permettent l'existence de l'instabilité, et permettant la caractérisation de son comportement linéaire. Les résultats analytiques sont ensuite comparés aux résultats linéaires numériques, obtenus grâce à un code développé durant cette thèse et basé sur les hypothèses du modèle, et ils sont en accord. Enfin, ce code est utilisé pour explorer le comportement non linéaire des particules énergétiques. Le mécanisme principalement responsable du changement de fréquence du mode ainsi que de l'éjection des particules est identifié et étudié en detail. / The wave-particle interaction in plasmas is an important research subject, for fundamental physical understanding as well as for the operation of fusion devices such as tokamaks. This interaction can cause the existence of unstable modes, such as the fishbone instability that is observed in tokamak plasmas. It results from the resonant interaction between an electro-magnetic wave living in the plasma and a population of supra-thermal particles. This mode causes the ejection of a portion of these energetic particles, and is thus detrimental to the confinment of energy in a tokamak, and it is characterized by a frequency down-chirping, i.e. a decrease of frequency of the mode during its evolution. In this thesis, a model for the fishbone instability is developed, that describes the thermal plasma with fluid equations and the supra-thermal particles with the kinetic Vlasov equation. This model is highly simplified in order to understand the basic mechanisms leading to destabilization, frequency chirping, and particle ejection. The linear theory of this model is then done, showing the conditions that lead to the existence of an instability, and that allow the characterization of its linear behavior. The linear analytic results are then compared to numerical linear results obtained with a code, based on the assumptions of the model, that was developed during this PhD and the results are found to be in good agreement. Finally, the code is used to explore the nonlinear behavior of energetic particles in the later phase of the fishbone instability. The main mechanism responsible for the frequency chirping and energetic particle ejection is identified and studied in detail.