Rozprawy doktorskie na temat „Plasma physics- Alfvenic turbulence”

The study of low-frequency turbulence in magnetized plasmas is a difficult problem due to both the enormous range of scales involved and the variety of physics encompassed over this range. Much of the progress that has been made in turbulence theory is based upon a result from incompressible magnetohydrodynamics (MHD), in which energy is only transferred from large scales to small via the collision of Alfv ́n waves propagating oppositely along the mean magnetic field. Improvements in laboratory devices and satellite measurements have demonstrated that, while theories based on this premise are useful over inertial ranges, describing turbulence at scales that approach particle gyroscales requires new theory. In this thesis, we examine the limits of incompressible MHD theory in describing collisions between pairs of Alfvén waves. This interaction represents the fundamental unit of plasma turbulence. To study this interaction, we develop an analytic theory describing the nonlinear evolution of interacting Alfv ́n waves and compare this theory to simulations performed using the gyrokinetic code AstroGK. Gyrokinetics captures a much richer set of physics than that described by incompressible MHD, and is well-suited to describing Alfvénic turbulence around the ion gyroscale. We demonstrate that AstroGK is well suited to the study of physical Alfvén waves by reproducing laboratory Alfvén dispersion data collected using the LAPD. Additionally, we have developed an initialization alogrithm for use with AstroGK that allows exact Alfvén eigenmodes to be initialized with user specified amplitudes and phases. We demonstrate that our analytic theory based upon incompressible MHD gives excellent agreement with gyrokinetic simulations for weakly turbulent collisions in the limit that k⊥ ρi << 1. In this limit, agreement is observed in the time evolution of nonlinear products, and in the strength of nonlinear interaction with respect to polarization and scale. We also examine the effect of wave amplitude upon the validity of our analytic solution, exploring the nature of strong turbulence. In the kinetic limit where k⊥ ρi ≥ 1 where incompressible MHD is no longer a valid description, we illustrate how the nonlinear evolution departs from our analytic expression. The analytic theory we develop provides a framework from which more sophisticated of weak and strong inertial-range turbulence theories may be developed. Characterization of the limits of this theory may provide guidance in the development of kinetic Alfvén wave turbulence.

Turbulence is a highly non-linear process ubiquitous in Nature. The nonlinearity is responsible for the coupling of many degrees of freedom leading to an unpredictable dynamical evolution of a turbulent system. Nevertheless, experimental observations strongly support the idea that turbulence at small scales achieves a statistically stationary state. This has motivated scientists to adopt a statistical approach for the study of turbulence. In both hydrodynamics (HD) and magnetohydrodynamics (MHD), fluctuations of bulk quantities that describe turbulent flows exhibit the property of statistical scale invariance, which is a form of self-similarity. For fully evolved turbulence in an infinite medium, one interesting consequence of this scale invariance is the power law dependence of the physical observables of the flow such that, for instance, the velocity field fluctuations along a given direction show power law power spectra and multiscaling for the various orders of the structure function within a certain range of scales, known as the inertial range. The characterization of such scaling is crucial in turbulence since it would fully quantify the process itself, distinguishing the latter from a wider class of scaling processes (e.g., stochastic self-similar processes). Experimentally, it has been observed that turbulent systems exhibit an extended self-similarity when either turbulence is not completely evolved or the system has finite size. As consequence of this, the moments of the structure function exhibit a generalized scaling, which points to a universal feature of finite range MHD turbulent ows and, more generally, of scale invariant processes that have finite cut-offs of the fields or parameters. However, the underling physics of this generalized similarity is still an open question. This thesis focuses on the quantification of statistical scaling in turbulent systems of finite size. We apply statistical analyses to the spatio-temporal fluctuations associated with line of sight intensity measurements of a solar quiescent prominence and data of the reconnecting fields in simulations of magnetic reconnection. We find that in both environments these fluctuations exhibit the hallmarks of finite range turbulence. In particular, an extended self-similarity is observed to hold the inertial range of turbulence, which is consistent with a generalized scaling for the structure function. Importantly, this generalized scaling is found to be multifractal in character as a signature of intermittency in the turbulence cascade. The generalized scaling recovered for finite range turbulence exhibits dependence on a function, the generalized function, which contains important information about the bounded turbulent flow such as some characteristics scale of the flow, the crossover from the small scale to the outer scale of turbulence and perhaps some characteristic features of the boundaries (future work). The quantification of the generalized scaling is performed thank to the application of statistical tools, some of which have been here introduced for the first time, which allow to identify the statistical properties of a wide class of scaling processes. Importantly, these techniques are powerful methodologies for testing fractal/multifractal scaling in self-similar and quasi self-similar systems, allowing us to distinguish turbulence from other processes that show statistical scaling.

As means of investigating the various mechanisms which contribute to the persistence of magnetized turbulence in the solar wind, this dissertation details the development of tools through which turbulence theories can be directly compared to in situ observations. This comparison is achieved though the construction of synthetic spacecraft time series from spectra of randomly phased linear eigenmodes. A broad overview of the current understanding of plasma turbulence through analytic theory, spacecraft observation, and numerical simulation is presented with particular emphasis on previous uses of linear eigenmode characteristics in the literature. An analytic treatment of relevant fluid and kinetic linear waves follows, providing motivation for the choice of three eigenmode characteristics for studying solar wind turbulence in this dissertation. The novel synthetic spacecraft time series method is next detailed and its use in describing magnetized turbulence justified. The three metrics are then individually employed as a means of comparing the turbulence models used to generate synthetic time series with in situ observations. These comparisons provide useful constraints on various proposed mechanisms for sustaining the turbulence cascade and heating the solar wind plasma.

The energy cascade process in turbulent flows is studied. Kolmogorov inertial range theories are critically reviewed and the multifractal characterization is discussed. Multiplicative cascade models are compared to the energy dissipation field (EDF) measured in the atmosphere. Landau's objection to the 1941 Kolmogorov theory is extended to the predictions of statistical fluid mechanics. The hypothesis $ rm Delta v( lambda L) { buildrel{d} over=} lambda sp{1/3} Delta v(L)$ is rejected with a statistical test. The moments $ rm langle( log varepsilon(L)) sp{p} rangle,$ where $ varepsilon$(L) denotes the EDF averaged over a volume of size L, are shown to be gaussian. For the EDF: Convergence tests showed that the exponents $ tau$(q) were not reliable for q $<$ 0; the correlations obey $ rm langle( mu sb{x}( delta)) sp{p}( mu sb{x+ delta}( delta)) sp{q} rangle propto delta sp{ gamma(p,q)}$ but $ gamma$ does not always equal the value obtained with a multinomial measure; a privileged scale ration r $ approx$ 1/2 is suggested by the prefactor oscillations of the correlation function. The implications of these results for the modelling of the EDF are discussed.

In tokamaks, heat and particle fluxes reaching the wall are often bursty and intermittent and understanding this behaviour is vital for the design of future reactors. Plasma edge turbulence plays an important role, its quantitative characterisation and modelling under different operating regimes is therefore an important area of research. Ion saturation current (Isat) measurements made in the edge region of the Large Helical Device (LHD) and Mega-Amp Spherical Tokamak (MAST) are analysed. Absolute moment analysis is used to quantify properties on different temporal scales of the measured signals, which are bursty and intermittent. In all data sets, two regions of power-law scaling are found, with the temporal scale τ≈40μs separating the two regimes. A monotonic relationship between connection length and skewness of the probability density function is found for LHD. A new numerical code, ‘HAWK,’ which solves the Hasegawa-Wakatani (HW) equations is presented. The HAWK code is successfully tested and used to study the HW model and modifications. The curvature-Hasegawa-Wakatani (CHW) equations include a magnetic field strength inhomogeneity, C = −∂lnB/∂x. The zonal-Hasegawa- Wakatani (ZHW) equations allow the self-generation of zonal flows. The statistical properties of the turbulent fluctuations produced by the HW model and variations thereof are studied. In particular, the probability density function of E × B density flux Γn = −n∂φ/∂y, structure functions, the bispectrum and transfer functions are investigated. Test particle transport is studied. For the CHW model, the conservation of potential vorticity Π = ∇2φ − n + (κ − C)x accounts for much of the phenomenology. Simple analytical arguments yield a Fickian relation Γn = (κ − C)Dx between the radial density flux Γn and the radial tracer diffusivity Dx. For the ZHW model, a subtle interplay between trapping in small scale vortices and entrainment in larger scale zonal flows determines the rate, character and Larmor radius dependence of the test particle transport. When zonal flows are allowed non-Gaussian statistics are observed. Radial transport (across the zones) is subdiffusive and decreases with the Larmor radius. Poloidal transport (along the zones), however, is superdiffusive and increases with small values of the Larmor radius.

The constrained decimation scheme (CDS) is applied to a turbulence model. The CDS is a statistical turbulence theory formulated in 1985 by Robert Kraichnan; it seeks to correctly describe the statistical behavior of a system using only a small sample of the actual dynamics. The full set of dynamical quantities is partitioned into groups, within each of which the statistical properties must be uniform. Each statistical symmetry group is then decimated down to a small sample set of explicit dynamics. The statistical effects of the implicit dynamics outside the sample set are modelled by stochastic forces.;These forces are not totally random; they must satisfy statistical constraints in the following way: Full-system statistical moments are calculated by interpolation among sample-set moments; the stochastic forces are adjusted by an iterative process until decimated-system moments match these calculated full-system moments. Formally, the entire infinite heirarchy of moments describing the system statistics should be constrained. In practice, a small number of low-order moment constraints are enforced; these moments are chosen on the basis of physical insights and known properties of the system.;The system studied in this work is the Betchov model--a large set of coupled, quadratically nonlinear ordinary differential equations with random coupling coefficients. This turbulence model was originally devised to study another statistical theory, the direct interaction approximation (DIA). By design of the Betchov system, the DIA solution for statistical autocorrelation is easy to obtain numerically. This permits comparison of CDS results with DIA results for Betchov systems too large to be solved in full.;The Betchov system is decimated and solved under two sets of statistical constraints. Under the first set, basic statistical properties of the full Betchov system are reproduced for modest decimation strengths (ratios of full-system size to decimated-system size); however, problems arise at stronger decimation. These problems are solved by the second set of constraints. The second constraint set is intimately related to the DIA; that relationship is shown, and results from the CDS under those constraints are shown to approach the DIA results as the decimation strength increases.

Analysis of the probability density functions (PDFs) of the velocity increment dvℓ and of their deformation is used to reveal the statistical structure of the intermittent energy cascade dynamics of turbulence. By analyzing a series of turbulent data sets including that of an experiment of fully developed low temperature helium turbulent gas flow (Belin, Tabeling, & Willaime, Physica D 93, 52, 1996), of a three-dimensional isotropic Navier-Stokes simulation with a resolution of 2563 (Cao, Chen, & She, Phys. Rev. Lett. 76, 3711, 1996) and of a GOY shell model simulation (Leveque & She, Phys. Rev. E 55, 1997) of a very big sample size (up to 5 billions), the validity of the Hierarchical Structure model (She & Leveque, Phys. Rev. Lett. 72, 366, 1994) for the inertial-range is firmly demonstrated. Furthermore, it is shown that parameters in the Hierarchical Structure model can be reliably measured and used to characterize the cascade process. The physical interpretations of the parameters then allow to describe differential changes in different turbulent systems so as to address non-universal features of turbulent systems. It is proposed that the above study provides a framework for the study of non-homogeneous turbulence. A convergence study of moments and scaling exponents is also carried out with detailed analysis of effects of finite statistical sample size. A quantity Pmin is introduced to characterize the resolution of a PDF, and hence the sample size. The fact that any reported scaling exponent depends on the PDF resolution suggests that the validation (or rejection) of a model of turbulence needs to carry out a resolution dependence analysis on its scaling prediction.

The transport of heat that results from turbulence is a major factor limiting the temperature gradient, and thus the performance, of fusion devices. We use nonlinear simulations to show that a toroidal equilibrium scale sheared flow can completely suppress the turbulence across a wide range of flow gradient and temperature gradient values. We demonstrate the existence of a bifurcation across this range whereby the plasma may transition from a low flow gradient and temperature gradient state to a higher flow gradient and temperature gradient state. We show further that the maximum temperature gradient that can be reached by such a transition is limited by the existence, at high flow gradient, of subcritical turbulence driven by the parallel velocity gradient (PVG). We use linear simulations and analytic calculations to examine the properties of the transiently growing modes which give rise to this subcritical turbulence, and conclude that there may be a critical value of the ratio of the PVG to the suppressing perpendicular gradient of the velocity (in a tokamak this ratio is equal to q/ε where q is the magnetic safety factor and ε the inverse aspect ra- tio) below which the PVG is unable to drive subcritical turbulence. In light of this, we use nonlinear simulations to calculate, as a function of three parameters (the perpendicular flow shear, q/ε and the temperature gradient), the surface within that parameter space which divides the regions where turbulence can and cannot be sustained: the zero- turbulence manifold. We are unable to conclude that there is in fact a critical value of q/ε below which PVG-driven turbulence is eliminated. Nevertheless, we demonstrate that at low values of q/ε, the maximum critical temperature gradient that can be reached without generating turbulence (and thus, we infer, the maximum temperature gradient that could be reached in the transport bifurcation) is dramatically increased. Thus, we anticipate that a fusion device for which, across a significant portion of the minor radius, the magnetic shear is low, the ratio q/ε is low and the toroidal flow shear is strong, will achieve high levels of energy confinement and thus high performance.

A method for simulating a turbulent binary fluid flow system based on the Lattice Boltzmann Method (LBM) is presented. The fluid equations up to the Navier-Stokes transport level are derived for this two fluid system, and results from numerical simulations using this method are shown. Finally, grid resolution is performed in a single fluid (LBM) simulation which determines the largest valid mesh size for a simulation that seeks to resolve physical structures of all scales.

Computer simulations of complex phenomena have become an invaluable tool for scientists in all disciplines. These simulations serve as a tool both for theorists attempting to test the validity of new theories and for experimentalists wishing to obtain a framework for the design of new experiments. Lattice Boltzmann Methods (LBM) provide a kinetic simulation technique for solving systems governed by non-linear conservation equations. Direct LBMs use the linearized single time relaxation form of the Boltzmann equation to temporally evolve particle distribution functions on a discrete spatial lattice. We will begin with a development of LBMs from basic kinetic theory and will then show how one can construct LBMs to model incompressible resistive magnetohydrodynamic (MHD) conservation laws. We will then present our work in extending existing models to the octagonal lattice, showing that the increased isotropy of the octagonal lattice produces better numerical stability and higher Reynolds numbers in MHD simulations. Finally, we will develop LBMs that use non-uniform grids and apply them to one dimensional MHD systems.

The increasing demand for new energy production has become the constant leitmotif of the society we live in. The impossibility of meeting such request in an economically feasible and environmentally friendly manner within the existing portfolio of options is now a global self-awareness. The International Energy Agency has been thoroughly documenting through its reports during the last years that the known reserves of natural gas and oil will be exhausted in decades, due to overpopulation and increasing energy demand. Consequently, a crucial issue will soon concern supply problems. This is where the research on fusion as energy source enters the picture. In order to demonstrate the feasibility of fusion as an energy source, the international scientific community has devoted countless efforts to the research on controlled thermonuclear fusion. The main and biggest experiment under construction, ITER, is the result of the cooperation among many countries throughout the world and it will be a test bench for fusion physics and fusion engineering. Among the different magnetic configurations suitable for fusion devices, the reversed-field pinch has demonstrated to be an excellent tool for plasma physics studies, although it is not accounted as a viable device for commercial energy production. The RFX-mod experiment hosted by Consorzio RFX in Padova is the biggest RFP device in the world. The research activity that will be presented in this thesis has been developed mainly at RFX-mod in Padova but has also involved the participation to an experimental campaign on the COMPASS tokamak in Prague. The research activity that will be presented in this thesis focuses on the characterization of 3D effects on transport mechanisms at the edge region of fusion plasmas in RFX-mod. The device is highly versatile: it can be operated both in reversed-field pinch and in tokamak magnetic configuration. A detailed description of transport properties at the plasma edge in both configurations will be given in the development of the thesis. The approach that will be followed can be described in terms of a twofold itinerary shared between the investigation of electrostatic fluctuations of transport properties through insertable probes and the study of magnetic topology modifications due to spontaneous 3D processes. The thesis is organized as follows: Part I, Introduction. In the first part of the thesis, all the background information needed for the development of the work will be introduced. In chapter 1 the concept of plasma and fusion physics will be discussed together with a detailed description of the two magnetic configurations for fusion devices relevant for analyses: reversed-field pinch (RFP) and tokamak. In chapter 2 the RFP dynamics will be described in details by introducing Taylor relaxation theory and the two main topologies also experimentally observed: the Single Helicity (SH) and the Multiple Helicity (MH) states. Then, RFX-mod edge region will be specifically described and the main tools used in the analyses will be introduced. The chapter will close with the introduction of a comparison between RFP and tokamak’s edge region through the analogy of a common 3D structure when external magnetic perturbations are applied. Part II, Transport analysis. In chapter 3 the two experimental configurations in which RFX-mod operates will be presented. The insertable U-probe used in the experiments will be described together with the theory upon which the collection of measurements relies. The investigation of electrostatic fluctuations of transport properties at the edge will be discussed. Studies on transport mechanism around different topological regions in presence of an externally applied magnetic perturbation will be shown for both reversed-field pinch and tokamak configuration in the RFX-mod device. Part III, Topology analysis. The study of magnetic topology modifications develops through analyses of spontaneous magnetic reconnection events in reversed-field pinch magnetic configuration. In chapter 4 reconnection models will be briefly discussed. Then, crash events in RFX-mod will be presented and the adopted analysis technique will be thoroughly explored. In the second part of the chapter the ion energy analyzer will be described together with its application in measurements of ion temperature profile in COMPASS tokamakand in RFX-mod. Part IV, Conclusions. In chapter 5 the results of the thesis are collected and discussed. In conclusion, a section entitled Summary and future perspectives is added where the main results are tautly summarized in view of future perspectives of research. Part V, Appendixes. In Appendix A a detailed description of MagnetoHydroDynamics framework for plasma physics is given. In Appendix B transport equations will be treated in details.
Il crescente aumento nella richiesta di produzione energetica è diventato un costante leitmotif che caratterizza la società in cui viviamo. L'impossibilità di riuscire a soddisfare tali richieste sfruttando opzioni già esistenti che siano economicamente vantaggiose ed al contempo rispettino l’ambiente, è ormai una consapevolezza globalmente diffusa. La International Energy Agency ha esaustivamente documentato attraverso i suoi report annuali che le riserve di gas naturale e combustibile fossile si esauriranno nel giro di qualche decade a causa della sempre più crescente richiesta di energia. Come provvedere a soddisfare le esigenze energetiche di una popolazione mondiale in continuo aumento diventerà ben presto un problema critico. E' all'interno di questo quadro globale che entra in gioco la ricerca sulla fusione come risorsa energetica. Al fine di poter dimostrare la sfruttabilità della fusione nucleare quale risorsa energetica, la comunità scientifica internazionale ha da anni continuato ad investire nella ricerca sulla fusione termonucleare controllata. Ad oggi è nelle fasi finali di costruzione il più grande esperimento che coinvolga trasversalmente ricercatori da ogni parte del mondo. L'esperimento è denominato ITER (International Thermonuclear Experimental Reactor) e rappresenterà un banco di prova per la fisica della fusione e l’ingegneria. Tra le possibili configurazioni magnetiche adottabili sperimentalmente in una macchina da fusione, quella a campo magnetico rovesciato si è rivelata essere un eccellente strumento per studiare la fisica del plasma e le innumerevoli sfide scientifiche che essa pone. Tuttavia, per svariati motivi non è previsto l'utilizzo di tale configurazione in un reattore a fusione che produca energia a fini commerciali. L'esperimento RFX-mod ospitato presso il Consorzio RFX a Padova è il reversed-field pinch (RFP) più grande al mondo. L'attività di ricerca che verrà presentata in questo lavoro di tesi è stata svolta principalmente a Padova su RFX-mod ma ha anche previsto e contemplato la partecipazione ad una campagna sperimentale sul tokamak COMPASS a Praga. L’attività di ricerca che verrà presentata in questa tesi si concentra sulla caratterizzazione degli effetti 3D sui meccanismi di trasporto nella regione più esterna del plasma di RFX-mod. La macchina risulta essere estremamente versatile in quanto sono possibili operazioni in configurazione a campo rovesciato e in configurazione tokamak. Nello svolgimento della tesi verrà fornita una descrizione dettagliata delle proprietà di trasporto al bordo del plasma in entrambe le configurazioni magnetiche. L'approccio che verrà seguito può essere descritto in termini di un duplice percorso condiviso tra l'investigazione delle fluttuazioni elettrostatiche delle proprietà di trasporto effettuato attraverso l'utilizzo di sonde inseribili nel plasma e lo studio dei cambiamenti della topologia magnetica dovuti a meccanismi spontanei di tipo 3D. La tesi viene così organizzata: Parte I, Introduzione. Nella prima parte della tesi verranno introdotte tutte le nozioni di base utili allo svolgimento del lavoro. Nel capitolo 1 sarà discusso il concetto di plasma e fisica della fusione assieme ad una descrizione dettagliata delle due configurazioni magnetiche rilevanti ai fini delle analisi effettuate: la configurazione reversed-field pinch (RFP) e tokamak. Nel capitolo 2 la dinamica di un RFP verrà dettagliatamente descritta attraverso la teoria di Taylor. Inoltre verranno discussi gli stati a singola e multipla elicità (stati SH e MH), caratteristici della dinamica di un RFP. Successivamente verrà descritta la regione più esterna del plasma di RFX-mod, anche attraverso gli strumenti principali utilizzati nelle analisi effettuate. Il capitolo si concluderà quindi con l'introduzione di una analogia, che sarà dominante in tutto il corpo della tesi, tra la regione esterna di un plasma di tipo RFP e di uno di tipo tokamak durante esperimenti che prevedano l'applicazione di perturbazioni magnetiche. Parte II, Analisi di trasporto. Il capitolo 3 si apre con la presentazione delle due configurazioni sperimentali adottate per RFX-mod ai fini delle analisi di trasporto. Negli esperimenti è stata utilizzata la sonda inseribile U-probe, che verrà descritta successivamente assieme alla teoria su cui si basano le misure da essa raccolte. Verranno quindi discussi i risultati derivanti dall'investigazione delle fluttuazioni elettrostatiche nella regione di bordo del plasma. Verranno di seguito presentati gli studi sui meccanismi di trasporto in differenti regioni topologiche in presenza di una perturbazione magnetica esternamente applicata. Tali risultati verranno mostrati per esperimenti condotti su RFX-mod sia in configurazione reversed-field pinch che in configurazione tokamak. Parte III, Analisi topologiche. Lo studio dei cambiamenti della topologia magnetica si sviluppa attraverso l'analisi di eventi spontanei di riconnessione magnetica in configurazione a campo rovesciato. Nel capitolo 4 verranno inizialmente discussi alcuni modelli di riconnessione magnetica. Verranno quindi presentati i cosiddetti eventi di crash all'interno di RFX-mod e verrà dettagliatamente descritta la tecnica di analisi adottata. Nella seconda parte del capitolo verranno descritti gli esperimenti effettuati sul tokamak COMPASS e su RFX-mod sfruttando un'altra sonda inseribile che ha lo scopo di analizzare il profilo di temperatura ionica. Parte IV, Conclusioni. Nel capitolo 5 sono raccolti e discussi i risultati della tesi. Infine, viene fornita una sezione in cui i principali risultati sono trattati sinteticamente insieme ai problemi rimasti aperti in vista di future prospettive di ricerca. Parte V, Appendici. In Appendice A è possibile trovare una descrizione dettagliata del formalismo della Magnetoidrodinamica mentre in Appendice B vengono trattate in dettaglio le equazioni per il trasporto utili ai fini della tesi.

Turbulence is a major factor limiting the achievement of better tokamak performance as it enhances the transport of particles, momentum and heat which hinders the foremost objective of tokamaks. Hence, understanding and possibly being able to control turbulence in tokamaks is of paramount importance, not to mention our intellectual curiosity of it. We take the first step by making measurements of turbulence using the 2D ($8$ radial $imes$ $4$ poloidal channels) beam emission spectroscopy (BES) system on the Mega Amp Spherical Tokamak (MAST). Measured raw data are statistically processed, generating spatio-temporal correlation functions to obtain the physical characteristics of the turbulence such as spatial and temporal correlation lengths as well as its motion. The reliability of statistical techniques employed in this work is examined by generating and utilizing synthetic 2D BES data. The apparent poloidal velocity of fluctuating density patterns is estimated using the cross-correlation time delay method. The experimental results indicate that the poloidal motion of fluctuating density patterns in the lab frame arises because the patterns are advected by the strong toroidal plasma flows while the patterns are aligned with the background magnetic fields which are not parallel to the flows. Furthermore, various time scales associated with the turbulence are calculated using statistically estimated spatial correlation lengths and correlation times of turbulence. We find that turbulence correlation time, the drift time associated with ion temperature or density gradients, the ion streaming time along the magnetic field line and the magnetic drift time are comparable and possibly scale together suggesting that the turbulence, determined by the local equilibrium, is critically balanced. Finally, we argue that we have produced a critical manifold in the experimentally obtained local equilibrium parameter space separating dominant turbulent transport from a non-turbulent or weakly turbulent state. It shows that the inverse ion-temperature-gradient scale length is correlated inversely with $q/arepsilon$ (safety factor/inverse aspect ratio) and positively with the plasma rotational shear. Practically, this means that we can attain the stiffer ion-temperature-gradient, thus hotter plasma core, without increasing the rotational shear.

Le contrôle du transport turbulent est l'une des clés pour l'amélioration du temps de confinement nécessaire à la réalisation de la fusion thermonucléaire contrôlée. La description de la turbulence cinétique du plasma est un problème à 3 coordonnées spatiales et 3 coordonnées en vitesse. La théorie comme la simulation pour un problème de si haute dimensionnalité sont très difficiles, et des modèles réduits sont nécessaires pour comprendre la turbulence dans les Tokamaks. La technique largement utilisée est de faire moyenner le mouvement cyclotron, qui est beaucoup plus rapide que le phénomène de turbulence. Une telle réduction permet de simplifier le problème à trois coordonnées spatiales des centres-guides des particules, une vitesse parallèle ou énergie et une vitesse perpendiculaire apparaissant comme l'invariant adiabatique. La description gyrocinétique non linéaire requiert des simulations numériques de haute performance massivement parallèles. Toute la difficulté est due aux termes non linéaires (crochets de Poisson) qui décrivent les interactions multi-échelles, ce qui constitue un défi tant pour la théorie que pour la simulation. Toute approche réduite, basée sur des hypothèses bien contrôlées, est donc intéressante à développer.Sur la base de cette ambition, cette thèse concerne la turbulence des particules piégées dans le plasma magnétisé. C'est un système 4D, obtenu après avoir fait la moyenne de la fonction de distribution des particules sur les mouvements cyclotron et de rebond, ce qui peut être considéré comme une forme réduite de la théorie gyrocinétique standard. Nous l'avons appelé "bounce averaged gyrokinetics" pendant ce travail. Même si cette description est grandement réduite par rapport à la théorie gyrocinétique, la simulation directe non-linéaire reste un challenge.Une description des termes non linéaires en coordonnées polaires est choisie, avec une grille logarithmique en norme du vecteur d'onde, tandis que les angles sont discrétisés sur une grille régulière. L'utilisation d'une grille logarithmique permet de prendre en compte une large gamme de vecteurs d'ondes, donc la physique à très petite échelle. De manière analogue aux modèles en couches en turbulence fluide et afin de simplifier le système, seules les interactions entre couches voisines sont considérées.Dans un premier temps, l'étude du système linéaire est présentée, en particulier les seuils des paramètres et l'instabilité linéaire permettant de retrouver la forte anisotropie des taux de croissance des modes d'ions piégés (ou TIM) et des modes d'électrons piégés (ou TEM). Ces études permettent également de valider les codes numériques non-linéaires vis-à-vis d'un solveur aux valeurs propres développé indépendamment.Dans un second temps, l'hypothèse isotrope pour les termes non linéaires est utilisée. Ainsi il n'y a pas d'information de phase exacte pour de tels modèles en couches 1D, ce qui laisse un paramètre libre dans les coefficients d'interaction. Une loi de puissance originale est mise en évidence, qui n'est pas affectée par la valeur du paramètre libre, mesurant l'intensité des effets non-linéaires relativement aux termes linéaires.À partir de la simulation du modèle isotrope, l'information de phase apparaît très importante. Puisque l'instabilité linéaire est anisotrope pour la fusion, la simulation du modèle anisotrope est donc réalisée dans un troisième temps. Le système résolu numériquement est réduit à une espèce cinétique, en supposant que les autres espèces sont adiabatiques. Deux systèmes différents peuvent ainsi être étudiés: ions cinétiques + électrons adiabatiques et électrons cinétiques + ions adiabatiques. Des spectres différents sont observés dans chacun de ces deux cas, et la validité de l'hypothèse adiabatique est discutée pour chaque espèce, avec pour base de comparaison une simulation cinétique à deux espèces
Turbulent transport is one of the keys to improve the energy confinement time required for thermonuclear fusion reactors. The description of the kinetic turbulence of the plasma is a problem with 3 spatial coordinates and 3 velocity coordinates. Both theory and simulation of a problem of such high dimensionality are very difficult, and reduced models are helpfull to understand turbulence in Tokamaks. A widely used technique consists into averaging the cyclotron motion, which is much faster than the turbulence time scale. Such a reduction makes it possible to simplify the problem to three spatial coordinates of the particle guide centers, a parallel velocity or energy, and a perpendicular velocity appearing as the adiabatic invariant. Nonlinear gyrokinetic description requires massively parallel high performance numerical simulations. The difficulty lies in the non-linear terms (Poisson hooks) that describe multi-scale interactions, which is a challenge for both theory and simulation. Any reduced approach, based on well-controlled hypotheses, is therefore interesting to develop.On the basis of this ambition, this thesis concerns the turbulence of particles trapped in magnetized plasma. It is a 4D system, obtained after averaging the particle distribution function on cyclotron and bounce motions, which can be considered as a reduced form of standard gyrokinetic theory. We called it "bounce averaged gyrokinetics" during this work. Even if this description is greatly reduced compared to the gyrokinetic theory, nonlinear direct simulation remains a challenge.A description of the nonlinear polar coordinate terms is chosen, with a logarithmic grid along the norm of the wave vector, while the angles are discretized on a regular grid. The use of a logarithmic grid makes it possible to take into account a wide range of wave vectors, so physics on a very small scale. In a similar way to shell models for fluid turbulence, and in order to simplify the system, only the interactions between neighboring shells are considered.In a first step, the study of the linear system is presented, in particular the paraetric dependence of the instability thresholds and the linear growth rate, allowing to recover the strong anisotropy of the growth rates of the trapped ion modes (or TIM) and the modes of trapped electrons (or TEM). These studies also make it possible to validate the non-linear numerical codes with respect to an independently developer eigenvalue solver.In a second step, the isotropic hypothesis for nonlinear terms is used. Thus, there is no exact phase information for such 1D layer models, which leaves with a free parameter in the interaction coefficients. An original power law is evidenced, which is unaffected by the value of the free parameter, measuring the intensity of the nonlinear effects relative to the linear terms.From the simulation of the isotropic model, the phase information appears very important. Since the linear instability is anisotropic for the fusion, the simulation of the anisotropic model is thus carried out in a third time. The numerically resolved system is reduced to a kinetic species, assuming that the other species are adiabatic. Two different systems can thus be studied: kinetic ions + adiabatic electrons and kinetic electrons + adiabatic ions. Different spectra are observed in each of these two cases, and the validity of the adiabatic hypothesis is discussed for each species, based on a kinetic simulation with two species

Dans cette thèse, nous nous sommes intéressés à l'interaction entre des écoulements cisaillés et la turbulence dans les plasmas chauds magnétisés. On s'est particulièrement focalisé sur l'étude de la dynamique complexe d'une barrière de transport et sur un moyen de contrôler ses oscillations de relaxations.

Renormalization group theory is applied to incompressible three-dimension Navier-Stokes turbulence so as to eliminate unresolvable small scales. The renormalized Navier-Stokes equation includes a triple nonlinearity with the eddy viscosity exhibiting a mild cusp behavior, in qualitative agreement with the test-field model results of Kraichnan. For the cusp behavior to arise, not only is the triple nonlinearity necessary but the effects of pressure must be incorporated in the triple term.;Renormalization group theory is also applied to a model Alfven wave turbulence equation. In particular, the effect of small unresolvable subgrid scales on the large scales is computed. It is found that the removal of the subgrid scales leads to a renormalized response function. (i) This response function can be calculated analytically via the difference renormalization group technique. Strong absorption can occur around the Alfven frequency for sharply peaked subgrid frequency spectra. (ii) With the {dollar}\epsilon{dollar} - expansion renormalization group approach, the Lorenzian wavenumber spectrum of Chen and Mahajan can be recovered for finite {dollar}\epsilon{dollar}, but the nonlinear coupling constant still remains small, fully justifying the neglect of higher order nonlinearities introduced by the renormalization group procedure.

A 2D-magnetohydrodynamic model of current-sheet dynamics caused by anomalous electrical resistivity as result of small-scale plasma turbulence is proposed. The anomalous resistivity is assumed to be proportional to the square of the gradient of the magnetic pressure as may be valid for instance in the case of lower-hybrid-drift turbulence. The initial resistivity pulse is given. Then the temporal and spatial evolution of the magnetic and electric fields, plasma density, pressure, convection and resistivity are considered. The motion of the induced electric field is discussed as indicator of the plasma disturbances. The obtained results found using much improved numerical methods show a magnetic field evolution with x-line formation and plasma acceleration. Besides, in the current sheet, three types of magnetohydrodynamic waves occur, fast magnetoacoustic waves of compression and rarefaction as well as slow magnetoacoustic waves.

The transport of heat out of tokamak plasmas by turbulence is the dominant mechanism limiting the performance of fusion reactors. Turbulence can be driven by the ion temperature gradient (ITG) and suppressed by toroidal equilibrium scale sheared flows. Numerical simulations attempting to understand, and ultimately reduce, turbulence are crucial for guiding the design and optimisation of future reactors. In this thesis, we investigate ion-scale turbulence by means of local gyrokinetic simulations in the outer core of the Mega Ampere Spherical Tokamak (MAST).We perform a parameter scan in the values of the ITG and the flow shear. We show that nonlinear simulations reproduce the experimental ion heat flux and that the experimentally measured values of the ITG and the flow shear lie close to the turbulence threshold. We demonstrate that the system is subcritical in the presence of flow shear, i.e., the system is formally stable to small perturbations, but transitions to a turbulent state given a large enough initial perturbation. We propose a scenario for the transition to subcritical turbulence previously unreported in tokamak plasmas: close to the threshold, the plasma is dominated by a low number of coherent long-lived structures; as the system is taken away from the threshold into the more unstable regime, the number of these structures increases until they fill the domain and a more conventional turbulence emerges. We make quantitative comparisons of correlation properties between our simulations and experimental measurements of ion-scale density fluctuations from the MAST BES diagnostic. We apply a synthetic diagnostic to our simulation data and find reasonable agreement of the correlation properties of the simulated and experimental turbulence, most notably of the correlation time, for which significant discrepancies were found in previous numerical studies of MAST turbulence. We show that the properties of turbulence are essentially functions of the distance to threshold, as quantified by the ion heat flux. We find that turbulence close to the threshold is strongly affected by flow shear, whereas far from threshold, the turbulence resembles a conventional ITG-driven, zonal-flow damped regime.

In tokamaks, turbulence is a key contributor to cross field transport. However, it is also responsible for the spontaneous generation of large scale structures such as zonal ows. These are of relevance to fusion plasmas as they can create transport barriers which aid plasma confinement. The interaction between drift waves and zonal ows can be investigated using reduced models such as the Hasegawa- Mima and Hasegawa-Wakatani equations. A four-wave truncated model is developed for the Extended-Hasegawa-Mima (EHM) equation. This produces a set of four ordinary differential equations (ODEs) that are used to investigate the modulational instability (MI), a mechanism by which drift waves can produce a zonal ow. These equations are linearised to produce a dispersion relation for the MI which is used to produce a set of maps of the linear growth rate of the MI. These show how additional modes become unstable as the gyroradius is increased. The truncated model and dispersion relation are then compared to measurements taken from simulations of the full EHM partial differential equation (PDE) which has been seeded with an appropriate initial condition. Good agreement is found when the pump wave has no component in the direction of the density gradient. A similar truncated model is derived for the Extended-Hasegawa-Wakatani (EHW) equations. As the EHW system has separate equations for density and potential this leads to a set of eight ODEs. The linearisation technique used for the EHM system cannot be applied here. Instead, approximations based on the built in EHW instability are made to calculate a linear growth rate for the zonal ow using the ODEs describing it. These analytical predictions are then compared to a full PDE simulation of the system, which is initialised using random noise. It is found that for particular sets of waves the ODEs provide a good prediction of the linear growth rate. A driving term is added to the EHM equation to reproduce the effect of the built in instability of the EHW equations. This causes a drift wave spectrum to grow when full EHW PDE simulations are seeded with random noise. The four-wave ODE model is updated to include this driving. The ODE model again produces good predictions for the growth rate of the zonal flow.

Plasma turbulence limits the performance of fusion reactors. Measuring and character- izing the turbulence properties is therefore a crucial issue in order to understand such phenomena. The goal of this thesis is to study the properties of plasma turbulence from ultrafast sweeping reflectometry measurements performed on the Tore Supra Tokamak. Reflectometry is a radar technique that is used to measure the electron density and its fluctuations. In the first part, we compare Langmuir probe and reflectometer data and discuss the possibility to characterize turbulence properties from the reconstructed fluctuating density profiles. Then, we show that the radial variation of the time and spatial scales of the turbulence as well as its radial velocity can be estimated from a cross-correlation analysis applied to the raw reflectometer signals. The modifications of the turbulence properties observed during a parametric scan are interpreted in the light of TEM and ITG turbulence. Finally, we show that the additional heating leads to a significant increase of the radial velocity in the plasma close to the tokamak wall.

Turbulence in the ionosphere is important to understand because it can negatively affect communication signals. This work examines different scenarios in the ionosphere in which turbulence may develop. The two main causes of turbulence considered in this work are the gradient drift instability (GDI) and the Kelvin-Helmholtz instability (KHI). The likelihood of the development of the GDI during the August 17, 2017 total solar eclipse is studied numerically. This analysis uses the ``Sami3 is Also a Model of the Ionosphere" (SAMI3) model to study the effect of the eclipse on the plasma density. The calculated GDI growth rates are small compared to how quickly the eclipse moves over the Earth. Therefore, the GDI is not expected to occur during the solar eclipse. A novel 2D electrostatic pseudo-spectral fluid model is developed to study the growth of these two instabilities and the problem of ionospheric turbulence in general. To focus on the ionospheric turbulence, a set of perturbed governing equations are derived. The model accurately captures the GDI growth rate in different limits; it is also benchmarked to the evolution of instability development in different collisional regimes of a plasma cloud. The newly developed model is used to study if the GDI is the cause of density irregularities observed in subauroral polarization streams (SAPS). Data from Global Positioning System (GPS) scintillations and the Super Dual Auroral Radar Network (SuperDARN) are used to examine the latitudinal density and velocity profiles of SAPS. It is found that the GDI is stabilized by velocity shear and therefore will only generate density irregularities in regions of low velocity shear. Furthermore, the density irregularities cannot extend through regions of large velocity shear. In certain cases, the turbulence cascade power laws match observation and theory. The transition between the KHI and the GDI is studied by understanding the effect of collisions. In low collisionality regimes, the KHI is the dominant instability. In high collisionality regimes, the GDI is the dominant instability. Using nominal ionospheric parameters, a prediction is provided that suggests that there exists an altitude in the upper textit{F} region ionosphere above which the turbulence is dominated by the KHI.
Doctor of Philosophy
In the modern day, all wireless communication signals use electromagnetic waves that propagate through the atmosphere. In the upper atmosphere, there exists a region called the ionosphere, which consists of plasma (a mixture of ions, electrons, and neutral particles). Because ions and electrons are charged particles, they interact with the electromagnetic communication signals. A better understanding of ionospheric turbulence will allow for aid in forecasting space weather as well as improve future communication equipment. Communication signals become distorted as they pass through turbulent regions of the ionosphere, which negatively affects the signal quality at the receiving end. For a tangible example, when Global Positioning System (GPS) signals pass through turbulent regions of the ionosphere, the resulting position estimate becomes worse. This work looks at two specific causes of ionospheric turbulence: the gradient drift instability (GDI) and the Kelvin-Helmholtz instability (KHI). Under the correct background conditions, these instabilities have the ability to generate ionospheric turbulence. To learn more about the GDI and the KHI, a novel simulation model is developed. The model uses a method of splitting the equations such that the focus is on just the development of the turbulence while considering spatially constant realistic background conditions. The model is shown to accurately represent results from previously studied problems in the ionosphere. This model is applied to an ionospheric phenomenon known as subauroral polarization streams (SAPS) to study the development of the GDI and the KHI. SAPS are regions of the ionosphere with large westward velocity that changes with latitude. The shape of the latitudinal velocity profile depends on many other factors in the ionosphere such as the geomagnetic conditions. It is found that for certain profiles, the GDI will form in SAPS with some of these examples matching observational data. At higher altitudes, the model predicts that the KHI will form instead. While the model is applied to just the development of the GDI and the KHI in this work, it is written in a general manner such that other causes of ionospheric turbulence can be easily studied in the future.

The goal of this work was to develop, introduce, and test a promising computational paradigm for the development of turbulence models for incompressible magnetohydrodynamics (MHD). MHD governs the behavior of an electrically conducting fluid in the presence of an external electromagnetic (EM) field. The incompressible MHD model is used in many engineering and scientific disciplines from the development of nuclear fusion as a sustainable energy source to the study of space weather and solar physics. Many interesting MHD systems exhibit the phenomenon of turbulence which remains an elusive problem from all scientific perspectives. This work focuses on the computational perspective and proposes techniques that enable the study of systems involving MHD turbulence. Direct numerical simulation (DNS) is not a feasible approach for studying MHD turbulence. In this work, turbulence models for incompressible MHD were developed from the variational multiscale (VMS) formulation wherein the solution fields were decomposed into resolved and unresolved components. The unresolved components were modeled with a term that is proportional to the residual of the resolved scales. Two additional MHD models were developed based off of the VMS formulation: a residual-based eddy viscosity (RBEV) model and a mixed model that partners the VMS formulation with the RBEV model. These models are endowed with several special numerical and physics features. Included in the numerical features is the internal numerical consistency of each of the models. Physically, the new models are able to capture desirable MHD physics such as the inverse cascade of magnetic energy and the subgrid dynamo effect. The models were tested with a Fourier-spectral numerical method and the finite element method (FEM). The primary test problem was the Taylor-Green vortex. Results comparing the performance of the new models to DNS were obtained. The performance of the new models was compared to classic and cutting-edge dynamic Smagorinsky eddy viscosity (DSEV) models. The new models typically outperform the classical models.

Experimental results concerning plasma turbulence pumped in theionosphere by powerful radio waves suggest that the turbulence is due todeterministic chaos. To investigate the possibility of deterministic chaosin the ionosphere coupled wave systems have been studied to see chaoticdynamics. If coupled waves can exhibit chaos it is a possible way tomodel ionospheric chaos. The result showed that chaos was present inboth wave systems studied which means that they could possibly explainthe chaos, to verify this more studies needs to be done on theparameters relevant to the coupled wave systems in the ionosphere andfind if they are in a regime where chaos develops
Studier av plasmaturbulens i jonosfären som pumpas av kraftfulla radiovågor antyder att turbulensen är kopplat till deterministiskt kaos. För att undersöka möjligheten för deterministiskt kaos i jonosfären studeras kopplade vågsystem om de kan innehålla kaotiska regimer. Om dessa system visar kaotiskt beteende skulle de kunna användas för att beskriva kaos i jonosfären. Resultatet visade att kaos var närvarande i de kopplade vågsystem som studerats, för att verifiera om de kan användas för att beskriva kaos i jonosfären måste närmare studier av de parametrar som modellen använder sig av göras för att se om de faller inom ett intervall där kaos uppstår.

Ce travail a porté sur l'étude des instabilités de gradient de température ioniques (ITG) en géométrie cylindrique, le champ magnétique étant supposé constant et dirigé selon l'axe du cylindre. Une fonction de distribution discrète en forme de marche d'escalier est utilisée pour décrire la direction de vitesse parallèle au champ magnétique. L'équation de Vlasov se résume à un système de type multi fluides couplés par l'équation de quasi neutralité. Chaque fluide est décrit par un système fermé d'équations (continuité, Euler et fermeture adiabatique), caractéristiques d'un fluide incompressible, d'ou la dénomination de sac d'eau ou “water bag”. Le recours à cette description water bag est particulièrement intéressant dans le cas de problèmes à une seule dimension en vitesse. Ainsi, dans le cas des plasmas fortement magnétisés, un modèle water bag peut se combiner avantageusement aux modèles dits girocinétiques. Les paramètres associés a la représentation water bag ont pu être identifiés et reliés aux grandeurs macroscopiques par le biais d'une méthode originale d'équivalence au sens des moments. L'analyse water bag des ITG a permis de valider le modèle et les méthodes choisies. Ce travail a également permis de montrer que le concept de water bag peut sans problème prendre en compte des effets variés comme ceux liés a l'introduction d'un rayon de Larmor fini, tout comme à la description d'un plasma composé de plusieurs espèces d'ions.

La turbulence au sein d’un plasma contribue de manière significative à l’augmentation du transport de l’énergie et des particules. Ce transport diminue la qualité de confinement du plasma réduisant la possibilité d’atteindre le seuil de fusion. Notre travail a consisté à étudier et à mesurer l’évolution des caractéristiques de la turbulence ainsi que son rôle durant la transition d’un mode à faible confinement (L-mode) à un mode de confinement amélioré (H-mode) des plasmas du tokamak ASDEX Upgrade. Nous avons, en particulier, étudié la phase de transition intermédiaire (I-phase) où la turbulence et le cisaillement des structures turbulentes par les flux interagissent. Une des théories prévoit que la turbulence au bord du plasma est stabilisée par des gradients de champs électriques radiaux: le cisaillement de flux E×B stabilise la turbulence et diminue la taille radiale des structures. Le mécanisme physique détaillé de la formation de la barrière de transport n’est pas encore bien compris. Afin d’étudier la dynamique radiale et temporelle de la transition L-H, nous nous sommes servis d’un réflectomètre à balayage en fréquence ultra-rapide. Durant nos campagnes expérimentales nous sommes parvenus à réduire ce temps de balayage à 1 μs. La dynamique de densité électronique, du niveau de turbulence et des spectres lors des transitions L-H ont été réalisées. Les mesures montrent que le niveau des fluctuations de grande échelle diminue après une transition L-H, ce qui confirme les prédictions théoriques. La I-phase a été documentée pour diverses conditions du plasma. Enfin, ces réflectomètres ont aussi permis l’observation de modes cohérents à haute fréquence au bord du plasma
Plasma confinement is limited by energy and particle transport, in which turbulence plays an important role. In this work the measurements of the turbulence characteristics carried out on the ASDEX Upgrade tokamak are presented during the transition from the Low (L) to the High (H) confinement mode which goes through an Intermediate (I) phase where turbulence and shear flows strongly interact. One of the most widely accepted theories concerning the L-H transition describes how the turbulence in the plasma edge is stabilized by radial electric field gradients: the E×B flow shear stabilizes turbulence and decreases the radial size of turbulent structures. As a consequence, a transport barrier forms in the edge where the plasma density, the temperature, and their gradients increase. The detailed physical mechanism of the formation of the transport barrier as well as the reason for the residual transport across this barrier are not yet well understood. The density dynamics is measured by an ultra-fast swept reflectometer with a time resolution as high as 1 μs. Studies of the electron density profile dynamics, the density turbulence level, radial wavenumber and frequency spectra during L-H transitions have been performed. The reflectometer measurements show that the density large scale fluctuations decrease after an L-H transition, which confirms the theoretical predictions of the turbulence reduction by sheared flows and supports previous experimental evidences. I-phases for various plasma conditions are documented and the density evolution is compared with the turbulence level. Moreover the results on high frequency coherent modes appearing at the plasma edge are presented

La reconnexion magnétique est un mécanisme fondamental de conversion d'énergie dans le plasma. Il se déroule dans les régions minces de fort courant appelées couches de courants, et produit le chauffage et l accélération des particules. Dans un milieu turbulent, la reconnexion magnétique a été observée dans de petites structures qui se forment dans celui-ci, et on a postulé que cela contribue de façon importante la dissipation de l'énergie turbulente l'échelle cinétique. Pour ce travail, nous examinons les données des satellites Custer dans la magnétogaine de la Terre, en aval du choc quasi-parallèle. La détection des couches de courant d'échelle ionique a été réalisé par l'application de la méthode de la variance partielle des incréments (PVI) pour des satellites multiples. Les proprietées des couches de courant observées étaient différentes pour des valeurs de l'indice PVI élevées(PV I > 3) et bas (PV I < 3). Nous avons observé une population distincte de haut indice PVI (> 3) structures qui représentaient ~ 20% du total. Ces couches de courant ont une rotation du champ magnétique élevée (> 90o). Afin d'estimer le chauffage local survenant dans ces couches de courant, une estimation de la température des électrons a été obtenue à haute résolution temporelle (125ms) parles distributions d'électrons partielles mesurées par Cluster. Cela a permis pour la première fois d'étudier le chauffage d'électrons localisés dans les couches de courant d'échelle ionique. L'augmentation observée de la température des électrons estimée dans les couches de courant aux PVI élevées suggèrent qu'ils sont importants pour le chauffage local d'électrons et de dissipation d'énergie. Nous avons également examiné les mesures l'intérieur de la région de diffusion d'une couche de courant o la reconnexion magnétique est en cours. Les observations simultanées par des satellites multiples permettent aussi d'étudier les distributions d'électrons et l'activité des ondes à des distances différentes de la ligne x. Des différences significatives ont été observées dans les populations d'électrons comme ils ont été chauffés en passant par la couche de courant. En particulier, les électrons sont chauffés dans la direction parallèle au champ magnétique proximité de la ligne x, alors qu'aucune variation significative n'a été observée dans la direction perpendiculaire. Cependant,la distribution est plus isotrope en aval de la ligne x, chauffées par des électrons dans la direction perpendiculaire
Magnetic reconnection is a fundamental energy conversion process in plasma. It occurs in thin regions of strong current known as current sheets and results in particle heating and acceleration. In turbulence, which is ubiquitous in space plasma, magnetic reconnection has been observed to occur in small scale structures that form therein, and is thought to contribute to dissipation of turbulent energy at kinetic scales. For this work we examine data from the Cluster spacecraft in the Earth's magnetosheath, downstream of the quasi-parallel shock. The detection of ion-scale current sheets was performed by implementing the PartialVariance of Increments (PVI) method for multiple spacecraft. The properties of the observed current sheets were different for high (> 3) and low (< 3) values of the PVI index. We observed a distinct population of high PVI (> 3) structures that accounted for ~ 20% of the total. Those current sheets have high magneticshear (> 90degrees). In order to estimate the local heating occurring within those current sheets, a proxy of the electron temperature was obtained at high time resolution(125ms) from the partial distributions measured by Cluster. This allowed for the first time to study the localized electron heating within ion-scale currentsheets. The observed enhancement of the estimated electron temperature withinthe high PVI current sheets suggest that they are important for local electron heating and energy dissipation. We also examined measurements inside the diffusion region of a thin reconnecting current sheet. Multi-spacecraft observationsallow as to study electron distributions and wave activity at different distances from the x-line. Significant differences were observed in the electron populations as they were heated going through the current sheet. In particular electrons were heated in the direction parallel to the magnetic field in close proximity to thex-line, whereas no significant variation was observed in the perpendicular direction. However, the distribution was more isotropic downstream of the x-line with electrons heated in the perpendicular direction

La fusion nucléaire est une solution technologique prometteuse pour une nouvelle source d'énergie. Cependant, utiliser la par fusion nucléaire confinement magnétique comme source d'énergie constitue un challenge scientifique et technologique car cela requière à la fois un bon confinement du plasma de cœur et un contrôle des flux de chaleurs arrivant à la paroi. Ce travail est motivé par la problématique de la gestion des flux de chaleur dans les réacteurs de fusion. Cela est nécessaire pour éviter d'endommager les coûteux composants faisant face au plasma. La compréhension des mécanismes physiques régissant le transport de la chaleur dans le plasma de bord est une tâche critique pour le design des futures machines. Dans ce contexte, il est nécessaire de faire des prédictions fiables de l'étalement de la chaleur dans le but de dimensionner correctement ces futures machines. Cela appelle à un fondement théorique décrivant la manière dont l'énergie s'échappe du plasma. Des études théoriques et expérimentales ont tenté aboutir à cette fin, cependant les mécanismes en jeux ne sont toujours pas clairs. Pour atteindre ce but, la modélisation numérique est un complément nécessaire aux expériences. Ce travail de thèse est dédié à l'étude numérique des différents aspects du transport de la chaleur dans le plasma de bord un utilisant les approches fluides. Une attention particulière est porté à deux mécanismes suspectés de joué un grand rôle dans le transport de la chaleur : le transport intermittent due à la turbulence et le transport convectif à large échelle par les vitesses dérives. Le problème a été traité avec une approche graduelle en utilisant différent outils numériques
Fusion devices are a promising solution for a new source of energy. However, using fusion reaction to produce power within a magnetic confinement is a scientific and technological challenge as it requires a high confinement in the core plasma at the same time as a good control of plasma exhaust on the material walls. This work is motivated by the key problematic of power handling in fusion power plants necessary to avoid damaging the expensive plasma facing components (PFC). The understanding of the physics underlying the heat transport, and more specifically is a critical task for the engineering design of future Tokamak devices. In this context, it is mandatory to make reliable predictions of the power spreading in order to correctly size the future Tokamaks. This calls for a theoretical ground describing the way energy escapes the core plasma through the separatrix and deposits on the PFCs. Some theoretical and experimental studies attempt to achieve such a task, however no definitive conclusion have been drawn yet. To achieve this goal, numerical modelling is a necessary complement to experimental results. This PhD work has been dedicated to the study of the different aspects of the heat transport in the edge plasma using a numerical fluid approach. Special focus was devoted to two types of mechanisms suspected to play an important role in the heat transport: intermittent turbulence; the large-scale convective transport

Cette thèse s'inscrit dans le contexte de l'étude de l'auto-organisation des plasmas chauds magnétisés. Nous nous intéressons en particulier aux deux objets que sont les étoiles et les tokamaks. Nous les étudions à l'aide de simulations numériques en utilisant des codes premiers principes dans le contexte des phénomènes de turbulence, de transport et de confinement dans les plasmas. La première partie de cette thèse s'attache à donner une introduction sur les caractéristiques des plasmas des étoiles et des tokamaks, ainsi que sur les raisons qui nous ont poussé à les étudier conjointement. Puis, nous développons en deuxième partie des travaux appliqués aux étoiles. A l'aide de simulations numériques, nous étudions pour la première fois en géométrie sphérique et en 3D l'interaction des mouvements turbulents avec un champ magnétique interne dans le Soleil, dans la région de la tachocline qui agit comme une barrière de transport du moment cinétique. Nous montrons qu'un tel champ magnétique ne peut expliquer l'épaisseur de la tachocline que nous observons, et donnons des pistes de réflexion pour comprendre cette épaisseur. Nous explorons également dans cette partie les implications que l'environnement d'une étoile (en particulier le vent de l'étoile, et les planètes gravitant autour) peut avoir sur son organisation interne. Cette étude nous permet aussi d'étudier l'interaction des vents stellaires avec les magnétosphères planétaires qui agissent comme des barrières de transport pour la matière. Des travaux spécifiques aux tokamaks sont ensuite présentés dans une troisième partie. Nous y développons une étude numérique des mécanismes expérimentaux conduisant à la création de barrières de transport dans les tokamaks. Ces barrières de transport permettent l'accès à des régimes de fusion nucléaire performants. Pour la première fois, nous montrons théoriquement comment déclencher la formation de ces barrières dans des simulations turbulentes de codes premiers principes. Enfin, la dernière partie présente les résultats des réflexions communes issue de cette thèse fai- sant le pont entre deux communautés scientifiques. L'utilisation d'une méthode spectrale originale pour l'analyse de phénomènes multi-échelles y est exposée. Elle est successivement développée puis appliquée pour mettre en évidence les mécanismes de saturation de la dynamo stellaire et de l'instabilité du gradient de température ionique dans les tokamaks. Un modèle unique traitant de l'interaction entre la turbulence et les écoulements de grande échelle est ensuite développé à la fois dans le contexte de la tachocline solaire et dans celui des tokamaks, formalisant l'analogie qui existe entre les deux objets de notre étude.

L'effet des fluctuations de vitesse sur le seuil de la dynamo, de l'induction magnétique, et ainsi que des effets non linéaires présents dans le régime de saturation sont étudiés avec une sélection de huit articles. Ces thèmes ont été abordés à travers des simulations numériques dans un domaine périodique tri-dimensionnel. Des simulations numériques directes (DNS) et des méthodes de modélisation sous maille (LES) de la turbulence, ont permis de mettre en évidence l'effet des fluctuation sur le seuil et de nombreux modes de dynamo engendrés dans des écoulements entretenus par différents forçages (Taylor-Green, ABC et G.O. Robert). Dans ces systèmes MHD pendant la phase de saturation, des effets non-linéaires apparaissent, comme des bifurcations sous critiques associées à des cycles d'hystérésis, ainsi qu'un comportement de turbulence intermittente On-Off. Une discussion et des perspectives sur ces thèmes sont présentées, ainsi qu'une annexe sur les méthodes numériques et les diagnostiques ayant été utilisés dans ces travaux.

Magnetic reconnection is a universal process occurring at boundaries between magnetized plasmas, where changes in the topology of the magnetic field lead to the transport of charged particles across the boundaries and to the conversion of electromagnetic energy into kinetic and thermal energy of the particles. Reconnection occurs in laboratory plasmas, in solar system plasmas and it is considered to play a key role in many other space environments such as magnetized stars and accretion disks around stars and planets under formation. Magnetic reconnection is a multi-scale plasma process where the small spatial and temporal scales are strongly coupled to the large scales. Reconnection is initiated rapidly in small regions by microphysical processes but it affects very large volumes of space for long times. The best laboratory to experimentally study magnetic reconnection at different scales is the near-Earth space, the so-called Geospace, where Cluster spacecraft in situ measurements are available. The European Space Agency Cluster mission is composed of four-spacecraft flying in a formation and this allows, for the first time, simultaneous four-point measurements at different scales, thanks to the changeable spacecraft separation. In this thesis Cluster observations of magnetic reconnection in Geospace are presented both at large and at small scales.

At large temporal (a few hours) and spatial (several thousands km) scales, both fluid and kinetic evidence of reconnection is provided. The evidence consist of ions accelerated and transmitted across the Earth’s magnetopause. The observations show that component reconnection occurs at the magnetopause and that reconnection is continuous in time.

The microphysics of reconnection is investigated at smaller temporal (a few ion gyroperiods) and spatial (a few ion gyroradii) scales. Two regions are important for the microphysics: the X-region, around the X-line, where reconnection is initiated and the separatrix region, away from the X-line, where most of the energy conversion occurs. Observations of a separatrix region at the magnetopause are shown and the microphysics is described in detail. The separatrix region is shown to be highly structured and dynamic even away from the X-line.

Finally the discovery of magnetic reconnection in turbulent plasma is presented by showing, for the first time, in situ evidence of reconnection in a thin current sheet found in the turbulent plasma downstream of the quasi-parallel Earth’s bow shock. It is shown that turbulent reconnection is fast and that electromagnetic energy is converted into heating and acceleration of particles in turbulent plasma. It is also shown that reconnecting current sheets are abundant in turbulent plasma and that reconnection can be an efficient energy dissipation mechanism.

L'objectif de la fusion par confinement magnétique, et notamment du tokamak, est de produire de l'énergie à partir des réactions de fusion nucléaire, dans un plasma à faible densité et haute température. Expérimentalement, une amélioration de la performance des tokamaks a été observée en présence de rotation toroïdale. Or, les sources extérieurs de quantité de mouvement seront très limitées dans les futurs tokamaks, et notamment ITER. Une compréhension de la physique de la génération intrinsèque de rotation toroïdale permettrait donc de prédire les profils de rotation dans les expériences futures. Parmi les mécanismes envisagés, on s'intéresse ici à la génération de rotation par la turbulence, qui domine le transport de la chaleur dans les tokamaks. Les plasmas de fusion étant faiblement collisionnels, la modélisation de cette turbulence suppose un modèle cinétique décrivant la fonction de distribution des particules dans l'espace des phases à six dimensions (position et vitesse). Cependant, ce modèle peut être réduit à cinq dimensions pour des fréquences inférieures à la fréquence cyclotronique des particules. Le modèle gyrocinétique qui découle de cette approximation est alors accessible avec les ressources numériques actuelles. Les travaux présentés portent sur l'étude du transport de quantité de mouvement toroïdale dans les plasmas de tokamak, dans le cadre du modèle gyrocinétique. Dans un premier temps, nous montrons que ce modèle réduit permet une description précise du transport de quantité de mouvement en dérivant une équation locale de conservation. Cette équation est vérifiée numériquement à l'aide du code gyrocinétique GYSELA. Ensuite, nous montrons comment la turbulence électrostatique peut briser l'axisymétrie du système, générant ainsi de la rotation toroïdale. Un lien fort entre transport de chaleur et transport de quantité de mouvement est mis en évidence, les deux présentant des avalanches à grande échelle. La dynamique du transport turbulent est analysée en détail et, bien que l'estimation standard gyro-Bohm soit vérifiée en moyenne, des phénomènes non-diffusifs sont observés. L'effet des écoulements de bord du plasma sur la rotation toroïdale dans le coeur est étudié en modifiant les conditions aux bords dans le code GYSELA. Enfin, le champ magnétique d'équilibre, qui n'est pas rigoureusement axisymétrique, peut également participer à la génération de rotation toroïdale, via des mécanismes purement collisionnels. Dans un tokamak, cet effet est suffisamment important pour entrer en compétition avec la rotation générée par la turbulence électrostatique.

La fusion par confinement magnétique est prometteuse en tant que future source d’énergie. Son efficience est cependant limitée par le transport de particules et de chaleur résultant de la turbulence du plasma. Une compréhension approfondie de la turbulence et des mécanismes qui la tempère est donc nécessaire. Le mode géo-acoustique (GAM) est une oscillation de l’écoulement du plasma, radialement localisée, qui contribue à la réduction du transport turbulent en cisaillant le champ de vitesse. Dans cette thèse on étudie le comportement fondamental du GAM par une étude expérimentale systématique de ses propriétés dans le tokamak ASDEX Upgrade. En particulier, le rôle de la géométrie du plasma sur les lois d’évolution de la fréquence et de l’amplitude du GAM, ainsi que sa structure radiale sont étudiés en détail. Les données expérimentales ont été obtenues à l'aide du diagnostic de réflectométrie Doppler par micro-ondes. Le type d’évolution de la fréquence du GAM est comparé à de multiples modèles qui reproduisent la loi de comportement fondamental attendu, mais sans fournir de prédiction précise de manière satisfaisante. L'amplitude GAM est étudiée en relation avec les taux d'amortissement prédits par les modèles pour les processus d'amortissement collisionnel et Landau non collisionnel. On trouve que les effets de largeur d'orbite finie doivent être pris en compte et que les effets d'amortissement collisionnel ne peuvent pas être négligés. En étudiant la structure radiale du GAM, trois états distincts sont identifiés pour différentes conditions de plasma. Les transitions entre ces états sont observées en variant la géométrie du plasma
Magnetic confinement fusion is a promising candidate for a future energy source. Its efficiency is limited by particle and heat transport due to plasma turbulence. A thorough understanding of the turbulence and turbulence moderation mechanisms, is therefore needed. The geodesic acoustic mode (GAM) is a radially localised plasma flow oscillation which contributes to the reduction of turbulent transport through velocity shearing. This thesis investigates the fundamental behaviour of the GAM through a systematic experimental study of its properties in the ASDEX Upgrade tokamak. In particular, the role of the plasma geometry on the scaling of the GAM frequency and amplitude, as well as the GAM radial structure are investigated in detail. The experimental data was obtained with the aid of the microwave Doppler reflectometry diagnostic. The GAM frequency scaling is compared with multiple models which reproduce the expected fundamental scaling behaviour, but do not give a satisfyingly accurate prediction. The GAM amplitude is studied in connection with damping rates predicted by models for collisional and collisionless Landau damping processes. It is found that finite orbit width effects need to be considered and that collisional damping effects cannot be neglected. In studying the GAM radial structure, three distinct states are identified for different plasma conditions. Transitions between these states are observed under variations of the plasma geometry

La turbulence tridimensionnelle se caractérise par sa capacité à transférer de l'énergie des grandes vers les petites échelles où elle est finalement dissipée. Lorsqu'elle se produit dans un plasma non-collisionnel comme le vent solaire, une modélisation cinétique semble a priori nécessaire. Toutefois, la complexité d'une telle approche limite les développements théoriques et condamne les expériences numériques à se restreindre à des nombres de Reynolds peu élevés. Dans quelles mesures un modèle mono-fluide comme la MHD Hall permet-il de rendre compte des phénomènes observés dans le vent solaire aux échelles sub-ioniques ? C'est la problématique à laquelle s'est attaquée cette thèse. L'idée directrice de ce travail est de tirer profit de la relative simplicité des modèles fluides et de la puissance algorithmique des méthodes pseudo-spectrales pour aborder la turbulence du vent solaire par des simulations numériques directes tridimensionnelles massivement parallèles à grands nombres de Reynolds. Ces simulations numériques ont permis de mettre en évidence l'existence d'une brisure spontanée de symétrie chirale en turbulence MHD Hall incompressible, ainsi que l'existence d'un nouveau régime appelé ion MHD (IMHD). Un modèle phénoménologique a été proposé pour rendre compte de ces résultats et de nouvelles prédictions ont été faites, puis confirmées numériquement. Enfin, l'étude de l'effet d'un fort champ magnétique uniforme sur la dynamique turbulente a permis de confirmer pour la première fois une ancienne conjecture. L'inertie des électrons a ensuite été prise en compte toujours dans un modèle fluide. Par une approche hydrodynamique classique, une loi universelle a été obtenue pour les fonctions de structure d'ordre trois. L'ensemble de ces résultats est qualitativement en accord avec les mesures in situ du vent solaire et remet en cause le paradigme selon lequel les raidissements successifs du spectre des fluctuations magnétiques sont provoqués nécessairement par des phénomènes d'origine cinétique. De manière plus générale, cette thèse soulève des questions fondamentales sur les processus non-collisionnels de dissipation dans les plasmas turbulents.

The purpose of this project is to investigate the spectral properties of turbulence in the magnetosheath of Saturn, using in-situ magnetic field measurements from the Cassini spacecraft. According to models of incompressible, turbulent fluids, the energy spectrum in the inertial range scales as the frequency to the power of -5/3, which has been observed in the near-Earth Solar wind but not in the Terrestrial magnetosheath unless close to the magnetopause. 120 time intervals for when Cassini is inside the magnetosheath are identified — 40 in each category of behind quasi-perpendicular bow shocks, behind quasi-parallel bow shocks, and inside the middle of the magnetosheath. The power spectral density is thereafter calculated for each interval, with logarithmic regressions performed at the MHD and sub-ion scales separated by the ion gyrofrequency. The results seem to indicate similar behaviour as in the magnetosheath of Earth, without significant difference between quasi-perpendicular and quasi-parallel cases except somewhat steeper exponents at the MHD scale for the former. These observations confirm the role of the bow shock in destroying the fully developed turbulence of the Solar wind, thus explaining the absence of the inertial range.
Syftet med detta projekt är att undersöka de spektrala egenskaperna hos turbulens i Saturnus magnetoskikt, med in-situ-mätningar av magnetfältet från Cassini-rymdsonden. Enligt modeller av inkompressibla, turbulenta fluider, är energispektrumet i det intertiala omfånget proportionellt mot frekvensen upphöjd i -5/3, vilket har observerats i den jordnära Solvinden men inte i det jordiska magnetoskiktet förutom nära magnetopausen. 120 tidsintervall för när Cassini befinner sig inuti magnetoskiktet identifieras — 40 styck i kategorierna bakom kvasi-vinkelräta bogchockar, bakom kvasi-parallella bogchockar, och inuti mellersta delen av magnetoskiktet. Effektspektraltätheten beräknas därefter för varje intervall, med logaritmiska regressioner på MHD- och subjon-skalorna som separeras av jongyrofrekvensen. Resultaten verkar tyda på liknande beteende som i Jordens magnetoskikt, utan märkvärdig skillnad mellan kvasi-vinkelräta och kvasi-parallella fall förutom något brantare exponenter på MHD-skalan för de förnämnda. Dessa observationer bekräftar bogchokens roll i förstörandet av den fullt utvecklade turbulensen i Solvinden, därmed förklarande avsaknaden av det inertiala omfånget.

Le contrôle de la turbulence dans les tokamaks est essentiel dans le cadre de la production d'énergie en régime stationnaire. Par ailleurs, les systèmes de chauffage produisent des particules énergétiques. Lorsque turbulence et particules énergétiques coexistent, leur interaction doit être prise en compte. Ceci constitue le cadre de ce manuscrit. Nous analysons (1) la génération de particules énergétiques et (2) l'impact de ces particules sur la turbulence. La génération de particules énergétiques est étudiée en quantifiant l'effet des particules énergétiques sur les propriétés des décharges ICRH d'ITER et introduisons la possibilité d'une anisotropie dans l'espace de vitesses, essentielle pour la modélisation de scénarios ICRH. Ceci est fait à travers le couplage d'un code full-wave 3D appelé EVE et d'un module appelé AQL, qui résout l'équation de Fokker-Planck en vitesse parallèle et perpendiculaire. L'effet des particules énergétiques sur la turbulence est mis en évidence à travers le code GYSELA en deux étapes. Dans un premier temps, nous démontrons l'excitation d'une classe de mode de particules énergétiques dans le domaine de la fréquence acoustique (EGAMs). Dans un second temps, les EGAMs sont excités en la présence de turbulence dans des simulations à forçage par le flux. Nous montrons que les EGAMs et la turbulence interagissent d'une manière extrêmement complexe. Notamment, nous montrons que le contrôle de la turbulence à travers un cisaillement oscillant excité par des particules énergétiques n'est pas immédiat. D'une part, la turbulence semblerait se propager en la présence d'EGAMs. D'autre part, le transport turbulent est modulé à la fréquence EGAM.

Le transport turbulent d'un plasma de décharge à travers un champ magnétique toroïdal a été étudié par diffusion collective de la lumière. Cette technique permet d'accéder à la transformée de Fourier spatiale des fluctuations de densité, résolue en temps. La continuité entre la diffusion incohérente et la diffusion collective a été montrée, justifiant par la même l'interprétation de la diffusion de la lumière aux grandes échelles comme étant une diffusion sur les fluctuations de la densité fluide. Un calcul a pour cela été mené, prenant en compte le caractère discret des particules diffusantes (les électrons) et les fluctuations induites par le mouvement thermique des différentes particules du plasma. Il en résulte que le caractère discret des diffuseurs est négligeable, quoique potentiellement sensible. Les conditions dans lesquelles il est possible d'identifier la fonction d'auto corrélation du signal diffusé à la fonction caractéristique de la distribution des déplacements turbulents ont par ailleurs été écrites. L'état stationnaire du plasma a été étudié et les fluctuations de densité, de température et de potentiel ont été observées simultanément, au moyen d'une sonde de Langmuir rapide. L'ajout d'une petite composante verticale au champ magnétique toroïdal permet d'obtenir un plasma uniforme. Le facteur de forme du plasma, sans et avec champ magnétique vertical additionnel, a été mesuré en fonction du vecteur d'onde d'analyse k en unités absolues. Les fonctions d'auto corrélation du signal diffusé, identifiées à la fonction caractéristique du déplacement turbulent, ont été analysées. Il s'est avéré que la statistique du déplacement turbulent à un temps donné présente les caractéristiques d'une marche de Lévy, avec un paramètre α proche de 1. La distribution du déplacement turbulent s'éloigne donc d'une gaussienne et se rapproche d'une lorentzienne. Il s'agit d'une mesure expérimentale qui peut être rapportée directement aux modèles théoriques.

Consideramos um modelo hamiltoniano do movimento eletrostático de deriva para investigar o trasnporte caótico de partículas na borda de plasmas confinados em Tokamaks. Este modelo leva em conta a turbulência eletrostática de deriva, responsável pelo transporte anômalo. O modelo Hamiltoniano provê as equações de movimento, que são dependentes de uma função para o potencial elétrico. Esta função é caracterizada por um potencial de equilíbrio mais um termo correspondente às ondas de deriva. Assumimos três diferentes perfis radiais para o campo elétrico radial de equilíbrio: um linear e outros dois não-monotônicos com extremos suaves. Para estes perfis, mostramos que o modelo pode ser reduzido a três mapas simpléticos bidimensionais e não integráveis: o mapa padrão, o mapa padrão não twist e um mapa modelo não twist introduzido neste trabalho. O mapa padrão não twist e o mapa modelo violam a condição twist, fundamental para os teoremas KAM e de Birkhoff. Para estes mapas não twist, estudaremos numericamente barreiras de transporte criadas próximas às curvas shearless. Mostramos que, para o mapa modelo, a barreira de transporte é robusta, isto é, persiste em um amplo intervalo de variação de um de seus parâmetros. Dentro da região da barreira, descrevemos o nascimento de cadeias de ilhas com períodos par e ímpar devido à variação do parâmetro de controle. Analisamos estes dois cenários calculando os números de rotação dentro da barreira e identificando as bifurcações que criam as ilhas. Finalmente, conjecturamos que todas as ilhas dentro da região da barreira são criadas por estes dois cenários. Além disso, se o número de rotação da curva shearless atinge um número racional, as cadeias de ilhas são criadas de acordo com os cenários descritos.
We consider a hamiltonian model of the electrostatic drift motion to investigate chaotic particle transport in the Tokamak plasma edge. This model takes into account the electrostatic drift turbulence, which is responsible for the anomalous transport. The Hamiltonian model provides the basic equations of motion, which are dependent on the form of an electric potential function. This function is characterized by the equilibrium potential and the term corresponding to the drift waves. We assume three diferent radial profiles for the equilibrium radial electric field: one linear and the other two non-monotonic with a smooth extremum. For these profiles, we show that the model can be reduced to three symplectic maps: the standard map, the nontwist standard map, and a nontwist model map introduced in this work. The nontwist standard map and the model map violate the twist condition, a property of fundamental importance for the applicability of the KAM and Birkhoff theorems. For these nontwist maps, we study numerically the transport barriers created around their shearless curves. We show for the model map that the transport barrier is robust,i.e., remains for a wide range of one of its parameters. Inside the barrier region, we describe the birth of island chains with even or odd periods due to the control parameter variation. We analyse these two scenarios by calculating the winding numbers inside the barrier region and identifying the bifurcations that create the islands. Finally, we conjecture that all the island chains inside the barrier are created by these two scenarios. Moreover, if the winding number of the shearless curve reachs a rational number, the island chains are created according to the described scenarios.

Etude de l'intermittence, un type de transition vers la turbulence rencontre en convection et dans la réaction de Belousov-Zhabotinsky. La mesure invariante dépend continument du paramètre de bifurcation. Etude d'un modèle de couplage résonnant d'ondes de dérivé dans une limite de dissipation forte par des méthodes perturbatives et l'utilisation du théorème de la variété stable. Etude de la génération périodique de solitons dans l'équation de Schrödinger cubique avec source. Travail de synthèse sur les méthodes de moyennisation et les théorèmes adiabatiques.

O Texas Helimak é uma máquina toroidal de confinamento de plasma cujas linhas de campo magnético têm forma helicoidal e no qual parâmetros do plasma (como a densidade e a temperatura) são similares aos da borda e da região externa (scrape-off-layer) de um tokamak. Nesta tese foram analisados o equilíbrio e as flutuações do plasma no Texas Helimak. São apresentadas a análise e a interpretação do controle da turbulência eletrostática e do transporte turbulento de partículas pelo potencial elétrico, bias, aplicado externamente. As alterações na turbulência e no transporte causadas pela mudança do potencial elétrico externo foram investigadas em uma região do plasma com gradientes radiais uniformes. As flutuações em descargas com bias positivo ou nulo apresentam espectros de potência de banda larga e uma PDF com uma cauda acentuada que revela a ocorrência intermitente de eventos extremos. Por outro lado, as flutuações em descargas com bias negativo possuem um espectro de potência mais estreito, uma PDF mais Gaussiana e um diagrama de recorrência com mais estruturas. Um modelo de quatro ondas acopladas foi utilizado para relacionar a largura de banda da turbulência com o tempo de interação entre as ondas do modelo. Perfis radiais do transporte turbulento de partículas na direção radial foram calculados, como função do bias, e comparados com os perfis da velocidade do fluxo de plasma e seu cisalhamento. Foi mostrado que o transporte depende do perfil radial da velocidade de fluxo do plasma. Nas descargas em que essa velocidade apresenta um ponto de máximo em seu perfil radial, o perfil do transporte possui um mínimo que foi interpretado, utilizando um modelo Hamiltoniano de ondas de deriva, como sendo resultado de uma barreira de transporte onde o cisalhamento do fluxo é nulo. Em outras descargas, máximos no perfil radial do transporte foram relacionados a ressonâncias que ocorrem onde a velocidade de fase da onda é igual à velocidade do plasma.
The Texas Helimak is a toroidal confinement of plasma device with helically magnetic field lines and which plasma parameters (like the density and temperature) are similar to the edge and the scrape-off-layer of a tokamak. This thesis analyzed the equilibrium and fluctuations in the Helimak Texas plasma. We present the analysis and interpretation of electrostatic control of turbulence and turbulent particle transport by electrical potential, bias, applied externally. Changes in transport and turbulence caused by the change of external electric potential were investigated in a region of uniform radial gradients plasma. Fluctuations in discharges with positive or zero bias have broadband power spectra and a PDF with an accentuated tail that reveals the intermittent occurrence of extreme events. Moreover, fluctuations in discharges with negative bias have narrow power spectra, a more Gaussian PDF and more structures in the recurrence diagram. A four coupled wave model was used to relate the bandwidth of turbulence with the interaction time between the waves in the model. Radial profiles of turbulent transport of particles in the radial direction were calculated as a function of bias and compared to the profiles of the plasma flow velocity and its shear. It was shown that the transport depends on the radial profile of the plasma flow velocity. In that discharges where the velocity radial profile presents a point of maximum, the transport profile has a minimum which was interpreted, using a drift wave model Hamiltonian, as a result of a shearless flow transport barrier. In other discharges, the maxima in the transport radial profiles were related with resonances that occur where the wave phase velocity is equal to the plasma velocity.

Electromagnetic waves can be used to transmit information over long distances and are therefore often employed for communication purposes. The electromagnetic waves are reflected off material objects on their paths and interact with the medium through which they propagate. For instance, the plasma in the ionosphere can refract and even reflect radio waves propagating through it. By increasing the power of radio waves injected into the ionosphere, the waves start to modify the plasma, resulting in the generation of a wide range of nonlinear processes, including turbulence, in particular near the reflection region. By systematically varying the injected radio waves in terms of frequency, power, polarisation, duty cycle, inclination, etc. the ionosphere can be used as an outdoor laboratory for investigating fundamental properties of the near-Earth space environment as well as of plasma turbulence. In such ionospheric modification experiments, it has been discovered that the irradiation of the ionosphere by powerful radio waves leads to the formation of plasma density structures and to the emission of secondary electromagnetic radiation, a phenomenon known as stimulated electromagnetic emission. These processes are highly repeatable and have enabled systematic investigations of the nonlinear properties of the ionospheric plasma. In this thesis we investigate features of the plasma density structures and the secondary electromagnetic radiation. In a theoretical study we analyse a certain aspect of the formation of the plasma structures. The transient dynamics of the secondary radiation is investigated experimentally in a series of papers, focussing on the initial stage as well as on the decay. In one of the papers we use the transient dynamics of the secondary radiation to reveal the intimate relation between certain features of the radiation and structures of certain scales. Further, we present measurements of unprecedentedly strong secondary radiation, attributed to stimulated Brillouin scattering, and report measurements of the secondary radiation using a novel technique imposed on the transmitted radio waves.

Les scénarios avancés, développés depuis moins d'une dizaine d'année avec la découverte des barrières internes de transport et la maîtrise du profil de courant, insufflent un nouvel élan au tokamak en direction d'un futur réacteur à fusion thermonucléaire contrôlée. Le Joint European Torus (JET) installé au Royaume-Uni, est actuellement le dispositif expérimental le plus performant au monde en terme de puissance fusion. Il a permis d'acquérir une riche expertise sur ces régimes à confinement amélioré. La réduction du transport turbulent, désormais indissociable de l'optimisation de la forme du profil de courant - obtenue par exemple avec l'onde hybride ou le courant autogénéré de bootstrap, peut être caractérisée simplement à l'aide d'un critère qui donne accès à la plupart des informations utiles concernant les barrières . Ses deux principaux domaines d'utilisation sont l'analyse des bases de données et les applications temps réel. Les modèles de transport dits de courbe en « S » exhibent des propriétés intéressantes que conforte l'expérience, tandis que les dépendances non-linéaires et multivariables de la diffusivité thermique du plasma peuvent être approchées grâce à un réseau de neurones, suggérant un nouveau moyen d'investigation et de modélisation du transport. Enfin, les toutes premières démonstrations expérimentales de contrôle en temps réel des barrières internes de transport et du profil de courant ont été réalisées sur JET, ouvrant la voie à des systèmes d'asservissement sophistiqués.

Incoherent scatter radar (ISR) measurements were used in conjunction with plasma simulations to study two micro-scale plasma processes that commonly occur in the auroral ionosphere. These are 1) ion acoustic turbulence and 2) Langmuir turbulence. Through an ISR experiment we investigated the dependence of ion acoustic turbulence on magnetic aspect angle. The results showed a very strong aspect angle sensitivity which could be utilized to classify the turbulence according to allowable generation mechanisms and sources of free energy. In addition, this work presents results that led to the discovery of a new type of ISR echo, explained as a signature of cavitating Langmuir turbulence. A number of incoherent scatter radar experiments, exploiting a variety of beam and pulse patterns, were designed or revisited to investigate the Langmuir turbulence underlying the radar echoes. The experimental results revealed that Langmuir turbulence is a common feature of the auroral ionosphere. The experimental efforts also led to uncovering a relationship between Langmuir turbulence and one type of natural electromagnetic emission that is sometimes detected on the ground, so-called “medium frequency burst”, providing an explanation for the generation mechanism of these emissions. In an attempt to gain insights into the source mechanism underlying Langmuir turbulence, 1-dimensional Zakharov simulations were employed to study the interactions of ionospheric electron beams with a broad range of parameters with the background plasma at the F region peak. A variety of processes were observed, ranging from a cascade of parametric decays, to formation of stationary wave packets and density cavities in the condensate region, and to direct nucleation and collapse at the initial stage of the turbulence. The simulation results were then compared with the ISR measurements where inconsistencies were found in the spectral details and intensity of the simulated and measured Langmuir turbulence echoes, suggesting the possibility that the direct energy for the turbulence was provided by unstable low-energy (5 − 20 eV) electron populations produced locally in the F region of the ionosphere rather than by electron beams originating from the magnetosphere.

Turbulence in plasma confined by a magnetic dipole is dominated by interchange fluctuations with complex dynamics and short spatial coherence. We report the first use of local current-collection feedback to modify, amplify, and suppress these fluctuations. The spatial extent of turbulence regulation is limited to a correlation length near the collector. Changing the gain and phase of collection results in power either extracted from or injected into the turbulence. This mechanism is analogous to the magnetospheric-ionospheric coupling by field-aligned currents. The measured plasma response shows some agreement with calculations of the linear response of global interchange-like MHD and entropy modes to current-collection feedback.

The turbulence and fluctuation induced transport in the edge plasma of the Tokoloshe tokamak was studied using a Langmuir probe array. In this thesis three separate experiments are presented, each of which examines a particular aspect of the edge plasma. In the first experiment measurements of edge plasma parameters are presented. These include standard parameters (such as Ne, Op , Te, etc.) as well as features such as the velocity shear, T(t) during periods of both high and low Mirnov activity, Te/Te and Q. These are compared with results from other machines as well as predictions of several turbulence theories. It was found that many of the results are very similar to those obtained on other machines and that, since the operating parameter space on Tokoloshe is well within the parameter space described by drift wave theories, resistivity-driven gradient driven turbulence theories do not describe the edge turbulence. In the second experiment external windings are used to produce fields which can slow and lock magnetic islands in the toroidally rotating plasma. Edge parameters are again presented and these results compared with those from the so-called 'reference' plasmas, i.e. ones in which no locking occurred. During locking some parameters are dramatically altered, e.g.Te/Te Standard transport theory ignores the effect of Te/Te since they are usually small in reference discharges. During the locked phase, however, certain measurements used to deduce T and Q are greatly affected by increases in Te/Te. As a result, certain assumptions regarding these measurements are no longer valid. Comparison of results for different island positions (produced by different coils) indicates that the assumption of poloidal and toroidal symmetry of edge conditions is invalid. The third experiment investigates the high frequency (~60 kHz), low amplitude, magnetic oscillation which characterises the locked phase and which exhibits some small degree of correlation with the fluctuations observed on (e.g.) Of'. Since over 80% of the spectral power of Te/Te lies below 70 kHz and since Of /Te depends strongly on Te/Te , it is suggested that the magnetic mode and these large variations in Te, may be due to a similar physical process.
Thesis (Ph.D.)-University of Natal, 1993.

Turbulence is ubiquitous in the flows of fluids and plasmas. This thesis is devoted to studies of the statistical properties of turbulence in the three-dimensional (3D) Hall magnetohydrodynamic (Hall-MHD) equations, the two-dimensional (2D) MHD equations, the one-dimensional (1D) hyperviscous Burgers equation, and the 3D Navier-Stokes equations. Chapter 1 contains a brief introduction to statistically homogeneous and isotropic turbulence. This is followed by an over-view of the equations we study in the subsequent chapters, the motivation for the studies and a summary of problems we investigate in chapters 2-6. In Chapter 2 we present our study of Hall-MHD turbulence [1]. We show that a shell-model version of the 3D Hall-MHD equations provides a natural theoretical model for investigating the multiscaling behaviors of velocity and magnetic structure functions. We carry out extensive numerical studies of this shell model, obtain the scaling exponents for its structure functions, in both the low-k and high-k power-law ranges of 3D Hall-MHD, and find that the extended-self-similarity procedure is helpful in extracting the multiscaling nature of structure functions in the high-k regime, which otherwise appears to display simple scaling. Our results shed light on intriguing solar-wind measurements. In Chapter 3 we present our study of the inverse-cascade regime in two-dimensional magnetohydrodynamic turbulence [2]. We present a detailed direct numerical simulation (DNS) of statistically steady, homogeneous, isotropic, two-dimensional magnetohydrodynamic (2D MHD) turbulence. Our study concentrates on the inverse cascade of the magnetic vector potential. We examine the dependence of the statistical properties of such turbulence on dissipation and friction coefficients. We extend earlier work significantly by calculating fluid and magnetic spectra, probability distribution functions (PDFs) of the velocity, magnetic, vorticity, current, stream-function, and magnetic-vector-potential fields and their increments. We quantify the deviations of these PDFs from Gaussian ones by computing their flatnesses and hyperflatnesses. We also present PDFs of the Okubo-Weiss parameter, which distinguishes between vortical and extensional flow regions, and its magnetic analog. We show that the hyperflatnesses of PDFs of the increments of the stream-function and the magnetic vector potential exhibit significant scale dependence and we examine the implication of this for the multiscaling of structure functions. We compare our results with those of earlier studies. In Chapter 4 we compare the statistical properties of 2D MHD turbulence for two different energy injection scales. We present systematic DNSs of statistically steady 2D MHD turbulence. Our two DNSs are distinguished by kinj, the wave number at which we inject energy into the system. In our first DNS (run R1), kinj = 2 and, in the second (run R2) kinj = 250. We show that various statistical properties of the turbulent states in the runs R1 and R2 are strikingly different The nature of energy spectrum, probability distribution functions, and topological structures are compared for the two runs R1 and R2 are found to be strikingly different. In Chapter 5 we study the hyperviscous Burgers equation for very high α, order of hyperviscosity [3]. We show, by using direct numerical simulations and theory, how, by increasing α in equations of hydrodynamics, there is a transition from a dissipative to a conservative system. This remarkable result, already conjectured for the asymptotic case α →∞ [U. Frisch et al., Phys. Rev. Lett. 101, 144501 (2008)], is now shown to be true for any large, but finite, value of α greater than a crossover value α crossover. We thus provide a self-consistent picture of how dissipative systems, under certain conditions, start behaving like conservative systems, and hence elucidate the subtle connection between equilibrium statistical mechanics and out-of-equilibrium turbulent flows. In Chapter 6 we show how to use asymptotic-extrapolation and Richardson extrapolation methods to extract the exponents ξ p that characterize the dependence of the order-p moments of the velocity gradients on the Reynolds number Re. To use these extrapolation methods we must have high-precision data for such moments. We obtain these high-precision data by carrying out the most extensive, quadruple precision, pseudospectral DNSs of the Navier-Stokes equation.

Turbulence is ubiquitous in the flows of fluids and plasmas. This thesis is devoted to studies of the statistical properties of turbulence in the three-dimensional (3D) Hall magnetohydrodynamic (Hall-MHD) equations, the two-dimensional (2D) MHD equations, the one-dimensional (1D) hyperviscous Burgers equation, and the 3D Navier-Stokes equations. Chapter 1 contains a brief introduction to statistically homogeneous and isotropic turbulence. This is followed by an over-view of the equations we study in the subsequent chapters, the motivation for the studies and a summary of problems we investigate in chapters 2-6. In Chapter 2 we present our study of Hall-MHD turbulence [1]. We show that a shell-model version of the 3D Hall-MHD equations provides a natural theoretical model for investigating the multiscaling behaviors of velocity and magnetic structure functions. We carry out extensive numerical studies of this shell model, obtain the scaling exponents for its structure functions, in both the low-k and high-k power-law ranges of 3D Hall-MHD, and find that the extended-self-similarity procedure is helpful in extracting the multiscaling nature of structure functions in the high-k regime, which otherwise appears to display simple scaling. Our results shed light on intriguing solar-wind measurements. In Chapter 3 we present our study of the inverse-cascade regime in two-dimensional magnetohydrodynamic turbulence [2]. We present a detailed direct numerical simulation (DNS) of statistically steady, homogeneous, isotropic, two-dimensional magnetohydrodynamic (2D MHD) turbulence. Our study concentrates on the inverse cascade of the magnetic vector potential. We examine the dependence of the statistical properties of such turbulence on dissipation and friction coefficients. We extend earlier work significantly by calculating fluid and magnetic spectra, probability distribution functions (PDFs) of the velocity, magnetic, vorticity, current, stream-function, and magnetic-vector-potential fields and their increments. We quantify the deviations of these PDFs from Gaussian ones by computing their flatnesses and hyperflatnesses. We also present PDFs of the Okubo-Weiss parameter, which distinguishes between vortical and extensional flow regions, and its magnetic analog. We show that the hyperflatnesses of PDFs of the increments of the stream-function and the magnetic vector potential exhibit significant scale dependence and we examine the implication of this for the multiscaling of structure functions. We compare our results with those of earlier studies. In Chapter 4 we compare the statistical properties of 2D MHD turbulence for two different energy injection scales. We present systematic DNSs of statistically steady 2D MHD turbulence. Our two DNSs are distinguished by kinj, the wave number at which we inject energy into the system. In our first DNS (run R1), kinj = 2 and, in the second (run R2) kinj = 250. We show that various statistical properties of the turbulent states in the runs R1 and R2 are strikingly different The nature of energy spectrum, probability distribution functions, and topological structures are compared for the two runs R1 and R2 are found to be strikingly different. In Chapter 5 we study the hyperviscous Burgers equation for very high α, order of hyperviscosity [3]. We show, by using direct numerical simulations and theory, how, by increasing α in equations of hydrodynamics, there is a transition from a dissipative to a conservative system. This remarkable result, already conjectured for the asymptotic case α →∞ [U. Frisch et al., Phys. Rev. Lett. 101, 144501 (2008)], is now shown to be true for any large, but finite, value of α greater than a crossover value α crossover. We thus provide a self-consistent picture of how dissipative systems, under certain conditions, start behaving like conservative systems, and hence elucidate the subtle connection between equilibrium statistical mechanics and out-of-equilibrium turbulent flows. In Chapter 6 we show how to use asymptotic-extrapolation and Richardson extrapolation methods to extract the exponents ξ p that characterize the dependence of the order-p moments of the velocity gradients on the Reynolds number Re. To use these extrapolation methods we must have high-precision data for such moments. We obtain these high-precision data by carrying out the most extensive, quadruple precision, pseudospectral DNSs of the Navier-Stokes equation.

Magnetic nozzles, like Laval nozzles, are observed in several natural systems and have application in areas such as electric propulsion and plasma processing. Plasma flowing through these nozzles is inherently tied to the field lines and must separate for momentum redirection or particle transport to occur. Plasma detachment and associated mechanisms from a magnetic nozzle are investigated. Experimental results are presented from the plume of the VASIMR® VX-200 device flowing along an axisymmetric magnetic nozzle and operated at two ion energies to explore momentum dependent detachment. The argon plume expanded into a 150m3 vacuum chamber where the background pressure was low enough that charge-exchange mean-free-paths were longer than experiment scale lengths. This magnetic nozzle system is demonstrated to hydrodynamically scale up to astrophysical plasmas, particularly the solar chromosphere, implying general relevance to all systems. Plasma parameters were mapped over a large spatial range using measurements from multiple plasma diagnostics. The data show that the plume does not follow the magnetic field lines. A mapped integration of the ion flux shows the plume may be divided into three regions where 1) the plume briefly follows the magnetic flux, 2) diverges quadratically before 3) expanding with linear trajectories. Transitioning from region 1→2, the ion flux departs from the magnetic flux suggesting ion detachment. An instability forms in region 2 driving an oscillating electric field that causes ions to expand before enhancing electron cross-field transport through anomalous resistivity. Transitioning from region 2→3 the electric field dissipates, the trajectories linearize, and the plume effectively detaches. A delineation of sub-to-super Alfvénic flow aligns well with the inflection points of the linearization without a change in magnetic topology. The detachment process is best described as a two part process: First, ions detach by a breakdown of the magnetic moment when the quantity |v/fcLB| becomes of order unity. Second, the turbulent electric field enhances electron transport up to a factor of 4±1 above collisional diffusion; electron cross-field velocities approximate that of the ions and depart on more centralized field lines. Electrons are believed to detach by breakdown of magnetic moment further downstream in the weaker magnetic field.

In this work the effect of elasticity on turbulent drag reduction due to polymers is investigated using a hybrid Direct Numerical Simulation (D.N.S) and Langevin dynamics approach. Simulations are run at a friction Reynolds number of Reτ = 560 for 960.000 dumbbells with Deborah numbers of De = 0, De = 1, and De = 10. The conclusions are that it is possible to simulate a drag reduced flow using hybrid D.N.S. with Langevin dynamics, that polymers, like other occurrences of drag reduction, reduce drag through streak stabilization, and that the essential property of polymers and fibers in having a drag reducing effect is their ability to exert a torque on the solvent when they orientate in the boundary layer of the turbulent flow.