Thesis (Ph. D.)--University of Texas at Austin, 2009. / Title from PDF title page (University of Texas Digital Repository, viewed on Sept. 9, 2009). Vita. Includes bibliographical references.

Magnetic flux continually emerges from the Sun, rising through the solar interior, emerging at the photosphere in the form of sunspots and expanding into the atmosphere. Observations of sunspot rotations have been reported for over a century and are often accompanied by solar eruptions and flaring activity. In this thesis, we present 3D numerical simulations of the emergence of twisted flux tubes from the uppermost layers of the solar interior, examining the rotational movements of sunspots in the photospheric plane. The basic experiment introduces the mechanism and characteristics of sunspot rotation by a clear calculation of rotation angle, vorticity, magnetic helicity and energy, whereby we find an untwisting of the interior portion of the field, accompanied by an injection of twist into the atmospheric field. We extend this model by altering the initial field strength and twist of the sub-photospheric tube. This comparison reveals the rotation angle, helicity and current show a direct dependence on field strength. An increase in field strength increases the rotation angle, the length of fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. The fieldline length is crucial as we predict the twist per unit length equilibrates to a lower value on longer fieldlines, and hence possesses a larger rotation angle. No such direct dependence is found when varying the twist but there is a clear ordering in rotation angle, helicity, and energy, with more highly twisted tubes undergoing larger rotation angles. We believe the final angle of rotation is reached when the system achieves a constant degree of twist along the length of fieldlines. By extrapolating the size of the modelled active region, we find rotation angles and rates comparable with those observed. In addition, we explore sunspot rotation caused by sub-photospheric velocities twisting the footpoints of flux tubes.

Cette thèse est dédiée aux processus de transport de moment cinétique et de flux magnétique dans les disques faiblement magnétisés et faiblement ionisés ; l’influence des effets microphysiques sur la dynamique du disque à grande échelle y est centrale. Dans un premier temps, j’exclue les effets de stratification et j’examine l’impact des effets MHD non-idéaux sur la turbulence dans le plan du disque. Je montre que l’écoulement peut spontanément s’organiser si la fraction d’ionisation est assez faible ; dans ce cas, l’accrétion est stoppée, et le disque exhibe des anneaux axisymétriques susceptibles d’affecter la formation planétaire. Dans un second temps, je caractérise l’interaction du disque avec un vent magnétisé via un modèle global de disque stratifié. Ce modèle est le premier à décrire globalement les effets MHD non-idéaux d’après un réseau chimique simplifié. Il révèle que le disque est essentiellement non-turbulent, et que le champ magnétique peut adopter différentes configurations globales, affectant drastiquement les processus de transport. Un nouveau processus d’auto-organisation est identifié, produisant aussi des structures axisymétriques, tandis que le précédent est invalidé par l’action du vent. Les propriétés des vents magnéto-thermiques sont examinées pour différentes magnétisations, permettant de discriminer les vents magnétisés des vents photo-évaporés par leur efficacité d’éjection. / This thesis is devoted to the transport of angular momentum and magnetic flux through weakly ionized and weakly magnetized accretion disks ; the role of microphysical effects on the large- scale dynamics of the disk is of primary importance. As a first step, I exclude stratification effects and examine the impact of non-ideal MHD effects on the turbulent properties near the disk midplane. I show that the flow can spontaneously organize itself if the ionization fraction is low enough ; in this case, accretion is halted and the disk exhibits axisymmetric structures, with possible consequences on planetary formation. As a second step, I study the disk-wind interaction via a global model of stratified disk. This model is the first to compute non-ideal MHD effects from a simplified chemical network in a global geometry. It reveals that the flow is essentially laminar, and that the magnetic field can adopt different global configurations, drastically affecting the transport processes. A new self-organization process is identified, also leading to the formation of axisymmetric structures, whereas the previous mechanism is discarded by the action of the wind. The properties of magneto-thermal winds are examined for various magnetizations, allowing discrimination between magnetized and photo-evaporative winds based upon their ejection efficiency.

Magnetic flux emergence is a fundamental process in the Sun, during which magnetic fields emerge from the solar interior to the surface, to build up active regions and give onset to spectacular dynamic phenomena, such as eruptions and jets. In this thesis, we performed 3D, resistive MHD simulations to study the emergence and the associated magnetic activity of a quadrupolar region in the Sun. Our aim behind the setup of this initial condition (i.e. a quadrupolar region) was to study a magnetic field configuration, which has not been studied in detail before, although it has been repeatedly observed in the Sun and it has been shown that it can host intense magnetic activity (e.g. in the form of jets, flares and eruptions). The results of our experiments showed that the internal dynamics of such regions leads to the onset of eruptions in the form of twisted magnetic flux tubes (flux ropes). These eruptions are recurrent but they cannot escape the outermost field of the emerging flux (envelope field). They remain confined within the envelope field, as the downward tension of the outermost field lines overwhelms the upward Lorentz force of the erupting field. When we add an ambient magnetic field in the solar atmosphere, external reconnection between the emerging and the ambient field triggers the emission of (standard) reconnection jets. The external reconnection also releases the tension of the ambient field lines and, thus, the eruptions move in an ejective way towards the outer space. Namely, the confined eruptions become ejective eruptions, which escape from the numerical domain. These ejective eruptions drive a newly observed class of jets, the so called "blowout" jets. Our experiments reproduce some of the main observed characteristics of the "blowout" jets. We showed that "blowout" jets emit hot and cool plasma into the outer solar atmosphere simultaneously, and they undergo untwisting motion due to the relaxation of twist during their ejection. We found that the untwisting motion of the "blowout" jets is associated with the propagation of torsional Alfvén waves. Finally, we performed a parametric study to explore the effect of the ambient field strength on the onset and dynamics of the eruptive events. We found that one of the main effects is that the stronger ambient field suppresses the vertical expansion of the magnetic envelope of the quadrupolar region due to the higher magnetic pressure above it. This result has an effect on the emission of jets, which are emitted due to reconnection between the two fields. When the ambient field is relatively weak, it is pushed away from the strong emerging field and reconnection between them is not so persistent. On the other hand, when the ambient field is relatively strong, we find that more jets are ejected due to more efficient and more frequent reconnection between the two flux systems. As a consequence, we find that more mass and flux is being transferred into the solar corona by the reconnection jets. Also, we find that there are more eruptions when the ambient field is stronger. The study of the total energy flux carried by the jets showed that it is sufficient to provide the energy required to accelerate the high speed solar wind. This indicates that the "blowout" jets may play an important role in driving the solar wind.

The problem of how the Sun's corona is heated is of central importance to solar physics research. In this thesis we model three main areas. The first, annihilation, is a feature of non-ideal MHD and focusses on how magnetic field of opposite polarity meets at a null point and annihilates, after having been advected with plasma toward a stagnation point in the plasma flow. Generally, the null point of the field and the stagnation point of the flow are coincident at the origin, but in chapter 2 a simple extension is considered where an asymmetry in the boundary conditions of the field moves the null point away from the origin. Chapter 3 presents a model of reconnective annihilation in three dimensions. It represents flux being advected through the fan plane of a 3D null, and diffusing through a thin diffusion region before being annihilated at the spine line, and uses the method of matched asymptotic expansions to find the solution for small values of the resistivity. The second area of the thesis covers null collapse. This is when the magnetic field in close proximity to a null point is disturbed, causing the field to fold up on itself and collapse. This is a feature of ideal MHD, and causes a strong current to build up, allowing non-ideal effects to become important. When using linearised equations for the collapse problem, we are in fact looking at a linear instability. If this instability initiates a collapse, this is only a valid model until non-linear effects become important. By talking about collapse in chapters 4 and 5 (as it is talked about in the literature), we mean that the linear instability initiates collapse, which in principle, non-linear effects could later stop. Chapter 4 introduces a two-dimensional model for collapse, using the ideal, compressible, linearised MHD equations. It is a general solution in which all spatially linear nulls and their supporting plasma flows and pressure gradients can be checked for susceptibility to collapse under open boundary conditions. Chapter 5 uses the model introduced in chapter 4 to investigate the collapse of three-dimensional, potential nulls (again, spatially linear) for all possible supporting plasma flows and pressure gradients. Using this model, all nulls under consideration are found to collapse and produce large currents, except for a group of 2D O-type nulls supported by highly super-Alfvenic plasma flows. The third area of this thesis involves numerically simulating a model of heating by coronal tectonics (Priest et al, 2002). A simple magnetic field is created and the boundary is driven, also in a simple manner. Current sheets which scale with grid resolution are seen to build up on the quasi-separatrix layers, and there is some evidence of magnetic reconnection.

Le moment cinétique d’une étoile, comme sa masse ou sa composition chimique, est l’une de ses propriétés fondamentales, l’un de celles qui varient à cours du temps et influent sur la structure de l’étoile. Celui-ci peut être global, on l’observe alors à travers la vitesse de rotation de surface d’une étoile, ou local, auquel cas il nous faut sonder l’intérieur stellaire et étudier les processus de redistribution au sein des régions internes du moment cinétique. Au cours de cette thèse dans le cadre du projet ToUpiES, nous nous sommes intéressés en particulier à l’évolution du moment cinétique des étoiles de faible masse au cours de leur jeunesse, qui est une période critique de leur vie en ce qui concerne l’impact et l’évolution du moment cinétique. Nous avons d’abord inclus au sein du code d’évolution STAREVOL les prescriptions les plus à jour pour l’extraction du moment cinétique par les vents magnétisés. L’étude systématique des combinaisons de ce freinage avec différentes prescriptions existantes pour le traitement de la turbulence horizontale et verticale dans la zone radiative des étoiles, nous a permis de sélectionner un jeu de prescriptions capable de reproduire, les périodes de rotation dans les amas ouverts pour une étoile de type solaire. Nous comparons ensuite l’application de ces processus de transport et d’extraction du moment cinétique à un modèle de 1, 2 masse solaire, aux autres processus jugés potentiellement efficaces pour transport le moment cinétique à ce jour (ondes internes de gravités, instabilité MHD de Tayler-Spruit, modes de gravités). Cela nous a permis de présenter dans chacun des cas les spécificités du profil de rotation prédit par ces différents modes de transport. Puis, nous avons mis en place un modèle rotationnel fonctionnel adapté à l’ensemble des étoiles de faible masse, permettant entre autre de reproduire les périodes de rotation observées dans les amas jeunes pour les étoiles de faible masse (avec une masse comprise entre 0, 2 et 1, 1 M⊙). Ceci a donné lieu à une grille de modèle d’évolution unique à ce jour. Enfin, cette grille a été utilisée dans le cadre de travaux dans différents domaines, tels que l’impact de l’évolution stellaire sur l’habitabilité d’un système, la caractérisation d’étoiles-hôte ou encore l’étude de l’évolution de la topologie magnétique au cours des phases jeunes. / The angular momentum content of a star, as its mass or its chemical composition is one of the fundamental properties of a star, one of those that evolves with time and modify the stellar structure. The angular momentum can be studied as a global property, we can then observe it through the surface rotation velocity, or a local property that vary inside the star, we therefore have to probe the stellar radiation zone and study the secular angular momentum redistribution processes that happen in this region. During this PhD, in the frame of the ToUpiES project, we have been especially interested in the evolution of the young low-mass stars angular momentum, since this phase of evolution is critical regarding the evolution of extraction and redistribution angular momentum processes. First, we included in the STAREVOL evolution code the most up-to-date prescription for the wind-driven angular momentum extraction. We led a systematic study of the various combination of this braking with the different existing prescriptions for the treatment of horizontal and vertical turbulent motions in stellar radiative zones. This allows us to select a set of prescription able to reproduce the observed rotation periods in young open clusters for a broad mass-range. Next, we analysed how these prescriptions for extraction and transport of angular momentum behave when applied to a 1.2M⊙ model. We compared the result to what is obtained with other processes estimated as potentially very efficient to redistribute angular momentum (internal gravity waves, MHD Tayler-Spruit instability, gravity modes). This allows us to derive in each case, the specificity of the rotation profiles predicted by the different transport processes. Then, we set up a functional rotational model adapted to almost the entire range low-mass stars, allowing to reproduce the observed low-mass stars rotation periods in young open clusters (with 0, 2M⊙ ≤M≤ 1, 1M⊙). This models can also predict the rotational evolution at different metallicities. Eventually, these models have been used in the frame of various works in different domains such as the characterisation of planet host-stars, the evolution of the magnetic topology during the young stellar phases or even the impact of stellar evolution on the habitability of a planetary system.

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

Au cours de ce travail, nous nous sommes attaché à la résolution numérique des équations de la Magnétohydrodynamique (MHD) auxquelles s'ajoute une loi hyperbolique de transport des erreurs de divergence.La première étape consista à symétriser le nouveau système de la MHD idéale afin d'en étudier le système propre, ce qui fut l'occasion de rappeler le rôle de l'entropie au niveau de ce calcul comme à celui de l'inégalité de Clausius-Duhem. La suite de cette thèse eut pour objectif la résolution de ces équations idéales à l'aide de schémas distribuant le résidu (notés RD). Les quatre principaux schémas connus furent testés, et nous avons montré entre autres que le schéma N, qui a fait ses preuves sur les équations d'Euler en mécanique des fluides, n'était pas adapté aux équations de la MHD. Les stratégies classiques de limitation et de stabilisation purent être revisitées à ce moment. Les équations étant instationnaires, il fallut intégrer une discrétisation en temps et une distribution spatiale des termes d'évolution (et d'éventuelles sources). Nous avons d'emblée opté pour une approche implicite permettant d'être performant sur les simulations longues des expériences de tokamaks, et de traiter la correction de la divergence d'une manière originale et efficace. Les problèmes de convergence de la méthode de Newton-Raphson n'ayant pas été pleinement résolus, nous nous sommes tournés vers une alternative explicite de type Runge-Kutta. Enfin, nous avons réétabli les principes de la montée en ordre (en théorie, jusqu'à des ordres arbitraires, en prenant en compte le phénomène de Gibbs) à l'aide de tout type d'élément fini (bien construit) 2D ou 3D, sans avoir pu valider tous ces aspects. Nous avons également pris en compte les équations complètes de la MHD réelle classique (i.e. sans effet Hall) à l'aide d'un couplage RD/Galerkin. / During this thesis, we worked on the numerical resolution of the Magnetohydrodynamic (MHD) equations, to which we added a hyperbolic transport equation for the divergence errors of the magnetic field.The first step consisted in symmetrizing the new ideal MHD system in order to study its eigensystem, which was the opportunity to remind the role of the entropy in this calculation as well as in the Clausius-Duhem inequality. Next, we aimed at solving these ideal equations by the mean of Residual Distribution (RD) schemes.The four main schemes were tested, and we showed among other things that the N scheme (although it has been proven very efficient with Euler equations in Fluid Mechanics) could not give satisfying results with the MHD equations. Classical strategies for the limitation and the stabilization were revisited then. Moreover,since we dealt with unsteady equations, we had to formulate atime discretization and a spatial distribution of the unsteady terms (as well as possible sources). We first choosed an implicit approach allowing us to be powerful on the long simulations needed for tokamak experiments, and to treat the divergence cleaning part in an original and efficient way. The convergence problems of our Newton-Raphson algorithm having not been fully resolved, we turned to an explicit alternative (Runge-Kutta type).Finally, we discussed about the principles of higher order schemes (theoretically, up to arbitrary orders, taking into account the Gibbs phenomenon) thanks to any type of 2D or 3D finite element (properly defined), without having been able to to validate all these aspects. We also implemented the dissipative part of the full MHD equations (in the classical sense, i.e. omitting the Hall effect) by the use of a RD/Galerkin coupling.

No description available.

en.txt After an introduction into current sheet physics, with emphasis to solar physics we showed some formulations of finite element method. We implemented and evaluated new discontinuous finite element with Taylor basis and introduced deal.II library with an example of burgers equation. While the program is dimension independent, we compared our solution with a one-dimensional analytical solution. Finally, using previously derived LSFEM formulation, we solved simple current sheet problem using deal.II. Stránka 1