L'astrophysique stellaire nécessite aujourd'hui de modéliser les champs magnétiques de grandes échelles, observés par spectropolarimétrie à la surface d'étoiles de type Ap/Bp et pouvant expliquer la rotation uniforme dans la zone radiative solaire déduite de l'héliosismologie. Durant ma thèse, je me suis attaché à décrire les possibles états d'équilibre magnétique dans les intérieurs stellaires. Les configurations trouvées sont mixtes poloïdales-toroïdales et minimisent l'énergie à hélicité donnée, en analogie aux états de Taylor rencontrés dans les sphéromaks. La prise en compte de l'auto-gravité m'a conduit à des équilibres de type « non force-free », qui vont donc influencer la structure stellaire. J'ai dérivé toutes les quantités physiques associées au champ magnétique puis quantifié les perturbations qu'elles induisent sur la gravité, les quantités thermodynamiques et énergétiques, pour une structure solaire et une étoile Ap. Des simulations MHD 3D m'ont permis de démontrer que ces équilibres forment une première famille d'états stables, la généralisation de tels états restant une question ouverte. J'ai montré qu'un champ magnétique dans la zone radiative solaire est susceptible de déformations comparables à une rotation élevée dans le coeur. Son influence sur la convection a aussi été examinée. J'ai également étudié l'interaction séculaire champ magnétique-rotation différentielle-circulation méridienne dans le but d'implémenter ses effets dans un code d'évolution stellaire nouvelle génération. Par ailleurs, les processus hydrodynamiques ont été comparés à ceux de la diffusion et d'un changement de l'efficacité de la convection dans une étoile cible du satellite CoRoT.

Many of the celestial bodies we know are found to be magnetized:the Earth, many of the planets so far discovered, the Sun and other stars,the interstellar space, the Milky Way and other galaxies.The reason for that is still to be fully understood, and this work is meant to be a step in that direction. The dynamics of the interstellar medium is dominated by events likesupernovae explosions that can be modelled as irrotational flows.The first part of this thesis is dedicated to the analysis of some characteristics of these flows, in particular how they influencethe typical turbulent magnetic diffusivity of a medium, and it is shownthat the diffusivity is generally enhanced, except for some specific casessuch as steady potential flows, where it can be lowered.Moreover, it is examined how such flows can develop vorticity when they occur in environments affected by rotation or shear,or that are not barotropic. Secondly, we examine helical flows, that are of basic importance for the phenomenon of the amplification of magnetic fields, namely the dynamo.Magnetic helicity can arise from the occurrence of an instability: here we focus on theinstability of purely toroidal magnetic fields, also known as Tayler instability.It is possible to give a topological interpretation of magnetic helicity.Using this point of view, and being aware that magnetic helicity is a conserved quantity in non-resistive flows,it is illustrated how helical systems preserve magnetic structureslonger than non-helical ones. The final part of the thesis deals directly with dynamos.It is shown how to evaluate dynamo transport coefficients with two of the most commonly used techniques, namely theimposed-field and the test-field methods.After that, it is analyzed how dynamos are affected by advectionof magnetic fields and material away from the domain in which theyoperate.It is demonstrated that the presence of an outflow, likestellar or galactic winds in real astrophysical cases,alleviates the so-calledcatastrophic quenching, that is the damping of a dynamoin highly conductive media, thus allowing the dynamo process to work better. / <p>At the time of the doctoral defence the following paper was unpublished and had a status as follows: Paper nr 5: Submitted</p>

This study uses the MHD (Magnetohydrodynamics) model to simulate unsteady two-dimensional transport variables in helium plasma under low pressure between two infinite planar electrodes suddenly biased by a negative voltage. Plasma has been widely used in etching, ion implantation, light source, and encountered in nuclear fusion, etc. Studying transport processes of plasmas therefore is important. By account for momentum exchange collisions, electric fields and magnetic fields the computed results in this work quantitatively show density, velocity, electric potential, temperature, viscosity, thermal conductivity of the ions and electrons across the sheath to the surfaces suddenly biased by a dc negative voltage.

Doctor of Philosophy / We investigate the linear growth and vertical structure of the magnetorotational instability (MRI) in weakly ionised, stratified accretion discs. The magnetic field is initially vertical and perturbations have vertical wavevectors only. Solutions are obtained at representative radial locations from the central protostar for different choices of the initial magnetic field strength, sources of ionisation, disc structure and configuration of the conductivity tensor. The MRI is active over a wide range of magnetic field strengths and fluid conditions in low conductivity discs. For the minimum-mass solar nebula model, incorporating cosmic ray and x-ray ionisation and assuming that charges are carried by ions and electrons only, perturbations grow at 1 AU for B < 8G. For a significant subset of these strengths (200mG < B < 5 G), the growth rate is of order the ideal MHD rate (0.75 Omega). Hall conductivity modifies the structure and growth rate of global unstable modes at 1 AU for all magnetic field strengths that support MRI. As a result, at this radius, modes obtained with a full conductivity tensor grow faster and are active over a more extended cross-section of the disc, than perturbations in the ambipolar diffusion limit. For relatively strong fields (e.g. B > 200 mG), ambipolar diffusion alters the envelope shapes of the unstable modes, which peak at an intermediate height, instead of being mostly flat as modes in the Hall limit are in this region of parameter space. Similarly, when cosmic rays are assumed to be excluded from the disc by the winds emitted by the magnetically active protostar, unstable modes grow at this radius for B < 2 G. For strong fields, perturbations exhibit a kink at the height where x-ray ionisation becomes active. Finally, for R = 5 AU (10 AU), unstable modes exist for B < 800 mG (B < 250 mG) and the maximum growth rate is close to the ideal-MHD rate for 20 mG < B < 500 mG (2 mG < B < 50 mG). Similarly, perturbations incorporating Hall conductivity have a higher wavenumber and grow faster than solutions in the ambipolar diffusion limit for B < 100 mG (B < 10 mG). Unstable modes grow even at the midplane for B > 100 mG (B ~ 1 mG), but for weaker fields, a small dead region exists. When a population of 0.1 um grains is assumed to be present, perturbations grow at 10 AU for B < 10 mG. We estimate that the figure for R = 1 AU would be of order 400 mG. We conclude that, despite the low magnetic coupling, the magnetic field is dynamically important for a large range of fluid conditions and field strengths in protostellar discs. An example of such magnetic activity is the generation of MRI unstable modes, which are supported at 1 AU for field strengths up to a few gauss. Hall diffusion largely determines the structure and growth rate of these perturbations for all studied radii. At radii of order 1 AU, in particular, it is crucial to incorporate the full conductivity tensor in the analysis of this instability, and more generally, in studies of the dynamics of astrophysical discs.

Αντικείμενο της παρούσας διδακτορικής διατριβής αποτέλεσε η ανάπτυξη μιας ακριβούς υπολογιστικής μεθοδολογίας για τη μελέτη της μαγνητοϋδροδυναμικής και θερμικής ροής ενός ηλεκτρικώς αγώγιμου ρευστού υπό την επίδραση ενός εξωτερικού μαγνητικού πεδίου, για μεγάλο φάσμα τιμών των παραμέτρων της ροής. Η μελέτη της διαμόρφωσης της μαγνητορευστοδυναμικής και θερμικής ροής των ηλεκτρικώς αγώγιμων ρευστών, όπως είναι τα υγρά μέταλλα, υπό την επίδραση της εφαρμογής ενός εξωτερικού μαγνητικού πεδίου, είναι ιδιαίτερα σημαντική για την εκτίμηση της μείωσης της αξονικής βαθμίδας της πίεσης, του συντελεστή μεταφοράς θερμότητας και άλλων φυσικών ποσοτήτων, σε μια σειρά προβλημάτων όπως είναι η σταθεροποίηση και ο περιορισμός του πλάσματος, η ψύξη των αντιδραστήρων σύντηξης με υγρά μέταλλα, η χύτευση μετάλλων με ηλεκτρομαγνητικά μέσα, η χρήση ηλεκτρομαγνητικών αντλιών για υγρά μέταλλα, στη γεωλογία, για τη μελέτη του εσωτερικού της Γης, και στην αστροφυσική όπου μελετώνται μεταξύ άλλων αστέρες, νεφελώματα και σχετικιστικά τζετ. Η ροή θεωρείται ασυμπίεστη και στρωτή, ενώ μελετάται για τις περιπτώσεις της πλήρως ανεπτυγμένης και της αναπτυσσόμενης ροή στην περιοχή μεταξύ δύο ομοαξονικών ευθύγραμμων ή καμπύλων αγωγών κυκλικής διατομής, υπό την επίδραση ισχυρού εξωτερικού μαγνητικού πεδίου. Τα τοιχώματα των αγωγών είναι ηλεκτρικώς μονωμένα και ανάλογα με το πρόβλημα βρίσκονται σε διαφορετικές σταθερές θερμοκρασίες ή σε διαφορετικές ροές θερμότητας. Από τα αποτελέσματα προέκυψε πως το μαγνητικό πεδίο έχει πολύ σημαντική επίδραση στην κατανομή της ταχύτητας και στην πτώση πίεσης, ενώ η επίδραση του στη μετάδοση θερμότητας στην περίπτωση των υγρών μετάλλων είναι μηδαμινή. / The aim of the present doctorate thesis was the development of an accurate και robust computational methodology for the study of the magnetohydrodynamic flow of an electrically conducting fluid under the effect of an external magnetic field, for large regions of values of the parameters of the flow. The study of the magnetohydrodynamic και thermal flow of an electrically conducting fluid, such as liquid metals, is very important for the estimation of the pressure drop, the heat transfer coefficient και other physical quantities in several engineering applications such as stabilization και control of plasma, fusion reactor blankets, metallurgy, electromagnetic pumps, geology for the study of the inner core of the earth και astrophysics where stars, nebula και relativity jets are studied. The flow is considered as incompressible και laminar και it is studied for the cases of the fully developed και the developing flow in the region between two homoaxial straight or curved ducts of circular cross-sections, under the effect of an external magnetic field. The duct walls are considered as electrically insulated και maintained at uniform temperatures or uniform heat fluxes. The results show that the magnetic field has a significant effect on the velocity distribution και the pressure drop και a minor effect on the heat transfer.

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

In this PhD Thesis, we have studied several problems related to statistical properties of homogeneous, isotropic and turbulent flow of conducting fluid with direct numerical simulations (DNS) of equations of magnetohydrodynamics (MHD) and simplified shell models. The Thesis begins with an introductory overview of several statistical characterisation of fluid turbulence and MHD turbulence. Chapter-1 discusses various challenges in turbulence in MHD context. This chapter also describes specific problems that are attempted in this Thesis. The first problem, contained in Chapter 2, deals with dynamo action in a shell model for magnetohydrodynamic (MHD) turbulence. We have carried out systematic and high-resolution studies of dynamo action in a shell model over a wide range of the magnetic Prandtl number PrMand the magnetic Reynolds number ReM. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium, first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the (PrM−1,ReM)plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena. In Chapter 3 we present the results of our detailed pseudospectral direct numerical simulation (DNS) studies, with up to 10243 collocation points, of in-compressible, magnetohydrodynamic (MHD) turbulence in three dimensions, without a mean magnetic field. Our study concentrates on the dependence of various statistical properties of both decaying and statistically steady MHD turbulence on the magnetic Prandtl number PrMover a large range, namely, 0.01 ≤PrM≤10. We obtain data for a wide variety of statistical measures such as probability distribution functions (PDFs) of moduli of the vorticity and current density, the energy dissipation rates, and velocity and magnetic-field increments, energy and other spectra, velocity and magnetic-field structure func-tions, which we use to characterise intermittency, isosurfaces of quantities such as the moduli of the vorticity and current, and joint PDFs such as those of fluid and magnetic dissipation rates. Our systematic study uncovers in-teresting results that have not been noted hitherto. In particular, we find a crossover from larger intermittency in the magnetic field than in the velocity field, at large PrM, to smaller intermittency in the magnetic field than in the velocity field, at low PrM. Furthermore, a comparison of our results for decaying MHD turbulence and its forced, statistically steady analogue suggests that we have strong universality in the sense that, for a fixed value of PrM, multi-scaling exponent ratios agree, at least within our error bars, for both decaying and statistically steady homogeneous, isotropic MHD turbulence. Chapter 4 is devoted to pseudospectral direct numerical simulation (DNS) studies of the three-dimensional magnetohydrodynamic (MHD) equations (3DRFMHD) stirred by a stochastic force with zero mean and a variance ∼ k−3, where kis the wavevector, for magnetic Prandtl numbers PrM=0.1,1, and 10. We obtain velocity and magnetic-field structure functions and, from these, the multiscaling exponent ratios ζp/ζ3by using the extended self similarity (ESS) procedure. These exponent ratios lie within error bars of their counterparts for conventional three-dimensinal MHD turbulence (3DMHD). We carry out a systematic comparison of the statistical properties of 3DMHD and 3DRFMHD turbulence by examining various probability distribution functions (PDFs), joint PDFs, and isosurfaces of quantities such as the moduli of the vorticity and the cur-rent density. In Chapter 5 we present a study of the multiscaling of time-depedent velocity and magnetic-field structure functions in homogeneous, isotropic fluid turbulence. We first present a generalisation for magnetohydrodynamics of the formalisn that has been developed for analogous studies of time-dependent structure functions in fluid turbulence. We then carry out a detailed numerical study of such time-dependent structure functions in a shell model for MHD turbulence. From this study we extract both eqaul-time and dynamic multiscaling exponents; however, we have not so far been able to come up with the MHD analogues of the linear bridge relations that relate equal-time and dynamic multiscaling exponents in fluid turbulence; indeed, it is not clear whether such bridge relations should exist for MHD turbulence.

Converging shocks have long been a topic of interest in theoretical fluid mechanics, and are of prime importance in inertial confinement fusion. However, tracking converging shocks in numerical schemes poses several challenges. Numerical schemes based on shock capturing inherently diffuse out shocks to multiple grid cells, making it hard to track the shock. Converging shocks are significantly harder to track, as this numerical smearing is much more significant when converging shocks approach the axis of convergence. To mitigate this problem, we transform the conservation laws to a non-inertial frame of reference in which the accelerating shock is stationary. A system of equations is derived based on the transformed conservation laws coupled to the shock speed obtained from jump conditions and a characteristic-based derivation of a relation governing shock acceleration. We solve these equations using a finite volume method. Our numerical results compare favorably with the analytical value of Guderley exponent for self-similarly converging cylindrical hydrodynamic shocks. Results for fast magnetosonic shock in MHD are also presented and compared with results from geometrical shock dynamics (GSD). Results from our shock fitting method, developed without any approximation to the original ideal magnetohydrodynamics equations, provide further credibility to GSD applied to converging fast magnetosonic shocks. This sort of shock fitting is a precursor to future multidimensional stability analysis of imploding shocks.

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