The Sun is surrounded by a 10^6 K hot atmosphere, the corona. The corona and the solar wind are fully ionized, and therefore in the plasma state. Magnetic fields play an important role in a plasma, since they bind electrically charged particles to their field lines. EUV spectroscopes, like the SUMER instrument on-board the SOHO spacecraft, reveal a preferred heating of coronal ions and strong temperature anisotropies. Velocity distributions of electrons can be measured directly in the solar wind, e.g. with the 3DPlasma instrument on-board the WIND satellite. They show a thermal core, an anisotropic suprathermal halo, and an anti-solar, magnetic-field-aligned, beam or "strahl". For an understanding of the physical processes in the corona, an adequate description of the plasma is needed. Magnetohydrodynamics (MHD) treats the plasma simply as an electrically conductive fluid. Multi-fluid models consider e.g. protons and electrons as separate fluids. They enable a description of many macroscopic plasma processes. However, fluid models are based on the assumption of a plasma near thermodynamic equilibrium. But the solar corona is far away from this. Furthermore, fluid models cannot describe processes like the interaction with electromagnetic waves on a microscopic scale. Kinetic models, which are based on particle velocity distributions, do not show these limitations, and are therefore well-suited for an explanation of the observations listed above. For the simplest kinetic models, the mirror force in the interplanetary magnetic field focuses solar wind electrons into an extremely narrow beam, which is contradicted by observations. Therefore, a scattering mechanism must exist that counteracts the mirror force. In this thesis, a kinetic model for electrons in the solar corona and wind is presented that provides electron scattering by resonant interaction with whistler waves. The kinetic model reproduces the observed components of solar wind electron distributions, i.e. core, halo, and a "strahl" with finite width. But the model is not only applicable on the quiet Sun. The propagation of energetic electrons from a solar flare is studied, and it is found that scattering in the direction of propagation and energy diffusion influence the arrival times of flare electrons at Earth approximately to the same degree. In the corona, the interaction of electrons with whistler waves does not only lead to scattering, but also to the formation of a suprathermal halo, as it is observed in interplanetary space. This effect is studied both for the solar wind as well as the closed volume of a coronal magnetic loop. The result is of fundamental importance for solar-stellar relations. The quiet solar corona always produces suprathermal electrons. This process is closely related to coronal heating, and can therefore be expected in any hot stellar corona. In the second part of this thesis it is detailed how to calculate growth or damping rates of plasma waves from electron velocity distributions. The emission and propagation of electron cyclotron waves in the quiet solar corona, and that of whistler waves during solar flares, is studied. The latter can be observed as so-called fiber bursts in dynamic radio spectra, and the results are in good agreement with observed bursts. / Die Sonne ist von einer 10^6 K heißen Atmosphäre, der Korona, umgeben. Sie ist ebenso wie der Sonnenwind vollständig ionisiert, also ein Plasma. Magnetfelder spielen in einem Plasma eine wichtige Rolle, da sie elektrisch geladene Teilchen an ihre Feldlinien binden. EUV-Spektroskope, wie SUMER auf der Raumsonde SOHO, zeigen eine bevorzugte Heizung koronaler Ionen sowie starke Temperaturanisotropien. Geschwindigkeitsverteilung von Elektronen können im Sonnenwind direkt gemessen werden, z.B. mit dem 3DPlasma Instrument auf dem Satelliten WIND. Sie weisen einen thermischen Kern, einen isotropen suprathermischen Halo, sowie einen anti-solaren, magnetfeldparallelen Strahl auf. Zum Verständnis der physikalischen Prozesse in der Korona wird eine geeignete Beschreibung des Plasms benötigt. Die Magnetohydrodynamik (MHD) betrachtet das Plasma einfach als elektrisch leitfähige Flüssigkeit. Mehrflüssigkeitsmodelle behandeln z.B. Protonen und Elektronen als getrennte Fluide. Damit lassen sich viele makroskopische Vorgänge beschreiben. Fluidmodelle basieren aber auf der Annahme eines Plasmas nahe am thermodynamischen Gleichgewicht. Doch die Korona ist weit davon entfernt. Ferner ist es mit Fluidmodellen nicht möglich, Prozesse wie die Wechselwirkung mit elektromagnetischen Wellen mikroskopisch zu beschreiben. Kinetische Modelle, die Geschwindigkeitsverteilungen beschreiben, haben diese Einschränkungen nicht und sind deshalb geeignet, die oben genannten Messungen zu erklären. Bei den einfachsten Modellen bündelt die Spiegelkraft im interplanetaren Magnetfeld die Elektronen des Sonnenwinds in einen extrem engen Strahl, im Widerspruch zur Beobachtung. Daher muss es einen Streuprozess geben, der dem entgegenwirkt. In der vorliegenden Arbeit wird ein kinetisches Modell für Elektronen in der Korona und im Sonnenwind präsentiert, bei dem die Elektronen durch resonante Wechselwirkung mit Whistler-Wellen gestreut werden. Das kinetische Modell reproduziert die beobachteten Bestandteile von Elektronenverteilungen im Sonnenwind, d.h. Kern, Halo und einen Strahl endlicher Breite. Doch es ist nicht nur auf die ruhige Sonne anwendbar. Die Ausbreitung energetischer Elektronen eines solaren Flares wird untersucht und dabei festgestellt, dass Streuung in Ausbreitungsrichtung und Diffusion in Energie die Ankunftszeiten von Flare-Elektronen bei der Erde in etwa gleichem Maße beeinflussen. Die Wechselwirkung von Elektronen mit Whistlern führt in der Korona nicht nur zu Streuung, sondern auch zur Erzeugung eines suprathermischen Halos, wie er im interplanetaren Raum gemessen wird. Dieser Effekt wird sowohl im Sonnenwind als auch in einem geschlossenen koronalen Magnetfeldbogen untersucht. Das Ergebnis ist von fundamentaler Bedeutung für solar-stellare Beziehungen. Die ruhige Korona erzeugt stets suprathermische Elektronen. Dieser Prozeß ist eng mit der Koronaheizung verbunden, und daher in jeder heißen stellaren Korona zu erwarten. Im zweiten Teil der Arbeit wird beschrieben, wie sich aus der Geschwindigkeitsverteilung der Elektronen die Dämpfung oder Anregung von Plasmawellen berechnen lässt. Die Erzeugung und Ausbreitung von Elektronenzyklotronwellen in der ruhigen Korona und von Whistlern während solarer Flares wird untersucht. Letztere sind als sogenannte fiber bursts in dynamischen Radiospektren beobachtbar, und die Ergebnisse stimmen gut mit beobachteten Bursts überein.

The topic of the master thesis are the numerical simulations of magnetoacoustic waves in the solar corona in relation to the reconnection of magnetic field. The first part is devoted to the basic description of the Sun, its atmosphere and the processes that occur in it. Other sections are devoted to the description of reconnection of magnetic field and the description of solar flares taking place in the solar corona in relation to the mechanisms of magnetic field reconnection. Then the attention is focused on plasma waves and oscilations. The last section aims to simulate the startup options of the reconnection of magnetic field by oscillations and waves in the Harris current-sheet. Numerical simulations are implemented in FLASH 3.3.

My diploma thesis is focused on the use of numerical computer codes for simulation in plasma astrophysics. They will learn the basic characteristics of the Sun, a closer focus on the solar corona and the solar corona heating problem. The following section is devoted to simulation software in plasma astrophysics, their installing and displaying the results using the visualization software. In the conclusion is demonstrated using this software on a model example and a simulation that performs simulation of impulsively generated waves in solar coronal loops.

One of the most persistent problem in solar physics is the identification of the mechanism that heats the solar corona and accelerates the fast solar wind. Magneto-hydrodynamic (MHD)waves play a crucial role in heating of the solar corona and acceleration of the solar wind. Different types of oscillations have been now observed by various instruments. These are interpreted as due to ubiquitous presence of MHD waves. The magnetic field plays a fundamental role in the propagation and properties of these MHD waves. The topology (structure)of the magnetic fields are different in different regions of the solar atmosphere viz., active regions (high-lying closed magnetic fields), quiet Sun (low-lying closed magnetic fields) and coronal holes (open magnetic fields). The purpose of this dissertation is to study the nature of these propagating MHD waves in different regions of the solar atmosphere. It is believed that polar coronal holes which connects the inner corona and the solar wind, are the source regions of the fast solar wind. The on-disk part of a polar coronal hole can be divided into network and internetwork regions. Long time series(sit-and-stare)data have been obtained from the SUMER/SoHO spectrometer in N iv 765Å and Ne viii 770Å spectral lines to search for the presence of waves in these two different regions from a statistical approach. The network bright regions indicate the presence of compressional waves with a dominant period of ≈ 25 min in both the lines. Moreover, we found that there is a difference in the nature of the wave propagation in the bright (‘network’), as opposed to the dark (‘internetwork’) regions, with the latter sometimes showing evidence of downwardly propagating waves that are not seen in the former. This is consistent with the magnetic topology, as open field lines are rooted in network regions whereas internetwork region has low lying closed field lines. From a measurement of propagation speeds, we found all waves are subsonic, indicating that the majority of them are slow magneto-acoustic in nature. The off-limb part of coronal holes can be divided into plume and inter-plume regions. The simultaneous observations were performed with EIS/Hinode and SUMER/SoHO spectrometer in Fe xii 195Å and Ne viii 770Å spectral lines respectively. We detected the presence of accelerating waves in a polar inter-plume region with a period of 15 min to 20 min in both the spectral lines and a propagation speed increasing from 130 ± 14 km s−1 just above the limb, to 330 ± 140 kms s−1 around 160” above the limb. These waves can be traced to originate from a bright region of the on-disk part of the coronal hole which can be visualized as the base of the coronal funnels. The adjacent plume region also shows the presence of propagating disturbance with the same range of periodicity but with propagation speeds in the range of 135 ± 18 kms s−1 to 165 ± 43 kms s−1 only. We found that the waves within the plumes are not observable (may be getting dissipated) far off-limb whereas this is not the case in the inter-plume region. We suggested that the waves are likely either Alfv´enic or fast magneto-acoustic in the inter-plume regions and slow magneto-acoustic in the plume regions. These results support the view that the inter-plume regions area preferred channel for the acceleration of the fast solar wind. The quiet Sun can be further divided into bright magnetic (network), bright non-magnetic and dark non-magnetic (internetwork) regions. Simultaneous observations were performed in Ca ii filtergram from SOT/Hinode, TRACE 1550Åpassband and with SUMER/SoHO spectrometer in N iv 765ÅandNe viii 770Åspectral lines to study the oscillations in these different regions. We detected the presence of long period oscillations with periods between 15 min to 30 min in bright magnetic regions. The oscillations were detected from chromospheric height to low coronal heights. Power maps showed that low period powers are mainly concentrated in dark regions whereas long period powers are concentrated in bright magnetic regions. We proposed that these 15 min and above periods can propagate up to the coronal heights through ‘magneto¬acoustic portals’. However in this case only with the spectral imaging data, it was not possible to identify the mode of wave propagation. To detect the presence of waves in active regions, we have analysed the imaging and spec¬troscopic data acquired during the total solar eclipse of 2006 and 2009 respectively. We found the oscillations of periods 27 s and 20 s in imaging data obtained in green (Fe xiv 5303Å) and red (Fe x 6374Å) coronal emission lines respectively. Significant oscillations with high proba¬bility estimates were detected at boundary of active region and in the neighbourhood, rather than within the loops itself. We also reported the detection of oscillations in intensity, velocity and line width having periods in the range of 25 s to 50 s with spectroscopic data again obtained in green and red coronal emission lines. These high frequency oscillations were interpreted in terms of presence of fast magneto-acoustic waves or torsional Alfv´en waves. These detected propagating MHD waves may carry sufficient energy to heat the corona and provide enough momenta to accelerate the fast solar wind. In addition, these waves may also provide input for the measurement of coronal magnetic field using the technique of ‘coronal seismology’.

La couche la plus externe de l’atmosphère solaire, la couronne, est composée de plasma dont la température dépasse de plusieurs ordres de grandeur celle de la surface.Expliquer comment la couronne est chauffée à des températures de l’ordre d’un million de degrés constitue un défi majeur de la physique solaire.Dans ce contexte, je m’intéresse au chauffage des boucles coronales (qui sont des structures composées de plasma confiné dans des tubes de champ magnétique) et plus particulièrement aux cycles de non-équilibre thermique (TNE).L’étude de ces cycles permet de caractériser le chauffage des boucles.Ces cycles se développent dans des boucles soumises à un chauffage fortement stratifié, localisé près de leurs pieds.Ils se traduisent notamment par une variation périodique de la température et de la densité du plasma dans la boucle.Ces variations engendrent des pulsations d’intensité de longue période, qui sont détectées depuis peu dans l’émission en extrême-ultraviolet (EUV) de certaines boucles coronales.Par ailleurs, des écoulements périodiques de plasma à températures coronales se produisent durant ces cycles.Dans certains cas, le plasma qui s’écoule peut refroidir de plusieurs ordres de grandeur et former de la pluie coronale périodique.Durant ma thèse, j’ai travaillé à la première détection de ces écoulements à haute et à basse température.En utilisant des séries temporelles de spectres EUV de l’instrument Hinode/EIS, j’ai mesuré la vitesse Doppler du plasma dans des boucles dans lesquelles on détecte des pulsations d’intensité.Cela m’a permis de détecter des écoulements de plasma à température coronale associé à certaines pulsations d’intensité.Par ailleurs, j’ai participé à la détection d’un événement de pluie coronale périodique (à température plus froide) dans des séries d’images de l’instrument SDO/AIA.Ces détections permettent de confirmer que les pulsations d’intensité de longue période sont bien le résultat de cycles de TNE, ainsi que d’apporter de nouvelles contraintes sur le chauffage des boucles coronales.Cela permet notamment de conclure que le chauffage des boucles coronales est localisé près de leurs pieds et que son temps de répétition est inférieur au temps de refroidissement du plasma.Afin de détecter les écoulements à haute température, j’ai dû corriger de nombreux effets instrumentaux de EIS.J’ai notamment développé une nouvelle méthode pour aligner les spectres avec des images de l’instrument AIA, qui permet de corriger l’angle de roulis et la variation aléatoire du pointage de EIS.En appliquant cette méthode à un grand nombre de spectres, j’ai réalisé la première mesure systématique de l’angle de roulis de l’instrument.Par la suite, j’ai réalisé des simulations numériques du cas de pluie coronale périodique.Dans ces simulations, j’ai calculé l’évolution du plasma dans la boucle pour différents paramètres de chauffage et différentes géométries du champ magnétique.Cela m’a permis d’identifier les paramètres de chauffage permettant de reproduire le comportement observé.Avec ces simulations, j’ai par ailleurs pu comprendre comment l’asymétrie de la boucle et du chauffage conditionnent la température minimale atteinte par les écoulements qui se forment lors des cycles de non-équilibre thermique. / The outermost layer of the solar atmosphere, the corona, is composed of plasma which is hotter than the surface by several orders of magnitude.One of the main challenges in solar physics is to explain how the corona is formed and heated to temperatures of a few million degrees.In this context, I focus on the heating of coronal loops (which are structures composed of plasma confined in magnetic field tubes), and more precisely on thermal non-equilibrium (TNE) cycles.Studying these cycles allows us to characterize the heating of coronal loops.These cycles occur in loops with a highly stratified heating, localized near their footpoints.Among other effects, they cause periodic variations of the temperature and density of the plasma in the loop.These variations result in long-period intensity pulsations, which have recently been detected in the extreme-ultraviolet (EUV) emission of some coronal loops.In addition, periodic flows of plasma at coronal temperatures occur during these cycles.In some cases, the flowing plasma can cool down by several orders of magnitude, and thus form periodic coronal rain.During my thesis, I worked on the first detection of these periodic plasma flows at coronal and lower temperatures.Using time series of spatially-resolved EUV spectra from the instrument Hinode/EIS, I measured the Doppler velocity of plasma in loops undergoing long-period intensity pulsations.This allowed me to detect flows of plasma at coronal temperatures associated with some maxima of the intensity pulsations.In addition, I took part in the detection of an event of periodic coronal rain (at cooler temperatures), using series of images from the instrument SDO/AIA.These detections confirm that the long-period intensity pulsations detected in coronal loops are indeed the result of TNE cycles, and allow better constrain the heating of the loops.From this, conclude that the heating of coronal loops is highly stratified, localized near their footpoints, with a repetition time shorter than the cooling time of the plasma.Detecting the flows of plasma at coronal temperatures required that I correct many EIS instrumental effects.To that aim, I developed a new method for coalinging EIS spectra with images from AIA.This method can correct the roll angle and the jitter (a random variation of the pointing) of EIS.By applying it to a large number of spectra, I carried out a comprehensive determination of the EIS roll angle.I also performed numerical simulations of the periodic coronal rain event.In these simulations, I computed the evolution of the plasma in the loop for different values of the heating parameters, as well as several magnetic field geometries.This allowed me to determine the heating parameters which are required to reproduce the observed behavior of this loop.By analyzing these simulations, I was also able to understand how the asymmetry of the loop and of the heating determine the minimum temperature of the plasma flows which form during thermal non-equilibrium cycles.

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L’utilisation d’une méthode d’assimilation de données, associée à un modèle de convection anélastique, nous permet la reconstruction des structures physiques d’une partie de la zone convective située en dessous d’une région solaire active. Les résultats obtenus nous informent sur les processus d’émergence des tubes de champ magnétique au travers de la zone convective ainsi que sur les mécanismes de formation des régions actives. Les données solaires utilisées proviennent de l’instrument MDI à bord de l’observatoire spatial SOHO et concernent principalement la région active AR9077 lors de l’ ́évènement du “jour de la Bastille”, le 14 juillet 2000. Cet évènement a conduit à l’avènement d’une éruption solaire, suivie par une importante éjection de masse coronale. Les données assimilées (magnétogrammes, cartes de températures et de vitesses verticales) couvrent une surface de 175 méga-mètres de coté acquises au niveau photosphérique. La méthode d’assimilation de données employée est le “coup de coude direct et rétrograde”, une méthode de relaxation Newtonienne similaire à la méthode “quasi-linéaire inverse 3D”. Elle présente l’originalité de ne pas nécessiter le calcul des équations adjointes au modèle physique. Aussi, la simplicité de la méthode est un avantage numérique conséquent. Notre étude montre au travers d’un test simple l’applicabilité de cette méthode à un modèle de convection utilisé dans le cadre de l’approximation anélastique. Nous montrons ainsi l’efficacité de cette méthode et révélons son potentiel pour l’assimilation de données solaires. Afin d’assurer l’unicité mathématique de la solution obtenue nous imposons une régularisation dans tout le domaine simulé. Nous montrons enfin que l’intérêt de la méthode employée ne se limite pas à la reconstruction des structures convectives, mais qu’elle permet également l’interpolation optimale des magnétogrammes photosphériques, voir même la prédiction de leur évolution temporelle. / We use a data assimilation technique, together with an anelastic convection model, in order to reconstruct the convective patterns below a solar active region. Our results yield information about the magnetic field emergence through the convective zone and the mechanisms of active region formation. The solar data we used are taken from the instrument MDI on board the spatial observatory SOHO on July 2000 the 14th for the event called ”bastille day event”. This specific event leads to a solar flare followed by a coronal mass ejection. Assimilated data (magnetograms, temperature maps and vertical velocity maps) cover an area of 175 Mm × 175 Mm at photospheric level. The data assimilation technique we used, the ”Nudging Back and Forth”, is a Newtonian re- laxation technique similar to the ”quasi linear inverse 3D”. Such a technique does not require computation of the adjoint equations. Thus, simplicity of this method is a numerical advantage. Our study shows with a simple test case the applicability of this method to a convection model treated with the anelastic approximation. We show the efficiency of the NBF technique and we detail its potential for solar data assimi- lation. In addition, to ensure mathematical unicity of the obtained solution, a regularization has been imposed in the whole simulation domain. This is a new approach. Finally, we show that the interest of such a technique is not limited to the reconstruction of convective patterns but that it also allows optimal interpolation of photospheric magnetograms and predictions.

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