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The problem of heating the solar corona requires the conversion of magnetic energy into thermal energy. Presently, there are two promising mechanisms for heating the solar corona: wave heating and nanoflare heating. In this thesis, we consider nanoflare heating only. Previous modelling has shown that the kink instability can trigger energy release and heating in large scale loops, as the field rapidly relaxes to a lower energy state under the Taylor relaxation theory. Two distinct experiments were developed to understand the coronal heating problem: the avalanche effect within a multiple loop system, and the importance of thermal conduction and optically thin radiation during the evolution of the kinked-unstable coronal magnetic field. The first experiment showed that a kink-unstable thread can also destabilise nearby threads under some conditions. The second experiment showed that the inclusion of thermal conduction and optically thin radiation causes significant change to the internal energy of the coronal loop. After the initial instability occurs, there is continual heating throughout the relaxation process. Our simulation results show that the data is consistent with observation values, and the relaxation process can take over 200 seconds to reach the final relaxed state. The inclusion of both effects perhaps provides a more realistic and rapid heating experiment compared to previous investigations.

Le chauffage de la couronne et la formation du vent solaire sont plus que jamais d'actualité en astrophysique stellaire. En ce qui concerne le vent solaire, nous avons cherché à vérifier l'hypothèse selon laquelle il est issu des frontières de régions actives. En combinant l'imagerie en rayons X et Extrême Ultra Violet (EUV), la spectroscopie EUV et les mesures de champ magnétique longitudinal au niveau de la photosphère, nous avons développé une technique d’estimation quantitative des échanges de masse entre deux régions actives. Nous avons ainsi montré que cet échange n'est pas négligeable devant le flux de matière participant au vent solaire. Une attention particulière a été apportée aux traitements des données spectroscopiques notamment en ce qui concerne la référence en longueur d'onde. En effet, celle-ci est cruciale pour déterminer les vitesses y compris leurs signes dans les échanges. Sur la thématique des micro-événements de chauffage, nous avons développé une méthode de détection à partir d'images prises à haute cadence en rayons X. A l'aide de données spectroscopiques, nous avons pu estimer les vitesses Doppler et l’élargissement Doppler des raies dans les événements et les comparer au reste du champ de vue. Nous en avons déduit l’énergie contenue dans les vitesses non résolues, susceptible de contribuer au chauffage, qui s’avère être comparable aux pertes radiatives observées dans les régions actives. / The coronal heating and the formation of the solar wind are one of the core issues in stellar astrophysics.Concerning the solar wind, we have undertaken to verify the hypothesis that its origin is located at the borders of active regions. By combining X-ray and Extreme Ultra Violet (EUV) images, EUV spectroscopy and measurements of the longitudinal magnetic field at the photosphere, we have developed a technique for quantitatively estimating the mass exchange between two active regions. We have shown that this mass exchange is significant compared to the flow of material involved in the solar wind. Particular attention was paid to the analysis of spectroscopic data and more specifically the issue of reference wavelength. Indeed, it is crucial to determine the speeds including their signs in the exchange. On the topic of heating micro-events, we have developed a method for detecting micro-events from high-cadence X-ray images. With the help of spectroscopic data, we have been able to estimate the Doppler velocities and Doppler broadening of the lines in the events and compare them to the rest of the field of view. We derived the energy in the unresolved velocities, which can contribute to the heating, which turns out to be comparable to the radiative losses observed in active regions.

Kontext: Die Sonnenkorona wird seit 1932 mit Koronographen beobachtet. Nur wenige Jahre später war klar, dass die Korona viel heißer ist als die sichtbare Sonnenoberfläche; seit dem ist der Mechanismus der koronalen Heizung ungeklärt. Viele Mechanismen wurden vorgeschlagen, die genügend Energie zur Basis der Korona liefern, es hat sich aber kein vollständig selbstkonsitentes Bild des Energietransports und der koronalen Dissipation etabliert. Ziele: Wir möchten ein selbstkosistentes Modell aufstellen, welches Bewegungen auf der Sonnenoberfläche enthält, welche das Magnetfeld verbiegen und verflechten, wodurch in der Korona Ströme induziert und Ohm’sch dissipiert werden. Die Modellbeschreibung soll durch den Vergleich von synthetischen mit realen Beobachtungen untermauert werden. Methoden: Wir treiben das 3D MHD Model mit beobachteten photosphärischen Magnetfeldern und Horizontalbewegungen an. Durch Wärmeleitung entlang des Feldes sowie Strahlungsverluste wird die koronale Energiebilanz realistisch. Wir synthetisieren Spektren in verschiedenen Emissionslinien mit einer Atom-Datenbank und der berechneten koronalen Plasmatemperatur sowie -dichte. Diese vergleichen wir mit entsprechenden Beobachtungen der Korona über der aktiven Region, mit der wir die Simulation antreiben. Wir vergleichen extrahierte Modell-Feldlinien mit empirischen und theoretischen Skalengesetzen, die die koronale Heizung entlang von Bögen voraussagen. Resultate: Im Modell bilden sich heiße koronale Bögen mit Temperaturen deutlich über 1 MK. Ihre 3D-Struktur entspricht den beobachteten koronalen Bögen; Doppler-Karten lassen auf ähnliche Plasmaströmungen entlang der Bögen schließen. An die Modell-Daten passen wir ein Skalengesetz an, welches von der Bogenlänge und der magnetischen Flussdichte an den Fußpunkten abhängt. Schlussfolgerungen: Aus der substanziellen Übereinstimmung zwischen Modell und Beobachtung schließen wir, dass das Modell eine genügende Beschreibung der Heizung und Wärmeleitung entlang von koronalen Bögen darstellt, um die Beobachtungen zu erklären.

This thesis comprises of essentially two parts. The first deals with materials in a fusion reactor and examines how neutron damage affects material in a fusion reactor, with focus on how this is important for plasma damage. The methods used are neutron transport, primary event analysis and molecular dynamics. It found that the neutron damage by 14 MeV neutrons is restricted to back scatter events within the surface (first 20 microns). Molecular dynamics analysis showed that the issue of cascades is heavily dependent on direction of primary event and the energy of such. Statistical analysis was done to provide a standard approach for modelling of damage through neutrons. The second deals with the relaxation of magnetic flux ropes with an emphasis on kink unstable flux ropes. A relaxation model was developed which shows good approximation to simulation results of merging magnetic flux ropes. Subsequently, work was done to establish the physical processes involved in relaxation. This was done by examining magnetohydrodynamic (MHD) simulations of two flux ropes, one unstable and one stable. It was found that there is is a clear distance at which merger does not occur any more. Furthermore, a critical current seems to be a requirement at the edge a stable flux rope.

This thesis presents a new computationally efficient method for modelling the response of the solar corona to the release of energy. During impulsive heating events, the coronal temperature increases which leads to a downward heat flux into the transition region (TR). The plasma is unable to radiate this excess conductive heating and so the gas pressure increases locally. The resulting pressure gradient drives an upflow of dense material, creating an increase in the coronal density. This density increase is often called chromospheric evaporation. A process which is highly sensitive to the TR resolution in numerical simulations. If the resolution is not adequate, then the downward heat flux jumps over the TR and deposits the heat in the chromosphere, where it is radiated away. The outcome is that with an under-resolved TR, major errors occur in simulating the coronal density evolution. We address this problem by treating the lower transition region as a discontinuity that responds to changing coronal conditions through the imposition of a jump condition that is derived from an integrated form of energy conservation. In this thesis, it is shown that this method permits fast and accurate numerical solutions in both one-dimensional and multi-dimensional simulations. By modelling the TR with this appropriate jump condition, we remove the influence of poor numerical resolution and obtain the correct evaporative response to coronal heating, even when using resolutions that are compatible with multi-dimensional magnetohydrodynamic simulations.

Il a été découvert récemment que les pulsations d’intensité de longue période (entre 3 et 16 heures) sont très répandues dans la couronne solaire et en particulier dans les boucles coronales. Les processus de chauffage des boucles coronales, qui permettent de porter le plasma à des températures de l’ordre du million de degrés et de le maintenir confiné à ces températures,restent mal compris. Ces pulsations dans l’extrême ultraviolet amènent de nouvelles contraintes observationnelles pour les modèles de boucles coronales et par conséquent pour mieux comprendre leur dynamique et leur chauffage. Le thème central de cette thèse est l’exploration des origines physiques possibles pour ce phénomène.J’ai dans un premier temps utilisé un code de détection, initialement développé pour les données de l’imageur SoHO/EIT, sur l’archive de l’instrument SDO/AIA. J’ai pu détecter des milliers d’événements sur six ans de données,la moitié d’entre eux se concentrant dans des régions actives et environ la moitié encore de ces événements pouvant êtreclairement identifiés dans des boucles. Parmi ces milliers d’événements, j’ai sélectionné trois cas associés à des boucles, avecun signal de détection fort et permettant d’explorer une large gamme de périodes.Grâce à l’utilisation des six bandes coronales d’AIA, j’ai pu dans un deuxième temps réaliser une analyse de lastructure thermique de ces boucles via la reconstruction de la mesure d’émission différentielle (DEM, pour Differential Emission Measure) et l’étude des décalages temporels entre les intensités des six bandes. La température et la densité du plasma reconstruites évoluent de façon périodique avec un retard temporel entre ces deux quantités. Ce comportement,caractéristique de cycles d’évaporation et de condensation du plasma, m’a permis de rapprocher ces pulsations d’intensité à un phénomène bien connu dans les simulations numériques et pour des structures comme les protubérances et la pluie coronale : l’absence d’équilibre thermique ou thermal non-equilibrium (TNE). Une analyse des caractéristiques des spectres de puissances observés a permis par ailleurs de confirmer cette conclusion. Le TNE intervient lorsque le chauffage dans les boucles est stratifié en altitude, avec un chauffage plus important à basse altitude et lorsque le chauffage est quasi-constant.L’identification non ambigüe du TNE dans les boucles a donc des implications très importantes pour la compréhension du chauffage des boucles.Dans un troisième temps, je me suis attachée à reproduire ces pulsations d’intensité par la simulation et à déterminer les propriétés intrinsèques des boucles qui favorisent l’apparition de ces cycles d’évolution dans certaines boucles. J’ai notamment utilisé des extrapolations du champ magnétique des trois régions étudiées en détail avec AIA, pour étudier la géométrie de boucles. Ces géométries ont ensuite été utilisées en entrée du code de simulation hydrodynamique 1D. J’ai alors balayé l’espace des paramètres des fonctions de chauffage utilisées et pu déterminer que les conditions d’apparition de cycles de TNE proviennent d’une combinaison de la géométrie de la boucle et des paramètres du chauffage (asymétrie et puissance). Ce qui explique que certaines boucles présentent des pulsations d’intensité et d’autres non. J’ai de plus étudiéune simulation en particulier, dont les paramètres physiques du plasma sont proches de ceux observés pour un cas étudié avec AIA. Les intensités EUV alors simulées reproduisent bien celles observées. Le modèle étudié permet d’expliquer les pulsations observées en terme de cycles d’évaporation et de condensation. / Long-period EUV intensity pulsations (periods from 3 to 16 hours) have been found recently to be very common in thesolar corona and especially in coronal loops. The heating mechanism(s) of solar coronal loops that generate million-degreeplasma and maintain it confined at this temperature remain unknown. These intensity pulsations (extreme ultraviolet)provide new constraints for loops models and thus to better understand coronal loops dynamics and heating. The centraltopic of this thesis is to explore the possible physical explanations for this phenomenon.First, I used a detection code, initially developed for SoHO/EIT images, on the SDO/AIA archive. I detected thousandsof events in the six years of data, half of them corresponding to active regions and about the half of whom are identifiedas corresponding to coronal loops. I selected three cases of long-period intensity pulsation events in loops, with a cleardetection signal and allowing to scan different periods.Second, using the six coronal channels of AIA, I made a detailed study of the thermal structure of these loops. I usedboth differential emission measure (DEM) reconstructions and an analysis of the time-lags between the intensities in thesix channels. The temperature and the density are found to be periodic with a time delay between these two physicalparameters of the plasma. This behavior is characteristic of evaporation and condensation cycles of the plasma and itallowed me to connect these intensity pulsations to thermal non-equilibrium (TNE), a well-know phenomenon in numericalsimulations and for structures such as prominences and coronal rain. Moreover, an analysis based only on the shape ofpower spectra allowed to confirm this conclusion. TNE happens when the heating is highly-stratified (mainly concentratedat low altitudes) and quasi-constant. Unambiguous identification of TNE in coronal loops has thus important implicationsfor understanding coronal heating.Third, I aimed at reproducing the observed intensity pulsations by simulations and at determining the intrinsicproperties of coronal loops that favor these particular cycles of evolution. I made extrapolations of the magnetic fieldfor the three regions studied to determine the loops geometry. These geometries have been then used as inputs for 1Dhydrodynamic simulations. I conducted a parameter space study that revealed that the TNE cycles occurrence is sensitiveto a combination of the loop geometry and heating parameters (asymmetry and heating power). This allows me to explainwhy these pulsations are encountered in some loops but not in all. I studied one simulation in particular, matching theobserved characteristics of the plasma evolution. I derived the corresponding AIA synthetic intensities which reproducedthe main characteristics of the observed pulsations. This model allows me to explain the observed pulsations as evaporationand condensation cycles.

Les grands événements de la couronne solaire (comme les flares avec une énergie de l'ordre de 10²³ J) ne suffisent pas à maintenir cette dernière aux températures de plus de un million de degrés qui y sont mesurées. La couronne doit alors être chauffée aux petites échelles, soit de façon continue, soit de façon intermittente. C'est pourquoi afin d'expliquer la température élevée de la couronne, beaucoup d'attention a été accordée aux distributions des énergies dissipées dans les plus petits événements (de l'ordre du mégamètre). En effet, si la distribution en énergie est assez pentue, les plus petits événements, qui sont inobservables, pourraient être les plus gros contributeurs à l'énergie totale dissipée dans la couronne. Des observations précédentes ont montré une large distribution en énergie mais ne permettent pas de conclure sur la valeur précise de la pente, et ces résultats s'appuient sur une estimation peu précise de l'énergie. D'autre part, des études spectroscopiques plus détaillées de structures comme les points brillants coronaux ne fournissent pas assez d'informations statistiques pour calculer leur contribution totale au chauffage. Nous voulons obtenir une meilleure estimation des distributions en énergies dissipées dans les événements de chauffage coronaux en utilisant des données de haute résolution dans plusieurs bandes de l'Extrême Ultra-Violet (EUV).Pour estimer les énergies correspondant aux événements de chauffage et déduire leur contribution, nous détectons des embrillancements dans cinq bandes EUV de l'instrument Atmospheric Imaging Assembly (AIA) à bord du satellite Solar Dynamics Observatory (SDO). Nous combinons les résultats de ces détections et nous utilisons des cartes de température et de mesure d'émission calculées à partir des mêmes observations pour calculer les énergies. Nous obtenons des distributions des surfaces, des durées de vie, des intensités et des énergies (thermique, radiative et de conduction) des événements. Ces distributions sont des lois de puissance, dont les paramètres indiquent que la population d'événements que nous avons observé n'est pas suffisante pour expliquer entièrement les températures coronales. Cependant, plusieurs processus physiques et biais observationnels peuvent être avancés pour expliquer l'énergie manquante. / To explain the high temperature of the corona, much attention has been paid to the distribution of energy in dissipation events. Indeed, if the event energy distribution is steep enough, the smallest, unobservable events could be the largest contributors to the total energy dissipation in the corona. Previous observations have shown a wide distribution of energies but remain inconclusive about the precise slope. Furthermore, these results rely on a very crude estimate of the energy. On the other hand, more detailed spectroscopic studies of structures such as coronal bright points do not provide enough statistical information to derive their total contribution to heating. We aim at getting a better estimate of the distributions of the energy dissipated in coronal heating events using high-resolution, multi-channel Extreme Ultra-Violet (EUV) data. To estimate the energies corresponding to heating events and deduce their distribution, we detect brightenings in five EUV channels of the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO). We combine the results of these detections and we use maps of temperature and emission measure derived from the same observations to compute the energies. We obtain distributions of areas, durations, intensities, and energies (thermal, radiative, and conductive) of events. These distributions are power-laws, but their parameters indicate that a population of events like the ones we observe is not sufficient to fully explain coronal temperatures. However, several processes or observational biases can be advanced to explain the missing energy.

We present observational and numerical evidence supporting the theory of impulsive heating of the solar corona. We have run numerical simulations solving the hydrodynamic equations for plasma confined to a magnetic flux tube, for the two distinct cases of steady and impulsive heating. We find that steady heating cannot explain the observed amount of low-temperature plasma in active regions on the sun. The results for impulsive heating closely match those of the observations. The ratio of heating time to cooling time predominantly determines the observed temperature distribution of the plasma. We have also identified an observational bias in calculating intensities of spectral lines in previous studies, which causes an under-estimation of low-temperature plasma. We predict Doppler shifts in the observed line emission that are in agreement with observations, and which may serve as a diagnostic of the strength of heating. We conclude that impulsive heating of active region coronal loops is more likely than steady heating.

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’.