The magnetic carpet is defined to be the small-scale photospheric magnetic field of the quiet Sun. Observations of the magnetic carpet show it to be highly dynamic, where the time taken for all flux within the magnetic carpet to be replaced is on the order of just a few hours. The magnetic carpet is continually evolving due to the Sun's underlying convection and the interaction of small-scale magnetic features with one another. Due to this, the small-scale coronal field of the magnetic carpet is also expected to be highly dynamic and complex. Previous modelling has shown that much of the flux from the magnetic carpet is stored along low-lying closed connections between magnetic features. This indicates that significant coronal heating could occur low down in the small-scale corona. In this thesis, a new two-component magnetic field model is developed for the evolution of the magnetic carpet. A 2D model is constructed to realistically simulate the evolution of the photospheric field of the magnetic carpet, where many of the parameters for the model are taken from observational studies. The photospheric model contains a granular and supergranular flow profile to describe the motion of the small-scale magnetic features, and includes the processes of flux emergence, cancellation, coalescence and fragmentation. This 2D model then couples to a 3D model as the lower boundary condition, which drives the evolution of the coronal field through a series of non-linear force-free states, via a magnetofrictional relaxation technique. We first apply the magnetofrictional technique to consider the coronal evolution of three basic small-scale photospheric processes: emergence, cancellation and flyby. We consider the interaction of the magnetic features with an overlying coronal magnetic field, and quantify magnetic energy build-up, storage and dissipation. The magnetofrictional technique is then applied to synthetic magnetograms produced from the 2D model, to simulate the evolution of the coronal field in a situation involving many hundreds of magnetic features. We conduct a preliminary analysis of the resultant 3D simulations, considering the magnetic energy stored and dissipated, as well as regions of enhanced velocity and electric current density within the coronal volume. The simulations show that the so-called 'quiet Sun' is not quiet and a significant amount of complex interactions take place.

Flux ropes are magnetic structures commonly found in the solar corona. They are thought to play an important role in solar flares and coronal mass ejections. Understanding their formation and eruption is of paramount importance for our understanding of space weather. In this thesis the magnetofrictional method is applied to simulate the formation of flux ropes and track their evolution up to eruption both in solar and stellar coronae. Initially, the coronal magnetic field of a solar active region is simulated using observed magnetograms to drive the coronal evolution. From the sequence of magnetograms the formation of a flux rope is simulated, and compared with coronal observations. Secondly a procedure to produce proxy SOLIS synoptic magnetograms from SDO/HMI and SOHO/MDI magnetograms is presented. This procedure allows SOLIS-like synoptic magnetograms to be produced during times when SOLIS magnetograms are not available. Thirdly, a series of scaling laws for the formation and life-times of flux ropes in stellar coronae are determined as a function of stellar differential rotation and surface diffusion. These scaling laws can be used to infer the response of stellar coronae to the transport of magnetic fields at their surface. Finally, global long-term simulations of stellar corona are carried out to determine the coronal response to flux emergence and differential rotation. A bipole emergence model is developed and is used in conjunction with a surface flux transport model in order to drive the global coronal evolution. These global simulations allow the flux, energy and flux rope distributions to be studied as a function of a star's differential rotation and flux emergence rate.

The main idea behind the work presented in this thesis is to investigate if it is possible to find a mechanism that leads to surface magnetic field concentrations and could operate under solar conditions without postulating the presence of magnetic flux tubes rising from the bottom of the convection zone, a commonly used yet physically problematic approach. In this context we study the ‘negative effective magnetic pressure effect’: it was pointed out in earlier work (Kleeorin et al., 1989) that the presence of a weak magnetic field can lead to a reduction of the mean turbulent pressure on large length scales. This reduction is now indeed clearly observed in simulations. As magnetic fluctuations experience an unstable feedback through this effect, it leads, in a stratified medium, to the formation of magnetic structures, first observed numerically in the fifth paper of this thesis. While our setup is relatively simple, one wonders if this instability, as a mechanism able to concentrate magnetic fields in the near surface layers, may play a role in the formation of sunspots, starting from a weak dynamo-generated field throughout the convection zone rather than from strong flux tubes stored at the bottom. A generalization of the studied case is ongoing. / <p>At the time of the the doctoral defence the following paper was unpublished and had a status as follows: Paper nr 7: Submitted</p>

Sunspots and active regions are two of the many manifestations of the solar magnetic field. This field plays an important role in causing phenomena such as coronal mass ejections, flares, and coronal heating. Therefore, it is important to study the origin of sunspots and active regions and determine the underlying mechanism which creates them. It is believed that flux tubes rising from the bottom of the convection zone can create sunspots. However, there are still unanswered questions about this model. In particular, flux tubes are expected to expand as they rise, hence their strength weakens and some sort of reamplification mechanism must complement this model to match the observational properties of sunspots. To compensate for the absence of such an amplification mechanism, the field strength of the flux tubes, when at the bot- tom of the convection zone, must be far stronger than present dynamo models can explain. In the last few years, there has been significant progress toward a new model of magnetic field concentrations based on the negative effective mag- netic pressure instability (NEMPI) in a highly stratified turbulent plasma. NEMPI is a large-scale instability caused by a negative contribution to the total mean-field pressure due to the suppression of the total turbulent pressure by a large-scale magnetic field. In this thesis, I study for the first time NEMPI in the presence of a dynamo-generated magnetic field in both spherical and Carte- sian geometries. The results of mean-field simulations in spherical geometry show that NEMPI and the dynamo instability can act together at the same time such that we deal with a coupled system involving both NEMPI and dynamo effects simultaneously. I also consider a particular two-layer model which was previously found to lead to the formation of bipolar magnetic structures with super-equipartition strength in the presence of a dynamo-generated field. In this model, the turbulence is forced in the entire domain, but the forcing is made helical in the lower part of the domain, and non-helical in the upper part. The study of such a system in spherical geometry showed that, when the stratification is strong enough, intense bipolar regions form and, as time passes, they expand, merge and create giant structures. To understand the underlying mechanism of the formation of such intense, long-lived bipolar structures with a sharp boundary, we performed a systematic numerical study of this model in plane parallel geometry by varying the magnetic Reynolds number, the scale separation ratio, and Coriolis number. Finally, I investigate the formation of the current sheet between bipolar regions and reconnection of oppositely orientated magnetic field lines and demonstrate that for large Lundquist numbers, S, the reconnection rate is nearly independent of S – in agreement with recent studies in identical settings.

No description available.

The literature on isolated bursts and possible mechanisms of origin has been critically reviewed, and observations point to a mechanism involving omission of electromagnetc radiation from plasma oscillations in the solar corona excited by outward travelling disturbances. Solar noise observations on 125 Mc./s. recorded at Rhodes University during the period November 26 1957 - February 6 1958 have been analysed by the author for isolated bursts, and these observations show the same general features reported by previous investigators. In interpretation of these records particular attention has been devoted to two aspects of isolated bursts; namely the preponderance on single frequency records of double-humped bursts, and the shape of isolated burst profiles. The authors suggests that a probable explanation of double-humped bursts observed on any frequency f is that the first hump represents omission at or near the level of zero refractive index for f radiation, and that the second hump corresponds to harmonic omission at the f/2 level. Source velocities may be calculated from the time delay between the peaks and an average value of 2 x 10⁴ km./sec. was obtained from an analysis of 21 double-humped bursts. This value is in very good agreement with that deduced by Wild (1950b) from the rate of frequency drift of peak intensity of isolated bursts. Simple isolated bursts had decay profiles which are approximatley exponential in shape, and this is usually interpreted in terms of the natural decay of plasma oscillations in the medium of origin. The author has verified that the exponential function is a good fit to the observed decay profiles, but shows that a relation of the form I - ¹/n (superscript) ⋉ t (where I is intensity and t is time) fits just as well. An alternative model is suggested which would lead to an exponential-like decay profile which is not determined by the natural decay of plasma oscillations. The work concludes with some suggestions for further research.

Solar magnetic fields span a wide range of spatial scales from sunspots and plages to magnetic bright points. A clear understanding of the physical processes underlying the evolution of these magnetic features requires high-resolution spectropolarimetric observations of solar active regions and comparisons with synthetic data from simulations. This thesis is based on observations with the Swedish 1-m Solar Telescope (SST) and the CRISP imaging spectropolarimeter which, processed with a sophisticated image restoration technique, produce data of unsurpassed quality. The Fe I 630.25 nm line is used for all the spectropolarimetric observations. It appears likely that present telescopes resolve the fundamental scales of penumbral filaments. However, the penumbrae of sunspots are still not fully understood, with various theoretical models competing to explain their fine structure and flows. We analyze spectropolarimetric observations with a resolution close to the SST diffraction limit of 0.16 arcsecond. Using inversion techniques, we map the line-of-sight velocities and the magnetic-field configuration of dark-cored penumbral filaments. Over the past decade, sunspots and quiet sun magnetic fields have received considerable attention, with intermediate plage regions being somewhat neglected. We perform a detailed analysis of a plage region and present the first observational evidence of a small-scale granular magneto-convection pattern associated with a plage region. Magnetic bright points are believed to be formed due to magnetic field intensification caused by flux-tube collapse involving strong downflows. Although magneto-hydrodynamic (MHD) simulations agree with this view, only a few observations with adequate spatial resolution exist in support of the simulations. We present several cases of bright-point formation associated with strong downflows, which qualitatively agree with simulations and past observations. However, we find the field intensification to be transient rather than permanent. / At the time of the doctoral defense, the following paper was unpublished: Paper 3: Accepted.

The chromosphere and transition region of the solar atmosphere provide an interface between the cool photosphere (6000 K) and the hot corona (1 million K). Both layers exhibit dramatic deviations from thermal and hydrostatic equilibrium in the form of intense plasma heating and mass transfer. The exact mechanisms responsible for transporting energy to the upper atmosphere remain unknown, but these must include a variety of energetic processes operating across many spatial and temporal scales. This dissertation comprises three studies of possible mechanisms for plasma heating and energy transport in the solar chromosphere and transition region. The first study establishes the theoretical framework for a collisional, two-stream plasma instability in the quiet-Sun chromosphere similar to the Farley-Buneman instability which actively heats the E-region of Earth's ionosphere. After deriving a linear dispersion relationship and employing a semi-empirical model of the chromosphere along with carefully computed collision frequencies, this analysis shows that the threshold electron drift velocity for triggering the instability is remarkably low near the temperature minimum where convective overshoots could continuously trigger the instability. The second study investigates simultaneous Interface Region Imaging Spectrograph (IRIS) observations of magnetohydrodynamic (MHD) waves in the chromospheres and transition regions of sunspots. By measuring the dominant wave periods, apparent phase velocities, and spatial and temporal separations between appearances of two observationally distinct oscillatory phenomena, the data show that these are consistent with upward-propagating slow magnetoacoustic modes tied to inclined magnetic field lines in the sunspot, providing a conduit for photospheric seismic energy to transfer upward. The third and final study focuses on intense, small-scale (1 arcsec) active region brightenings known as IRIS UV bursts. These exhibit dramatic FUV/NUV emission line splitting and deep absorption features, suggesting that they result from reconnection events embedded deep in the cool lower chromosphere. IRIS FUV spectral observations and Solar Dynamics Obser- vatory/Helioseismic and Magnetic Imager (SDO/HMI) magnetograms of a single evolving active region reveal that bursts prefer to form during the active region's emerging phase. These bursts tend to be spatially coincident with small-scale, photospheric, bipolar regions of upward and downward magnetic flux that dissipate as the active region matures.

The measurement of vector magnetic fields on the sun is one of the most important diagnostic tools for characterizing solar activity. The ubiquitous solar wind is guided into interplanetary space by open magnetic field lines in the upper solar atmosphere. Highly-energetic solar flares and Coronal Mass Ejections (CMEs) are triggered in lower layers of the solar atmosphere by the driving forces at the visible ``surface'' of the sun, the photosphere. The driving forces there tangle and interweave the vector magnetic fields, ultimately leading to an unstable field topology with large excess magnetic energy, and this excess energy is suddenly and violently released by magnetic reconnection, emitting intense broadband radiation that spans the electromagnetic spectrum, accelerating billions of metric tons of plasma away from the sun, and finally relaxing the magnetic field to lower-energy states. These eruptive flaring events can have severe impacts on the near-Earth environment and the human technology that inhabits it. This dissertation presents a novel inversion method for inferring the properties of the vector magnetic field from telescopic measurements of the polarization states (Stokes vector) of the light received from the sun, in an effort to develop a method that is fast, accurate, and reliable. One of the long-term goals of this work is to develop such a method that is capable of rapidly-producing characterizations of the magnetic field from time-sequential data, such that near real-time projections of the complexity and flare-productivity of solar active regions can be made. This will be a boon to the field of solar flare forecasting, and should help mitigate the harmful effects of space weather on mankind's space-based endeavors. To this end, I have developed an inversion method based on genetic algorithms (GA) that have the potential for achieving such high-speed analysis.

Increasing observational evidence of wave modes brings us to a closer understanding of the solar corona. Coronal seismology allows us to combine wave observations and theory to determine otherwise unknown parameters. The period ratio, P₁/2P₂, between the period P₁ of the fundamental mode and the period P₂ of its first overtone is one such tool of coronal seismology and its departure from unity provides information about the structure of the corona. In this thesis we consider the period ratio P₁/2P₂ of coronal loops from a theoretical standpoint. Previous theory and observations indicate that the period ratio is likely to be less than unity for oscillations of coronal loops. We consider the role of damping and density structuring on the period ratio. In Chapter 2 we consider analytically the one-dimensional wave equation with the inclusion of a generic damping term for both uniform and non-uniform media. Results suggest that the period ratio is dominated by longitudinal structuring rather than damping. In Chapter 3 we consider analytically the effects of thermal conduction and compressive viscosity on the period ratio for a longitudinally propagating sound wave. We find that damping by either thermal conduction or compressive viscosity typically has a small effect on the period ratio. For coronal values of thermal conduction the effect on the period ratio is negligible. For compressive viscosity the effect on the period ratio may become important for some short hot loops. In Chapter 4 we extend the analysis of Chapter 3 to include radiative cooling and find that it too has a negligible effect on the period ratio for typical coronal values. As an extension to the investigation, damping rates are considered for thermal conduction, compressive viscosity and radiative cooling. The damping time is found to be optimal for each mechanism in a different temperature range, namely below 1 MK for radiative cooling, 2 − 6 MK for thermal conduction and above 6 MK for compressive viscosity. In Chapter 5 we consider analytically the period ratio for the fast kink, sausage and n = N modes of a magnetic slab, discussing both an Epstein density profile and a simple step function profile. We find that transverse density structuring in the form of an Epstein profile or a step function profile may contribute to the shift of the period ratio for long thin slab-like structures. The similarity in the behaviour of the period ratio for both profiles means either can be used as a robust model. We consider also other profiles numerically for the kink mode, which are found to be either slab-like or Epstein-like suggesting again that it is not necessary to distinguish the nature of the density profile when considering the period ratio.