In this thesis I study the magnetic activity of young stars via observations of stellar prominences on single stars and by applying the Zeeman Doppler imaging (ZDI) technique to map the magnetic fields and measure differential rotation of a young binary system. Stellar prominences can be observed as absorption transients in the rotationally broadened chromospheric lines of rapidly rotating stars. Observations of Speedy Mic(K3V) reveal a densely packed prominence system at heights far above the stellar co-rotation radius. Further observations were used to estimate prominence column densities and masses. From very high signal-to-noise observations, loops of emission are found that trace the path of prominences seen transiting the stellar disc. I also present what appears to be the first observation of an erupting stellar prominence on AB Doradus (K0V). I modify an existing ZDI code so that it can recover the magnetic maps of a binary system. The new code is applied to observations of the pre-main sequence binary system HD 155555 (G5IV+K0IV). The radial magnetic maps reveal a complex surface magnetic topology with mixed polarities at all latitudes and rings of azimuthal field present on both stars. The evolution of the relative field strengths between observations in 2004 and 2007 could be indicative of a magnetic activity cycle. I adapt the sheared image technique for measuring differential rotation parameters to the binary case. Both stellar components of HD 155555 are found to have rates of differential rotation similar to those of the same spectral type main sequence single stars. This is in apparent conflict with previous work on evolved binary systems where low rates of differential rotation were found, leading to the suggestion of suppression by binary tidal forces. I find that the depth of convection zone alone can likely explain the differential rotation results without invoking tidal forces.

In magnetised plasmas, magnetic reconnection is the process of magnetic field merging and recombination through which considerable amounts of magnetic energy may be converted into other forms of energy. Reconnection is a key mechanism for solar flares and coronal mass ejections in the solar atmosphere, it is believed to be an important source of heating of the solar corona, and it plays a major role in the acceleration of particles in the Earth's magnetotail. For reconnection to occur, the magnetic field must, in localised regions, be able to diffuse through the plasma. Ideal locations for diffusion to occur are electric current layers formed from rapidly changing magnetic fields in short space scales. In this thesis we consider the formation and nature of these current layers in magnetised plasmas. The study of current sheets and current layers in two, and more recently, three dimensions, has been a key field of research in the last decades. However, many of these studies do not take plasma pressure effects into consideration, and rather they consider models of current sheets where the magnetic forces sum to zero. More recently, others have started to consider models in which the plasma beta is non-zero, but they simply focus on the actual equilibrium state involving a current layer and do not consider how such an equilibrium may be achieved physically. In particular, they do not allow energy conversion between magnetic and internal energy of the plasma on their way to approaching the final equilibrium. In this thesis, we aim to describe the formation of equilibrium states involving current layers at both two and three dimensional magnetic null points, which are specific locations where the magnetic field vanishes. The different equilibria are obtained through the non-resistive dynamical evolution of perturbed hydromagnetic systems. The dynamic evolution relaxes via viscous damping, resulting in viscous heating. We have run a series of numerical experiments using LARE, a Lagrangian-remap code, that solves the full magnetohydrodynamic (MHD) equations with user controlled viscosity and resistivity. To allow strong current accumulations to be created in a static equilibrium, we set the resistivity to be zero and hence simply reach our equilibria by solving the ideal MHD equations. We first consider the relaxation of simple homogeneous straight magnetic fields embedded in a plasma, and determine the role of the coupling between magnetic and plasma forces, both analytically and numerically. Then, we study the formation of current accumulations at 2D magnetic X-points and at 3D magnetic nulls with spine-aligned and fan-aligned current. At both 2D X-points and 3D nulls with fan-aligned current, the current density becomes singular at the location of the null. It is impossible to be precisely achieve an exact singularity, and instead, we find a gradual continuous increase of the peak current over time, and small, highly localised forces acting to form the singularity. In the 2D case, we give a qualitative description of the field around the magnetic null using a singular function, which is found to vary within the different topological regions of the field. Also, the final equilibrium depends exponentially on the initial plasma pressure. In the 3D spine-aligned experiments, in contrast, the current density is mainly accumulated along and about the spine, but not at the null. In this case, we find that the plasma pressure does not play an important role in the final equilibrium. Our results show that current sheet formation (and presumably reconnection) around magnetic nulls is held back by non-zero plasma betas, although the value of the plasma pressure appears to be much less important for torsional reconnection. In future studies, we may consider a broader family of 3D nulls, comparing the results with the analytical calculations in 2D, and the relaxation of more complex scenarios such as 3D magnetic separators.

Magnetic plasma expulsion uses a magnetic field distortion to redirect incident charged particles around a certain area for the purposes of shielding. Computational studies are carried out and for certain values of magnetic field, magnetic plasma expulsion is found to effectively shield a sizable area. There are however many plasma behaviors and interactions that must be considered. Applications to a new cryogenic antimatter trap design are discussed.

yes / A comprehensive spectral analysis of both the solar background magnetic field (SBMF) in cycles 21-23 and the sunspot magnetic field in cycle 23 reported in our recent paper showed the presence of two principal components (PCs) of SBMF having opposite polarity, e. g., originating in the northern and southern hemispheres, respectively. Over a duration of one solar cycle, both waves are found to travel with an increasing phase shift toward the northern hemisphere in odd cycles 21 and 23 and to the southern hemisphere in even cycle 22. These waves were linked to solar dynamo waves assumed to form in different layers of the solar interior. In this paper, for the first time, the PCs of SBMF in cycles 21-23 are analyzed with the symbolic regression technique using Hamiltonian principles, allowing us to uncover the underlying mathematical laws governing these complex waves in the SBMF presented by PCs and to extrapolate these PCs to cycles 24-26. The PCs predicted for cycle 24 very closely fit (with an accuracy better than 98%) the PCs derived from the SBMF observations in this cycle. This approach also predicts a strong reduction of the SBMF in cycles 25 and 26 and, thus, a reduction of the resulting solar activity. This decrease is accompanied by an increasing phase shift between the two predicted PCs (magnetic waves) in cycle 25 leading to their full separation into the opposite hemispheres in cycle 26. The variations of the modulus summary of the two PCs in SBMF reveals a remarkable resemblance to the average number of sunspots in cycles 21-24 and to predictions of reduced sunspot numbers compared to cycle 24: 80% in cycle 25 and 40% in cycle 26.

This thesis describes a portfolio of work aimed at the high field applications of superconductors and can be split into four main topics: The thermal stability of technical superconductors. This section investigates the effects of thermal perturbations on technical superconducting wire used in MRI scanner construction. The ultimate aim of this section is to predict how the architecture of the wire may affect its thermal stability. To this end a detailed finite element analysis model was constructed, verified by detailed experimental data, which could then be used to quickly and easily vary the wire’s parameters. Design of a high field pulsed electromagnetic coil for flux trapping in superconductors. This section details the design, construction and testing of a novel pulsed high field magnet. The design uses finite element analysis to predict the electromagnetic, thermal and structural properties of the coil. Explosive testing of high tensile fibres used in the construction of the high field coil. This section describes the refinement and use of a novel method for testing the mechanical properties of high tensile fibres in cylindrical geometries by using highly pressurized copper vessels. Pulsed field magnetization of bulk high temperature superconductors. This section discusses the process of magnetizing bulks of high temperature superconductors by using pulsed magnetic fields. It investigates how the trapped field varies with the magnitude and rise-time of the magnetizing field, sample temperature and time after magnetization.

The structure of the magnetic field is often an important factor in many energetic processes in the solar corona. To determine the topology of the magnetic field features such as null points, separatrix surfaces, and separators must be found. It has been found that these features may be preferred sites for the formation of current sheets associated with the accumulation of free magnetic energy. Over the last decade, it also became clear that the geometrical analogs of the separatrices, the so-called quasi separatrix layers, have similar properties. This thesis has the aim of investigating these properties and to find correlations between these quantities. Our goal is to determine the relation between the geometrical features associated with the QSLs and with current structures, sites of reconnection and topological features. With these aims we conduct three different studies. First, we investigate a non linear force free magnetic field extrapolation from observed magnetogram data taken during a solar flare eruption concentrating our attention on two snapshots, one before the event and one after. We determine the QSLs and related structures and by considering carefully how these change between the two snapshots we are able to propose a possible scenario for how the flare occurred. In our second project we consider potential source distributions. We take different potential point source models: two four sources models already presented in the literature and a random distribution of fifteen sources. From these potential models we conduct a detailed analysis of the relationship between topological features and QSLs. It is found that the maxima of the Q-factor in the photosphere are located near and above the position of the subphotospheric null points (extending part way along their spines) and that their narrow QSLs are associated with the curves defined by the photospheric endpoints of all fan field lines that start from subphotospheric sources. Our last study investigates two different flux rope emergence simulations. In particular, we take one case with and one without an overlying magnetic field. Here, we can identify the QSLs, current, and sites of reconnection and determine the relation between them. From this work we found that not all high-Q regions are associated with current and/or reconnection and vice-versa. We also investigated the geometry of the field lines associated with high-Q regions to determine which geometrical behaviour of the magnetic field they are associated with. Those that are associated with reconnection also coincide with topological features such as separators.

This thesis considers the properties of MHS equilibria formed through non-resistive MHD relaxation of analytical non-potential magnetic field models, which contain two null points connected by a generic separator. Four types of analytical magnetic fields are formulated, with different forms of current. The magnetic field model which has a uniform current directed along the separator, is used through the rest of this thesis to form MHS equilibria and to study reconnection. This magnetic field, which is not force-free, embedded in a high-beta plasma, relaxes non-resistively using a 3D MHD code. The relaxation causes the field about the separator to collapse leading to a twisted current layer forming along the separator. The MHS equilibrium current layer slowly becomes stronger, longer, wider and thinner with time. Its properties, and the properties of the plasma, are found to depend on the initial parameters of the magnetic field, which control the geometry of the magnetic configuration. Such a MHS equilibria is used in a high plasma-beta reconnection experiment. An anomalous resistivity ensures that only the central strong current in the separator current layer is dissipated. The reconnection occurs in two phases characterised by fast and slow reconnection, respectively. Waves, launched from the diffusion site, communicate the loss of force balance at the current layer and set up flows in the system. The energy transport in this system is dominated by Ohmic dissipation. Several methods are presented which allow a low plasma-beta value to be approached in the single-separator model. One method is chosen and this model is relaxed non-resistively to form a MHS equilibrium. A twisted current layer grows along the separator, containing stronger current than in the high plasma-beta experiments, and has a local enhancement in pressure inside it. The growth rate of this current layer is similar to that found in the high plasma-beta experiments, however, the current layer becomes thinner and narrower over time.

Obtivemos mapas de Poincaré das linhas de força do campo magnético resultante da superposição linear do campo magnético de um plasma toroidal em equilíbrio com o campo magnético de correntes helicoidais externas. Devido a falta de simetria do campo magnético não podemos definir uma expressão analítica que descreva os mapas; estes foram, então, obtidos pela integração numérica da equação das linhas de força dVET.lxVET.B = 0. Nos mapas de Poincaré aparecem as ilhas magnéticas principais e as ilhas magnéticas secundárias. As ilhas magnéticas secundárias surgem devido a geometria toroidal. Sobre uma mesma superfície ressonante, as ilhas não tem tamanhos iguais. / Poincaré maps of magnetic field lines of a toroidal helical system were made. The magnetic field is a linear superposition of the magnetic fields produced by a toroidal plasma in equilibrium and by external helical currents. We do not have an analytical expression for the Poincaré maps since the magnetic field do not have symmetry. In order to obtain the maps, the equation dl x B = O is numerically integrated. In the Poincaré maps, the principal and the secondary magnetic islands were observed. The islands do not have equal widths in the same resonant surface.

Observations of the surface of the Sun reveal multi-scaled, mixed magnetic features that carpet the entire solar surface. Not surprisingly, the global magnetic fields extrapolated from these observations are highly complex. This thesis explores the topology of the Sun's global coronal magnetic fields. The magnetic skeleton of a magnetic field provides us with a way of examining the magnetic field and quantifying its complexity. Using specialised codes to find the magnetic skeletons which were written during the course of this work, we first examine potential field extrapolations of the global solar coronal magnetic field determined from observed synoptic magnetograms from the Heliospheric Magnetic Imager on the Solar Dynamics Observatory. The resolution of the PFSS models is found to be very important for discovering the true nature of the global magnetic skeleton. By increasing the maximum number of harmonics used in the potential field extrapolations and, therefore, the grid resolution, 60 times more null points may be found in the coronal magnetic field. These high resolution fields also have a large global separator network which connects the coronal magnetic field over large distances and involves between 40 % and 60 % of all the null points in the solar atmosphere. This global separator network exists at both solar minimum and solar maximum and has separators that reach high into the solar atmosphere (> 1R☉) even though they connect null points close to the solar surface. These potential field extrapolations are then compared with magnetohydrostatic (MHS) extrapolations of the coronal magnetic field which also provide us with information about the plasma in the corona. With a small component of electric current density in the direction perpendicular to the radial direction, these MHS fields are found to have a plasma beta and pressure typical of the corona. As this small component of electric current density grows, the heliospheric current sheet is warped significantly and the magnetic field, plasma beta and pressure become unphysical. Torsional spine reconnection is also studied local to a single null point. First using a dynamical relaxation of a spiral null point under non-resistive magnetohydrodynamics (MHD) to a MHS equilibrium is form in which a current layer has built up around the spine lines. Then the reconnection under resistive MHD in this current sheet is studied. The current about the spine lines is dissipated and the magnetic energy is mainly converted into heat directly as the field lines untwist about the spine line.

Obtivemos mapas de Poincaré das linhas de força do campo magnético resultante da superposição linear do campo magnético de um plasma toroidal em equilíbrio com o campo magnético de correntes helicoidais externas. Devido a falta de simetria do campo magnético não podemos definir uma expressão analítica que descreva os mapas; estes foram, então, obtidos pela integração numérica da equação das linhas de força dVET.lxVET.B = 0. Nos mapas de Poincaré aparecem as ilhas magnéticas principais e as ilhas magnéticas secundárias. As ilhas magnéticas secundárias surgem devido a geometria toroidal. Sobre uma mesma superfície ressonante, as ilhas não tem tamanhos iguais. / Poincaré maps of magnetic field lines of a toroidal helical system were made. The magnetic field is a linear superposition of the magnetic fields produced by a toroidal plasma in equilibrium and by external helical currents. We do not have an analytical expression for the Poincaré maps since the magnetic field do not have symmetry. In order to obtain the maps, the equation dl x B = O is numerically integrated. In the Poincaré maps, the principal and the secondary magnetic islands were observed. The islands do not have equal widths in the same resonant surface.