The complete set of Kubo conductivity tensors are computed for two- and three-dimensional linear magnetic null systems using collisionless single-particle simulations. Chaos regions are constructed for each case, along with the complete Lyapunov spectrum. It is found that stochastic frequency mixing of particle bounce motion, as well as gyromotion, contribute significantly to the conductivity. For many cases, the conductivity curve is well approximated by power-laws, resulting in a divergent value of the direct-current conductivity, while others can be described by a sum of Maxwellian curves. The energy dissipation of these systems is also briefly discussed.

Thesis (Ph.D.) - University of St Andrews, May 2009.

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.

Magnetic reconnection is an important mechanism for the restructuring of magnetic fields, and the conversion of magnetic energy into plasma heating and non-thermal particle kinetic energy in a wide range of laboratory and astrophysical plasmas. In this thesis, reconnection is studied in two semi-collisional plasma environments: flares in the solar corona, and the start-up phase of the Mega-Ampere Spherical Tokamak (MAST) magnetic confinement device. Numerical simulations are presented using two different plasma descriptions; the test-particle approach combined with analytical magnetohydrodynamic fields is used to model populations of high-energy particles, and a two-fluid approach is used to model the bulk properties of a semi-collisional plasma. With the first approach, a three-dimensional magnetic null-point is examined as a possible particle acceleration site in the solar corona. The efficiency of acceleration, both within the external drift region and in the resistive current sheet, is studied for electrons and protons using two reconnection models. Of the two models, it is found that the fan-reconnection scenario is the most efficient, and can accelerate bulk populations of protons due to fast and non-uniform electric drifts close to the fan current-sheet. Also, the increasing background field within the fan-current sheet is shown to stabilise particle orbits, so that the energy gain is not limited by ejection. With the second approach, the effects of two-fluid physics on merging flux-ropes is examined, finding fast two-fluid tearing-type instabilities when the strength of dissipation is weak. The model is then extended to the tight-aspect ratio toroidal-axisymmetric geometry of the MAST device, where the final state after merging is a MAST-like spherical tokamak with nested flux-surfaces and a monotonically increasing q-profile. It is also shown that the evolution of simulated 1D radial density profiles closely resembles the Thomson scattering electron density measurements in MAST. An intuitive explanation for the origin of the measured density structures is proposed, based upon the results of the toroidal Hall-MHD simulations.

The million-degree temperature of the solar corona might be due to the combined effect of barely distinguishable energy releases, called nanoflares, that occur throughout the solar atmosphere. Unfortunately, the high density of nanoflares, implied by this hypothesis, means that conclusive verification is beyond present observational capabilities. Nevertheless, it might be possible to investigate the plausibility of nanoflare heating by constructing a magnetohydrodynamic (MHD) model; one that can derive the energy of nanoflares, based on the assumption that the ideal kink instability of a twisted coronal loop triggers a relaxation to a minimum energy state. The energy release depends on the current profile at the time when the ideal kink instability threshold is crossed. Subsequent to instability onset, fast magnetic reconnection ensues in the non-linear phase. As the flare erupts and declines, the field transitions to a lower energy level, which can be modelled as a helicity-conserving relaxation to a linear force-free state. The aim of this thesis is to determine the implications of such a scheme with respect to coronal heating. Initially, the results of a linear stability analysis for loops that have net current are presented. There exists substantial variation in the radial magnetic twist profiles for the loop states along the instability threshold. These results suggest that instability cannot be predicted by any simple twist-derived property reaching a critical value. The model is applied such that the loop undergoes repeated episodes of instability followed by energy-releasing relaxation. Photospheric driving is simulated as an entirely random process. Hence, an energy distribution of the nanoflares produced is collated. These results are discussed and unrealistic features of the model are highlighted.

京都大学 / 新制・課程博士 / 博士(理学) / 甲第24415号 / 理博第4914号 / 新制||理||1702(附属図書館) / 京都大学大学院理学研究科物理学・宇宙物理学専攻 / (主査)准教授 浅井 歩, 教授 一本 潔, 教授 横山 央明 / 学位規則第4条第1項該当 / Doctor of Science / Kyoto University / DFAM

In this thesis we investigate current sheets in the solar corona. The well known 1D model for the tearing mode instability is presented, before progressing to 2D where we introduce a non-uniform resistivity. The effect this has on growth rates is investigated and we find that the inclusion of the non-uniform term in η cause a decrease in the growth rate of the dominant mode. Analytical approximations and numerical simulations are then used to model current sheet formation by considering two distinct experiments. First, a magnetic field is sheared in two directions, perpendicular to each other. A twisted current layer is formed and we find that as we increase grid resolution, the maximum current increases, the width of the current layer decreases and the total current in the layer is approximately constant. This, together with the residual Lorentz force calculated, suggests that a current sheet is trying to form. The current layer then starts to fragment. By considering the parallel electric field and calculating the perpendicular vorticity, we find evidence of reconnection. The resulting temperatures easily reach the required coronal values. The second set of simulations carried out model an initially straight magnetic field which is stressed by elliptical boundary motions. A highly twisted current layer is formed and analysis of the energetics, current structures, magnetic field and the resulting temperatures is carried out. Results are similar in nature to that of the shearing experiment.

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.

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.