A new method is developed for treating atoms and molecules in a magnetic field in a gauge-invariant way using the Rayleigh-Ritz energy variational principle. The energy operator depends on the vector potential which must be chosen in some gauge. In order to adapt the trial wave function to the gauge of the vector potential, the trial wave function can be multiplied by a phase factor which depends on the spatial coordinates. When the energy expectation value is minimized with respect to the phase function, the equation for charge conservation for stationary states is obtained. This equation can be solved for the phase function, and the solution used in the energy expectation value to obtain a gauge-invariant energy. The method is applicable to all quantum mechanical systems for which the variational principle can be applied. It ensures satisfaction of the charge conservation condition, a gauge-invariant energy, and the best upper bound to the ground-state energy which can be obtained for the form of trial wave function chosen.

The extreme temperatures and nonthermal nature of the solar corona and solar wind arise from an unidentified physical mechanism that preferentially heats certain ion species relative to others. Spectroscopic indicators of unequal temperatures commence within a fraction of a solar radius above the surface of the Sun, but the outer reach of this mechanism has yet to be determined. Here we present an empirical procedure for combining interplanetary solar wind measurements and a modeled energy equation including Coulomb relaxation to solve for the typical outer boundary of this zone of preferential heating. Applied to two decades of observations by the Wind spacecraft, our results are consistent with preferential heating being active in a zone extending from the transition region in the lower corona to an outer boundary 20-40 solar radii from the Sun, producing a steady-state super-massproportional a-to-proton temperature ratio of 5.2-5.3. Preferential ion heating continues far beyond the transition region and is important for the evolution of both the outer corona and the solar wind. The outer boundary of this zone is well below the orbits of spacecraft at 1 au and even closer missions such as Helios and MESSENGER, meaning it is likely that no existing mission has directly observed intense preferential heating, just residual signatures. We predict that the Parker Solar Probe will be the first spacecraft with a perihelion sufficiently close to the Sun to pass through the outer boundary, enter the zone of preferential heating, and directly observe the physical mechanism in action.

In this dissertation we consider the dynamics of the solar interior, with particular focus on angular momentum balance and magnetic field confinement within the tachocline. In Part I we review current knowledge of the Sun's rotation. We summarise the main mechanisms by which angular momentum is transported within the Sun, and discuss the difficulties in reconciling the observed uniform rotation of the radiative interior with purely hydrodynamical theories. Following Gough & McIntyre (1998) we conclude that a global-scale interior magnetic field provides the most plausible explanation for the observed uniform rotation, provided that it is confined within the tachocline. We discuss potential mechanisms for magnetic field confinement, assuming that the field has a roughly axial-dipolar structure. In particular, we argue that the field is confined, in high latitudes, by a laminar downwelling flow driven by turbulence in the tachocline and convection zone above. In Part II we describe how the magnetic confinement picture is affected by the presence of compositional stratification in the 'helium settling layer' below the convection zone. We use scaling arguments to estimate the rate at which the settling layer forms, and verify our predictions with a simple numerical model. We discuss the implications for lithium depletion in the convection zone. In Part III we present numerical results showing how the Sun's interior magnetic field can be confined, in the polar regions, while maintaining uniform rotation within the radiative envelope. These results come from solving the full, nonlinear equations numerically. We also show how these results can be understood in terms of a reduced, analytical model that is asymptotically valid in the parameter regime of relevance to the solar tachocline. In Part IV we discuss how our high-latitude model can be extended to a global model of magnetic confinement within the tachocline.

Part I of this dissertation is concerned with the problem of the magnetic field dependence of the surface impedance of superconductors, with particular reference to tin. In chapter 1 the predictions of the simple theory for the behaviour of the surface impedance for different frequencies and fieid configurations are described and compared with the results of previous experiments. Chapter 2 deals with the experimental side of the present work, where a frequency of 170 Mc/s was used, and in chapter 3 the results obtained are discussed. In chapter 4 the attempts which have been made to account theoretically for the experimental observations are reviewed. Part II of the dissertation is concerned with another problem in superconductivity, namely the behaviour of superconducting systems partitioned by thin barriers of substances which in bulk are not superconducting. The theory of such systems is developed, the consequences investigated in some detail and the present experimental situation reviewed.

No description available.

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.

Jatos e discos de acreção associados a objetos galácticos e extragalácticos tais como, microquasares (i.e., buracos negros de massa estelar presentes em alguns sistemas binários estelares), núcleos ativos de galáxias (NAGs) e objetos estelares jovens (OEJs), frequentemente exibem eventos de ejeção de matéria quase periódicos que podem fornecer importantes informações sobre os processos físicos que ocorrem nas suas regiões mais internas. Entre essas classes de objetos, os microquasares com emissão transiente em raios-X vêm sendo identificados em nossa Galáxia desde a última década, e tal como os NAGs e quasares distantes, alguns desses sistemas também produzem jatos colimados com velocidades aparentemente superluminais, não deixando dúvidas de que se tratam de um gás ejetado com velocidades relativísticas. Um exemplo amplamente observado em comprimentos de onda do rádio aos raios-X é o microquasar GRS 1915+105 (e.g., Dhawan et al.,2000), que foi o primeiro objeto galáctico a exibir evidências de um jato com movimento aparentemente superluminal (Mirabel e Rodríguez, 1998, 1994). Um modelo para explicar a origem dessas ejeções superluminais, bem como a emissão rádio sincrotrônica em flares não muito diferentes dos que ocorrem na coroa solar, foi desenvolvido por de Gouveia Dal Pino e Lazarian (2005), onde é invocado um processo de reconexão magnética violenta entre as linhas de campo magnético que se erguem do disco de acreção e as linhas da magnetosfera da fonte central. Em episódios de acreção onde a razão entre a pressão efetiva do disco e a pressão magnética diminui para valores menores ou da ordem de 1 e as taxas de acreção se aproximam da taxa crítica de Eddington, a reconexão pode tornar-se violenta e libera grandes quantidades de energia magnética em pouco tempo. Parte dessa energia aquece o gás, tanto da coroa quanto do disco, e parte acelera as partículas a velocidades relativísticas por um processo de Fermi de primeira ordem, pela primeira vez estudado em zonas de reconexão magnética por esses autores, produzindo um espectro sincrotrônico de lei de potência com índice espectral comparável às observações. Neste trabalho realizamos um estudo complementar, iniciado por Piovezan (2009), no qual generalizamos o modelo acima descrito para o caso dos NAGs. Nesse estudo, constatamos que a atividade de reconexão magnética na região coronal, na base de lançamento do jato, pode explicar a origem das ejeções relativísticas, dos microquasares aos NAGs de baixa luminosidade (tais como galáxias Seyfert e LINERS). A potência liberada em eventos de reconexão magnética em função das massas dos buracos negros dessas fontes, de 5 massas solares a 10^10 massas solares, obedece a uma correlação que se mantém por todo esse intervalo, abrangendo 10^9 ordens de magnitude. Essa correlação implica em uma dependência quase linear (em um diagrama log-log), aproximadamente independente das características físicas locais dos discos de acreção dessas fontes. Além do mais, ela é compatível com o chamado plano fundamental, obtido empiricamente, que correlaciona a emissão rádio e raios-X dos microquasares e NAGs às massas dos seus buracos negros (veja Merloni et al., 2003). Assim, o modelo de de Gouveia Dal Pino e Lazarian (2005), oferece uma interpretação física simples para a existência dessa correlação empírica, como devida à atividade magnética coronal nessas fontes. Já os quasares e NAGs mais luminosos não satisfazem à mesma correlação, possivelmente porque a densidade ao redor da região coronal nessas fontes é tão alta que mascara a emissão devida à atividade magnética. A emissão rádio nesses casos deve-se, possivelmente, a regiões mais externas do jato supersônico, onde ele já expandiu o suficiente para tornar-se opticamente fino e visível, e onde os elétrons relativísticos são possivelmente produzidos em choques (veja também de Gouveia Dal Pino et al., 2010a,b). Paralelamente, investigamos a formação de eventos de reconexão magnética através de simulações magnetohidrodinâmicas axissimétricas (2.5D-MHD), da interação entre o campo magnético poloidal ancorado no disco de acreção viscoso (satisfazendo ao modelo padrão de Shakura e Sunyaev, 1973) e a magnetosfera dipolar da fonte central em rotação. Para esse fim, consideramos condições iniciais semelhantes às dos OEJs. Nos testes preliminares aqui realizados, a reconexão magnética das linhas ocorre em presença de uma resistividade numérica, que não é intensa o bastante para determinar um processo de reconexão a taxas da ordem da velocidade de Alfvén, ou seja, ela é essencialmente lenta. Ainda assim, pudemos identificar alguns dos efeitos previstos pelo modelo de reconexão magnética rápida aqui estudado. Por exemplo, verificamos que a frequência e a intensidade com que eventos de reconexão magnética podem ocorrer é sensível tanto à topologia inicial do campo magnético do sistema quanto às taxas de acreção do disco (como previsto pelo modelo de de Gouveia Dal Pino e Lazarian, 2005), de modo que tais eventos ocorrem de forma mais eficiente em regimes de alta taxa de acreção. Finalmente, além da investigação sobre o desenvolvimento de eventos de reconexão magnética, pudemos também examinar a partir das simulações a formação natural de funis de acreção, os quais são colunas de acreção que conduzem gás do disco para a superfície da fonte central através das linhas do campo magnético. Os resultados desse estudo foram comparados com as observações de funis de acreção de objetos estelares jovens. / Jets and accretion disks associated with galactic and extragalactic objects such as microquasars (i.e., stellar-mass black holes occurring in some binary stellar systems), active galactic nuclei (AGNs) and young stellar objects (YSOs), often exhibit quasi-periodic ejections of matter that may offer important clues about the physical processes that occur in their inner regions. Among these classes of objects, microquasars with transient emission in X-rays have been identified in our Galaxy since the last decade and like AGNs and distant quasars, some of them also produce collimated jets with apparent superluminal speeds, leaving no doubt that we are also dealing with ejected gas with relativistic velocities. One example widely investigated from radio wavelengths to X-rays is the microquasar GRS 1915+105 (e.g., Dhawan et al.,2000), which was the first Galactic object to show evidence of a jet with apparent superluminal motion (Mirabel e Rodríguez, 1998, 1994). A model to explain the origin of the superluminal ejections and the synchrotron radio emission in flares which are not very different from those occurring in the solar corona, was developed by de Gouveia Dal Pino e Lazarian (2005), where they invoked a process of violent magnetic reconnection between the magnetic field lines that arise from the accretion disk and the lines of the magnetosphere of the central source. In accretion episodes where the ratio between the effective disk pressure and magnetic pressure decreases to values smaller than the unity and the accretion rate approaches the critical Eddington rate, the reconnection may become violent and releases large amounts of magnetic energy in a short time. Part of this energy heats the coronal and the disk gas and part accelerates particles to relativistic velocities through a first-order Fermi-like process, which was investigated for the first time in magnetic reconnection by these authors and results a synchrotron radio power-law spectrum that is compatible to the observations. In the present work we conducted a complementary study, initiated by Piovezan (2009), which generalize the model described above for the case of AGNs. We found that the activity due to magnetic reconnection in the coronal region, at the base of the launching jet, can explain the origin of relativistic ejections from microquasars to low luminous AGNs (LLAGNs, such as Seyfert galaxies and LINERs). The power released by magnetic reconnection events as a function of the black hole masses of these sources, between 5 solar mass and 10^10 solar mass, obeys a correlation that is maintained throughout this interval, spanning 10^9 orders of magnitude. This correlation implies an almost linear dependence (in a log-log diagram), which is approximately independent of the physical properties of the accretion disks of these sources. Moreover, it is compatible with the so-called fundamental plan obtained empirically, which correlates the radio and X-rays emission of microquasars and AGNs with the masses of their black holes (see Merloni et al., 2003). Thus, the model of de Gouveia Dal Pino e Lazarian (2005) provides a simple physical interpretation for the existence of this empirical correlation as due to coronal magnetic activity in these sources. More luminous AGNs and quasars do not seem to obey the same correlation, possibly because the density around the coronal region in these sources is so high that it \"masks\" the emission due to the magnetic activity. The radio emission in these cases is possibly due regions further out of the supersonic jet, where it has already expanded enough to become optically thin and visible and where the relativistic electrons are probably accelerated in shocks (see also de Gouveia Dal Pino et al., 2010a,b). In addition, we investigated the development of magnetic reconnection events through axisymmetric magnetohydrodynamic simulations (2.5D-MHD) of the interaction between the poloidal magnetic field that arises from the viscous accretion disk (which satisfies the standard model of Shakura e Sunyaev, 1973) and the dipolar magnetosphere of the rotating central source. To this aim, we considered initial conditions which are compatible to those of YSOs. In the preliminary tests conducted here, magnetic reconnection occurs in the presence of numerical resistivity only, which is not intense enough to determine a process of reconnection with rates of the order of the Alfvén speed, i.e., it is essentially slow. Nevertheless, we were able to identify some of the effects predicted by the model of fast magnetic reconnection studied here. For example, we found that the frequency and strength with which events of magnetic reconnection can occur is sensitive to both the initial topology of the magnetic field of the system and the accretion disk rates (as predicted by the model of de Gouveia Dal Pino e Lazarian, 2005), so that such events occur more efficiently under high accretion rates. Finally, besides the investigation of the development of magnetic reconnection events, we could also examine in our numerical studies the natural formation of funnel flows which are accretion columns that transport gas from the accretion disk to the surface of the central source along the magnetic field lines. The results of these studies were compared with the observations of funnel flows in young stellar objects.

Thesis (Ph.D.)--Boston University / The formation, evolution and eruption of solar active regions is a main theme in solar physics. Ultimately the goal is predicting when, where and how an eruption will occur, which will greatly aid space weather forecasting. Special kinds of S-shaped active regions (sigmoids) facilitate this line of research, since they provide conditions that are easier to disentangle and have a high probability for erupting as flares and/or coronal mass ejections (CME). Several theories have been proposed for the formation, evolution, and eruption of solar active regions. Testing these against detailed models of sigmoidal regions can provide insight into the dominant mechanisms and conditions required for eruption. This thesis explores the behavior of solar sigmoids via both observational and magnetic modeling studies. Data from the most modern space-based solar observatories are utilized in addition to state-of-the-art three-dimensional data-driven magnetic field modeling to gain insight into the physical processes controlling the evolution and eruption of solar sigmoids. We use X-ray observations and the magnetic field models to introduce the reader to the underlying magnetic and plasma structure defining these regions. By means of a large comprehensive observational study we investigate the formation and evolution mechanism. Specifically, we show that flux cancellation is a major mechanism for building the underlying magnetic structure associated with sigmoids, namely magnetic flux ropes. We make use of topological analysis to describe the complicated magnetic field structure of the sigmoids. We show that when data-driven models are used in sync with MHD simulations and observations we can arrive at a consistent picture of the scenario for CME onset, namely the positive feedback between reconnection at a generalized X-line and the torus instability. In addition we show that topological analysis is of great use in analyzing the post-eruption flare- and CME-associated observational features. Such analysis is used to extend the standard 2D flare/CME models to 3D and to find potentially large implications of topology to understanding 3D reconnection and the seed populations of energetic particles in CMEs.

The International Workshop on "Measuring Techniques in Liquid Metal Flows" (MTLM Workshop) was organised in frame of the Dresden "Innovationskolleg Magnetofluiddynamik". The subject of the MTLM Workshop was limited to methods to determine physical flow quantities such as velocity, pressure, void fraction, inclusion properties, crystallisation fronts etc. The present proceedings contain abstracts and viewgraphs of the oral presentations. During the last decades numerical simulations have become an important tool in industry and research to study the structure of flows and the properties of heat and mass transfer. However, in case of liquid metal flows there exists a significant problem to validate the codes with experimental data due to the lack of available measuring techniques. Due to the material properties (opaque, hot, chemical aggressive) the measurement of flow quantities is much more delicate in liquid metals compared to ordinary water flows. The generalisation of results obtained by means of water models to real liquid metal flows has often to be considered as difficult due to the problems to meet the actual values of non-dimensional flow parameters (Re, Pr, Gr, Ha, etc.). Moreover, a strong need has to be noted to make measuring techniques available to monitor and to control flow processes in real industrial facilities.

Induction heating is a common industrial process used for the reheating of billets before extrusion or forging. In this work the influence of the coil and work piece geometry, the effect of the electrical properties of the work piece, and the coil current and frequency, on the magnetic flux density and resulting work piece heating rates were studied. A combination of 1D analytical solutions, 2D axial symmetric finite element modelling and precise measurements has been used. Dozens of heating and magnetic field experiments have been conducted, with steadily increasing sophistication and measurement accuracy. The development of the experimental techniques will be described in the ‘cover’ and related to the later results published in the supplements. Experimental results are compared to predictions obtained from analytical and numerical models. The published measurements obtained for the billet heating experiments consisted of: billet electrical conductivity with &lt;0.5% error, applied currents with &lt;1% error, magnetic flux densities with 1-2% error, calorifically determined heating rates with &lt;2% error and electrical reactive power with &lt;~2% error. 2 D axial symmetric finite element models were obtained, which describe the measured results with less than a 2% difference (i.e. an ‘error’ of the same magnitude as the measurement uncertainty). Heating and reactive power results predicted by the FEM model are in excellent agreement with analytical solutions from 50 Hz to 500 kHz (differences from &lt;1% to 6%). A modified 1D short coil correction factor is presented which accounts for the interaction of the coil and work piece geometry, electrical properties and operating frequency, on the average magnetic flux density of the coil/work piece air-gap and the resulting heating rate. Using this factor, the average magnetic flux density in the air-gap can be estimated analytically within 2-3% and the heating rates of billets of known electrical properties can be estimated, with typical errors on the order of 5%. / <p>QC 20130618</p>