Numerical Simulation Of Solar Coronal Magnetic Fields

Many aspects of solar activity are believed to be due to the stressing of the coronal magnetic field by footpoint motions at the photosphere. The results are presented of a fully spectral numerical simulation which is the first 3-D time dependent simulation of footpoint stressing in a geometry appropriate for the corona. An arcade is considered that is initially current-free and impose a smooth footpoint motion that produces a twist in the field of approx 2 pi. The footprints were fixed and the evolution was followed until the field relaxes to another current-free state. No evidence was seen for any instability, either ideal or resistive and no evidence for current sheet formation. The most striking feature of the evolution is that in response to photospheric motions, the field expands rapidly upward to minimize the stress. The expansion has two important effects. First, it suppresses the development of dips in the field that could support dense, cool material. For the motions assumed, the magnetic field does not develop a geometry suitable for prominence formation. Second, the expansion inhibits ideal instabilities such as kinking. The results indicate that simple stearing of a single arcade is unlikely to lead to solar activity such as flares or prominences. Effects are discussed that might possibly lead to such activity. Dahlburg, Russell B. and Antiochos, Spiro K. and Zang, T. A. Langley Research Center ...

Many aspects of solar activity are believed to be due to the stressing of the coronal magnetic field by footpoint motions at the photosphere. We present the results of a fully spectral numerical simulation which, to our knowledge, is the first 3-d time dependent simulation of footpoint stressing in a geometry appropriate for the corona. We consider an arcade that is initially current-free and impose a smooth footpoint motion that produces a twist in the field of approximately 2 pi. We then fix the footpoints and follow the evolution until the field relaxes to another current-free state. We see no evidence for any instability, either ideal or resistive and no evidence for current sheet formation. The most striking feature of the evolution is that in response to photospheric motions, the field expands rapidly upward to minimize the stress. The expansion has two important effects. First, it suppresses the development of dips in the field that could support dense, cool material. For the motions that we assume, the magnetic field does not develop a geometry suitable for prominence formation. Second, the expansion inhibits ideal instabilities such as kinking. Our results indicate that simple stearing of a single arcade is unlikely to lead to solar activity such as flares or prominences. We discuss effects that might possibly lead to such activity.

The book covers intimately all the topics necessary for the development of a robust magnetohydrodynamic (MHD) code within the framework of the cell-centered finite volume method (FVM) and its applications in space weather study. First, it presents a brief review of existing MHD models in studying solar corona and the heliosphere. Then it introduces the cell-centered FVM in three-dimensional computational domain. Finally, the book presents some applications of FVM to the MHD codes on spherical coordinates in various research fields of space weather, focusing on the development of the 3D Solar-InterPlanetary space-time Conservation Element and Solution Element (SIP-CESE) MHD model and its applications to space weather studies in various aspects. The book is written for senior undergraduates, graduate students, lecturers, engineers and researchers in solar-terrestrial physics, space weather theory, modeling, and prediction, computational fluid dynamics, and MHD simulations. It helps readers to fully understand and implement a robust and versatile MHD code based on the cell-centered FVM.

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Starting in 1995 numerical modeling of the Earth’s dynamo has ourished with remarkable success. Direct numerical simulation of convection-driven MHD- ow in a rotating spherical shell show magnetic elds that resemble the geomagnetic eld in many respects: they are dominated by the axial dipole of approximately the right strength, they show spatial power spectra similar to that of Earth, and the magnetic eld morphology and the temporal var- tion of the eld resembles that of the geomagnetic eld (Christensen and Wicht 2007). Some models show stochastic dipole reversals whose details agree with what has been inferred from paleomagnetic data (Glatzmaier and Roberts 1995; Kutzner and Christensen 2002; Wicht 2005). While these models represent direct numerical simulations of the fundamental MHD equations without parameterized induction effects, they do not match actual pla- tary conditions in a number of respects. Speci cally, they rotate too slowly, are much less turbulent, and use a viscosity and thermal diffusivity that is far too large in comparison to magnetic diffusivity. Because of these discrepancies, the success of geodynamo models may seem surprising. In order to better understand the extent to which the models are applicable to planetary dynamos, scaling laws that relate basic properties of the dynamo to the fundamental control parameters play an important role. In recent years rst attempts have been made to derive such scaling laws from a set of numerical simulations that span the accessible parameter space (Christensen and Tilgner 2004; Christensen and Aubert 2006).

Magnetism defines the complex and dynamic solar corona. It determines the magnetic loop structure that dominates images of the corona, and stores the energy necessary to drive coronal eruptive phenomena and flare explosions. At great heights the corona transitions into the ever-outflowing solar wind, whose speed and three-dimensional morphology are controlled by the global coronal magnetic field. Coronal magnetism is thus at the heart of any understanding of the nature of the corona, and essential for predictive capability of how the Sun affects the Earth. Coronal magnetometry is a subject that requires a concerted effort to draw together the different strands of research happening around the world. Each method provides some information about the field, but none of them can be used to determine the full 3D field structure in the full volume of the corona. Thus, we need to combine them to understand the full picture. The purpose of this Frontiers Research Topic on Coronal Magnetometry is to provide a forum for comparing and coordinating these research methods, and for discussing future opportunities.

This volume gives a comprehensive and integrated overview of current knowledge and understanding of corotating interaction regions (CIRs) in the solar wind. It is the result of a workshop at ISSI, where space scientists involved in the Ulysses, Pioneer, Voyager, IMP-8, Wind, and SOHO missions exchanged their data and interpretations with theorists in the fields of solar and heliospheric physics. The book provides a broad synthesis of current understanding of CIRs, which form at the interface between the fast solar wind originating in the northern and southern coronal holes and the slow solar wind that originates near and within coronal streamers surrounding the heliomagnetic equator. CIRs are the dominant structure in the heliosphere near and beyond Earth on the declining phase and near the minimum of the 11-year solar activity cycle. Particles energized at the shocks that bound CIRs at heliospheric distances beyond the orbit of Earth are the dominant energetic particle population observed in the outer heliosphere at these times. Papers included in this volume cover the subject of CIRs from their dissipation in the outer hemisphere, and include discussions of complexities associated with their evolution with distance from the Sun, their three-dimensional structure, and the myriad effects that CIRs have on energetic particles throughout the heliosphere. The book is intended to provide scientists active in space physics research with an up-to-date status report on current understanding of CIRs and their effects in the heliosphere, and also to serve the advanced graduate student with introductory material on this active field of research.

Solar eruptive phenomena, such as flares and coronal mass ejections (CMEs), derive their energy from complex magnetic fields and are the principal source of disturbances that affect space weather. Although physical mechanism and dynamic morphology of flares have been a subject of intense research, many aspects of the flaring process still remain unclear. The objective of this dissertation is to advance the understanding of the physics behind solar flares based on observations, simulations and nonlinear force-free (NLFF) field modeling of magnetic fields. The data used in this study are obtained from several ground-based or space-borne instruments, including BBSO/DVMG, Hinode/SOT/SP, SDO/HMI and GOES. In addition, the advanced coronal modeling method was utilized to extrapolate NLFF magnetic fields. This dissertation focuses on the magnetic properties (magnetic inclination angle, transverse magnetic field, Lorentz force, etc.) and their evolution associated with flares. The observation is also compared with numerical MHD simulations and theoretical models. The main findings in this dissertation are briefly summarized as follows: (1) the white-light observation of S sunspots reveal the rapid penumbral decay and central umbral/penumbral darkening associated with flares; (2) the magnetic inclination angle shows an increase in the decayed peripheral penumbra and a decrease in the central area close to the flaring polarity inversion line (PIL) after major flares; (3) magnetic field observations indicate a rapid and permanent enhancement of the transverse magnetic field in the umbral core or inner penumbral region, while that in the outer decayed penumbral region decreases; (4) the downward Lorentz force exerted on the flaring area displays a sudden enhancement after flares; (5) the footpoint of flare ribbons shows slow shearing followed by fast diverging and deshearing motion. The remote Ha brightenings appear in the first stage of the eruption while the associated hard X-ray emission occurs in the later phase. These results provide strong evidence favoring superimposed effects of both the tether-cutting model, in which a short and flat loop forms near the photosphere after the eruption, and the back reaction of the coronal magnetic field following the energy release. The major contribution of this dissertation is: (1) First study of 3-D magnetic field change associated with flares in the perspective of magnetic inclination angle and transverse magnetic field; (2) First successful comparison of the numerical simulation, observation and theory of solar flare associated magnetic field changes; (3) First clear evidence of the two stage magnetic reconnection (implosion and explosion); (4) First evidence in support of the conservation of momentum in solar flare. To understand the radio emission produced by electrons at the very acceleration site of a solar flare, two competing acceleration models-stochastic acceleration by cascading MHD turbulence and regular acceleration in collapsing magnetic traps were studied. It is found that the radio emission from the acceleration sites (1) has sufficiently strong intensity to be observed by currently available radio instruments and (2) has spectra and light curves which are distinctly different in these two competing models, which makes them observationally distinguishable.

In 2010, NASA and the National Science Foundation asked the National Research Council to assemble a committee of experts to develop an integrated national strategy that would guide agency investments in solar and space physics for the years 2013-2022. That strategy, the result of nearly 2 years of effort by the survey committee, which worked with more than 100 scientists and engineers on eight supporting study panels, is presented in the 2013 publication, Solar and Space Physics: A Science for a Technological Society. This booklet, designed to be accessible to a broader audience of policymakers and the interested public, summarizes the content of that report.