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1.
Axially symmetric constant-alpha force-free magnetic fields in toroidal flux ropes with elliptical cross sections are constructed in order to investigate how their alphas and magnetic helicities depend on parameters of the flux ropes. Magnetic configurations are found numerically using a general solution of a constant-alpha force-free field with an axial symmetry in cylindrical coordinates for a wide range of oblatenesses and aspect ratios. Resulting alphas and magnetic helicities are approximated by polynomial expansions in parameters related to oblateness and aspect ratio. These approximations hold for toroidal as well as cylindrical flux ropes with an accuracy better than or of about 1%. Using these formulae, we calculate relative helicities per unit length of two (probably very oblate) magnetic clouds and show that they are very sensitive to the assumed magnetic cloud shapes (circular versus elliptical cross sections). 相似文献
2.
Tilaye Tadesse Alexei A. Pevtsov T. Wiegelmann P. J. MacNeice S. Gosain 《Solar physics》2014,289(11):4031-4045
Solar eruptive phenomena, like flares and coronal mass ejections (CMEs), are governed by magnetic fields. To describe the structure of these phenomena one needs information on the magnetic flux density and the electric current density vector components in three dimensions throughout the atmosphere. However, current spectro-polarimetric measurements typically limit the determination of the vector magnetic field to only the photosphere. Therefore, there is considerable interest in accurate modeling of the solar coronal magnetic field using photospheric vector magnetograms as boundary data. In this work, we model the coronal magnetic field for global solar atmosphere using nonlinear force-free field (NLFFF) extrapolation codes implemented to a synoptic maps of photospheric vector magnetic field synthesized from the Vector Spectromagnetograph (VSM) on Synoptic Optical Long-term Investigations of the Sun (SOLIS) as boundary condition. Using the resulting three-dimensional magnetic field, we calculate the three-dimensional electric current density and magnetic energy throughout the solar atmosphere for Carrington rotation 2124 using our global extrapolation code. We found that spatially, the low-lying, current-carrying core field demonstrates a strong concentration of free energy in the active-region core, from the photosphere to the lower corona (about 70 Mm). The free energy density appears largely co-spatial with the electric current distribution. 相似文献
3.
To model irregularities in the magnetic structure of solar flux ropes or in interplanetary magnetic clouds, we propose the following approach. A local irregularity in the form of a compact toroid is added into a cylindrical linear force-free magnetic structure. The radius of the cylinder and the small radius of the toroid are the same, since the force-free parameter α is constant, that is, we have in total a linear force-free configuration, too. Meanwhile, the large radius of the toroid can be smaller. The effect of such modeling depends on the aspect ratio of the compact toroid, its location and orientation, and on its magnetic field magnitude in comparison with that of the cylinder. 相似文献
4.
T. Wiegelmann J. K. Thalmann B. Inhester T. Tadesse X. Sun J. T. Hoeksema 《Solar physics》2012,281(1):37-51
The Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) provides photospheric vector magnetograms with a high spatial and temporal resolution. Our intention is to model the coronal magnetic field above active regions with the help of a nonlinear force-free extrapolation code. Our code is based on an optimization principle and has been tested extensively with semianalytic and numeric equilibria and applied to vector magnetograms from Hinode and ground-based observations. Recently we implemented a new version which takes into account measurement errors in photospheric vector magnetograms. Photospheric field measurements are often affected by measurement errors and finite nonmagnetic forces inconsistent for use as a boundary for a force-free field in the corona. To deal with these uncertainties, we developed two improvements: i) preprocessing of the surface measurements to make them compatible with a force-free field, and ii) new code which keeps a balance between the force-free constraint and deviation from the photospheric field measurements. Both methods contain free parameters, which must be optimized for use with data from SDO/HMI. In this work we describe the corresponding analysis method and evaluate the force-free equilibria by how well force-freeness and solenoidal conditions are fulfilled, by the angle between magnetic field and electric current, and by comparing projections of magnetic field lines with coronal images from the Atmospheric Imaging Assembly (SDO/AIA). We also compute the available free magnetic energy and discuss the potential influence of control parameters. 相似文献
5.
Flux ropes are twisted magnetic structures that can be detected by in-situ measurements in the solar wind. However, different properties of detected flux ropes suggest different types of flux-rope populations. As such, are there different populations of flux ropes? The answer is positive and is the result of the analysis of four lists of flux ropes, including magnetic clouds (MCs), observed at 1 AU. The in-situ data for the four lists were fitted with the same cylindrical force-free field model, which provides an estimate of the local flux-rope parameters such as its radius and orientation. Since the flux-rope distributions have a broad dynamic range, we went beyond a simple histogram analysis by developing a partition technique that uniformly distributes the statistical fluctuations across the radius range. By doing so, we found that small flux ropes with radius R<0.1 AU have a steep power-law distribution in contrast to the larger flux ropes (identified as MCs), which have a Gaussian-like distribution. Next, from four CME catalogs, we estimated the expected flux-rope frequency per year at 1 AU. We found that the predicted numbers are similar to the frequencies of MCs observed in-situ. However, we also found that small flux ropes are at least ten times too abundant to correspond to CMEs, even to narrow ones. Investigating the different possible scenarios for the origin of these small flux ropes, we conclude that these twisted structures can be formed by blowout jets in the low corona or in coronal streamers. 相似文献
6.
7.
The global 3-dimensional topology of the magnetic field of the weakly flaring active region AR 5420 in the early phase has been estimated using a series of photospheric longitudinal and vector magnetogams together with Hα filtergrams and white-light images. As a physical model for this task, we have used the assumption ofa force-free magnetic field character. An arcade-like structure of the magnetic field has been identified in the preflare phase with an apparent sheared configuration already present in the current-free field case. This system might have been an important source of generation of a field-aligned current system for the eruptions that followed. That was, in particular, suggeted by a significant extension of the active region area in the observation period from June 22 to 25, 1984, that resulted in a stronger shear of the detected arcade-like system. The atmospheric electric currents generated in such a way and the transition triggered by a large-amplitude perturbation generated by new flux emergences on June 23 at this place together might be the reason of the sequence of flares observed. Despite the changes in the Hα structure, the global force-free character of the field did not change significantly over the time of observations. The invariance (in the first order) of the force-free (nearly current-free) character of the magnetic field is consistent with the occurrence of relatively small flares only. 相似文献
8.
Reliable measurements of the solar magnetic field are restricted to the level of the photosphere. For about half a century attempts have been made to calculate the field in the layers above the photosphere, i.e. in the chromosphere and in the corona, from the measured photospheric field. The procedure is known as magnetic field extrapolation. In the superphotospheric parts of active regions the magnetic field is approximately force-free, i.e. electric currents are aligned with the magnetic field. The practical application to solar active regions has been largely confined to constant-α or linear force-free fields, with a spatially constant ratio, α, between the electric current and the magnetic field. We review results obtained from extrapolations with constant-α force-free fields, in particular on magnetic topologies favourable for flares and on magnetic and current helicities. Presently, different methods are being developed to calculate non-constant-α or nonlinear force-free fields from photospheric vector magnetograms. We also briefly discuss these methods and present a comparison of a linear and a nonlinear force-free magnetic field extrapolation applied to the same photospheric boundary data. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
9.
A major solar active event called Bastille Day Event occurred in AR 9077 on July 14, 2000. Simultaneous occurrence of a filament
eruption, a flare and a coronal mass ejection was observed in this event. Previous analyses of this event show that before
the event, there existed an activation and eruption of a huge trans-equatorial filament, which might play a crucial role in
triggering the Bastille Day event. This implies that independent flux systems are closely related to and affect each other,
which has encouraged us to investigate the catastrophic behavior of a multiple coronal flux rope system with the use of a
2.5-D time-dependent MHD model. A force-free field that contains three separate coronal flux ropes is taken to be the initial
state. Starting from this state, we increase either the annular or the axial flux of a certain flux rope to examine the catastrophic
behavior of the system in two regimes, the ideal MHD regime and the resistive MHD regime. It is found that a catastrophe occurs
if the flux exceeds a certain critical value, or the magnetic energy of the system exceeds a certain threshold: the rope of
interest breaks away from the base and escapes to infinity, leaving a current sheet below. Moreover, the destiny of the remainder
flux ropes relies on whether reconnection takes place across the current sheet. In the ideal MHD regime, i.e., in the absence of reconnection, these ropes remain to be attached to the base in equilibrium, whereas in the resistive MHD
regime they abruptly erupt upward during reconnection and escape to infinity. Reconnection causes the field lines to close
back to the base and thus changes the background field outside the attached flux ropes in such a way that the constraint on
these ropes is substantially relaxed and the corresponding catastrophic energy threshold is reduced accordingly, leading to
a catastrophic eruption of these ropes. Since magnetic reconnection is generally inevitable when a current sheet forms and
develops through an eruption of one flux rope, the eruption of this flux rope must lead to an eruption of the others. This
provides an example to demonstrate the interaction between several independent magnetic flux systems in different regions,
as implied by the Bastille Day event, and may serve as a possible mechanism for sympathetic events occurring on the Sun. 相似文献
10.
We present a simplified analytic model of a quadrupolar magnetic field and flux rope to model coronal mass ejections. The model magnetic field is two-dimensional, force-free and has current only on the axis of the flux rope and within two current sheets. It is a generalization of previous models containing a single current sheet anchored to a bipolar flux distribution. Our new model can undergo quasi-static evolution either due to changes at the boundary or due to magnetic reconnection at either current sheet. We find that all three kinds of evolution can lead to a catastrophe, known as loss of equilibrium. Some equilibria can be driven to catastrophic instability either through reconnection at the lower current sheet, known as tether cutting, or through reconnection at the upper current sheet, known as breakout. Other equilibria can be destabilized through only one and not the other. Still others undergo no instability, but they evolve increasingly rapidly in response to slow steady driving (ideal or reconnective). One key feature of every case is a response to reconnection different from that found in simpler systems. In our two-current-sheet model a reconnection electric field in one current sheet causes the current in that sheet to increase rather than decrease. This suggests the possibility for the microscopic reconnection mechanism to run away. 相似文献
11.
This paper treats the prominence model of Low (1993) to examine more complicated sheet currents than those used in the original model. Nonlinear force-free field solutions, in Cartesian coordinates, invariant in a given direction, are presented to show the possibility of an inverse-polarity prominence embedded in a large twisted flux tube. The force-free solution is matched to an external, unsheared, potential coronal magnetic field. These new solutions are mathematically interesting and allow an investigation of different profiles of the current intensity, magnetic field vector and mass density in the sheet. These prominence models show a general increase in magnetic field strength with height in agreement with observations. Other prominence properties are shown to match the observed values. 相似文献
12.
We model solar coronal mass ejections (CMEs) as expanding force-free magnetic structures and find the self-similar dynamics of configurations with spatially constant ??, where J=?? B, in spherical and cylindrical geometries, expanding spheromaks and Lundquist fields, respectively. The field structures remain force-free, under the conventional non-relativistic assumption that the dynamical effects of the inductive electric fields can be neglected. While keeping the internal magnetic field structure of the stationary solutions, expansion leads to complicated internal velocities and rotation, caused by inductive electric fields. The structure depends only on overall radius R(t) and rate of expansion $\dot{R}(t)$ measured at a given moment, and thus is applicable to arbitrary expansion laws. In case of cylindrical Lundquist fields, magnetic flux conservation requires that both axial and radial expansion proceed with equal rates. In accordance with observations, the model predicts that the maximum magnetic field is reached before the spacecraft reaches the geometric center of a CME. 相似文献
13.
Based on photospheric vector magnetograms obtained at Huairou Solar Observing Station, we have studied the evolution of magnetic
nonpotentiality in NOAA AR 9077 from 11 to 15 July 2000. We focus our analysis on the daily change of nonpotential characteristics
in the photospheric magnetic field preceding the `Bastille Day' flare. We have identified the following evolving patterns:
(1) The shear-angle distribution underwent dramatic change in the filament channel. At a key site of the filament environment,
the magnetic shear changed sign from positive to negative. (2) The old current systems disrupted, and new but weaker systems
formed before this major event. Similar changes are identified for the longitudinal current helicity. (3) The source field
weakened before the flare, and the density of free magnetic energy decreased at the photospheric level. These obvious changes
lasted at least nine hours before the `Bastille Day' flare, and they took place where a large amount of magnetic flux disappeared
in magnetic flux cancellation. The site of dramatic changes is also found to coincide with the base of helical magnetic ropes
which were seen in a 3-D force-free reconstruction. We suggest that the observed evolution of the magnetic nonpotentiality
represents a continuous transportation of magnetic energy and complexity from the lower atmosphere to the corona. This transportation
seems to be responsible for the energy build-up for the major flare. Moreover, the slow magnetic reconnection in the lower
atmosphere, observed as magnetic flux cancellation, appears to play a key role in this energy build-up process.
Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1023/A:1014258426134 相似文献
14.
The force-free electromagnetic field represents a natural generalization of the well-known force-free magnetic field model and allows the magnetic field to maintain electric charge separation.The basic equation for the cylindrical oscillations of the force-free electromagnetic field is obtained and solved for a linear case. The spectrum of possible resonances in a magnetized atmosphere is discussed. 相似文献
15.
The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free “potential-field” extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this model – in particular the flux ropes – varies over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, non-potential, magnetic structure at all latitudes. 相似文献
16.
S. Régnier 《Solar physics》2012,277(1):131-151
In the last decades, force-free-field modelling has been used extensively to describe the coronal magnetic field and to better
understand the physics of solar eruptions at different scales. Especially the evolution of active regions has been studied
by successive equilibria in which each computed magnetic configuration is subject to an evolving photospheric distribution
of magnetic field and/or electric-current density. This technique of successive equilibria has been successful in describing
the rate of change of the energetics for observed active regions. Nevertheless the change in magnetic configuration due to
the increase/decrease of electric current for different force-free models (potential, linear and nonlinear force-free fields)
has never been studied in detail before. Here we focus especially on the evolution of the free magnetic energy, the location
of the excess of energy, and the distribution of electric currents in the corona. For this purpose, we use an idealised active
region characterised by four main polarities and a satellite polarity, allowing us to specify a complex topology and sheared
arcades to the coronal magnetic field but no twisted flux bundles. We investigate the changes in the geometry and connectivity
of field lines, the magnetic energy and current-density content as well as the evolution of null points. Increasing the photospheric
current density in the magnetic configuration does not dramatically change the energy-storage processes within the active
region even if the magnetic topology is slightly modified. We conclude that for reasonable values of the photospheric current
density (the force-free parameter α<0.25 Mm−1), the magnetic configurations studied do change but not dramatically: i) the original null point stays nearly at the same location, ii) the field-line geometry and connectivity are slightly modified, iii) even if the free magnetic energy is significantly increased, the energy storage happens at the same location. This extensive
study of different force-free models for a simple magnetic configuration shows that some topological elements of an observed
active region, such as null points, can be reproduced with confidence only by considering the potential-field approximation.
This study is a preliminary work aiming at understanding the effects of electric currents generated by characteristic photospheric
motions on the structure and evolution of the coronal magnetic field. 相似文献
17.
Knowledge regarding the coronal magnetic field is important for the understanding of many phenomena, like flares and coronal
mass ejections. Because of the low plasma beta in the solar corona, the coronal magnetic field is often assumed to be force-free
and we use photospheric vector magnetograph data to extrapolate the magnetic field into the corona with the help of a nonlinear
force-free optimization code. Unfortunately, the measurements of the photospheric magnetic field contain inconsistencies and
noise. In particular, the transversal components (say B x and B y) of current vector magnetographs have their uncertainties. Furthermore, the magnetic field in the photosphere is not necessarily
force free and often not consistent with the assumption of a force-free field above the magnetogram. We develop a preprocessing
procedure to drive the observed non–force-free data towards suitable boundary conditions for a force-free extrapolation. As
a result, we get a data set which is as close as possible to the measured data and consistent with the force-free assumption. 相似文献
18.
T. Takakura 《Solar physics》1982,113(1-2):221-228
Evolution of a filamentary magnetic flux tube emerging from the photosphere is investigated in the assumption that the magnetic field is force-free and unchanged during the evolution.If a characteristic radius of the flux tube is 3 km or less setting the field to 1000G, the temperature increases at first due to Joule heating up to about one million degree keeping the plasma density almost constant, and then the density decreases down to a critical value at which a current instability may occur. Thus, a.strong field-aligned electric field of 200 million volts or more is expected to be produced during the following anomalous Ohmic decay of the magnetic field as already shown by a numerical simulation. 相似文献
19.
Markus J. Aschwanden 《Solar physics》2013,287(1-2):323-344
We derive an analytical approximation of nonlinear force-free magnetic field solutions (NLFFF) that can efficiently be used for fast forward-fitting to solar magnetic data, constrained either by observed line-of-sight magnetograms and stereoscopically triangulated coronal loops, or by 3D vector-magnetograph data. The derived NLFFF solutions provide the magnetic field components B x (x), B y (x), B z (x), the force-free parameter α(x), the electric current density j(x), and are accurate to second-order (of the nonlinear force-free α-parameter). The explicit expressions of a force-free field can easily be applied to modeling or forward-fitting of many coronal phenomena. 相似文献
20.
M. A. Raadu 《Solar physics》1972,22(2):425-433
Energy storage in chromospheric flux ropes is discussed, in the context of solar flares. The structure is represented by a cylindrically symmetric magnetic field of finite length. The field is assumed to be approximately force-free. The stability of the field to a kink perturbation is investigated. Flux ropes are rooted in dense photospheric material. So the ends of the field lines are taken to be fixed on rigid boundaries for all perturbations. An energy perturbation method is used and the boundary conditions give a stabilizing effect. It is shown that for a moderate degree of twisting the fields are stable to a kink perturbation. Thus energy can be stored in cylindrical fields prior to release in a solar flare.The National Center for Atmospheric Research is sponsored by the National Science Foundation. 相似文献