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1.
We develop an approach to deriving the three-dimensional non-force-free coronal magnetic field from vector magnetograms. Based
on the principle of minimum dissipation rate, a general non-force-free magnetic field is expressed as the superposition of
one potential field and two constant-α (linear) force-free fields. Each is extrapolated from its bottom boundary data, providing the normal component only. The
constant-α parameters are distinct and determined by minimizing the deviations between the numerically computed and measured transverse
magnetic field at the bottom boundary. The boundary conditions required are at least two layers of vector magnetograms, one
at the photospheric level and the other at the chromospheric level, presumably. We apply our approach to a few analytic test
cases, especially to two nonlinear force-free cases examined by Schrijver et al. (Solar Phys.
235, 161, 2006). We find that for one case with small α parameters, the quantitative measures of the quality of our result are better than the median values of those from a set
of nonlinear force-free methods. The reconstructed magnetic-field configuration is valid up to a vertical height of the transverse
scale. For the other cases, the results remain valid to a lower vertical height owing to the limitations of the linear force-free-field
solver. Because our method is based on the fast-Fourier-transform algorithm, it is much faster and easy to implement. We discuss
the potential usefulness of our method and its limitations. 相似文献
2.
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
3.
T. Wiegelmann 《Solar physics》2007,240(2):227-239
We describe a newly developed code for the extrapolation of nonlinear force-free coronal magnetic fields in spherical coordinates.
The program uses measured vector magnetograms on the solar photosphere as input and solves the force-free equations in the
solar corona. The method is based on an optimization principle and the heritage of the newly developed code is a corresponding
method in Cartesian geometry. We test the newly developed code with the help of a semi-analytic solution and rate the quality
of our reconstruction qualitatively by magnetic field line plots and quantitatively with a number of comparison metrics. We
find that we can reconstruct the original test field with high accuracy. The method is fast if the computation is limited
to low co-latitudes (say 30°≤θ≤150°), but it becomes significantly slower if the polar regions are included. 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.
Tilaye Tadesse T. Wiegelmann P. J. MacNeice B. Inhester K. Olson A. Pevtsov 《Solar physics》2014,289(3):831-845
Measurements of magnetic fields and electric currents in the pre-eruptive corona are crucial to the study of solar eruptive phenomena, like flares and coronal mass ejections (CMEs). However, spectro-polarimetric measurements of certain photospheric lines permit a determination of the vector magnetic field only at 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 above multiple active regions with the help of a potential field and a nonlinear force-free field (NLFFF) extrapolation code over the full solar disk using Helioseismic and Magnetic Imager (SDO/HMI) data as boundary conditions. We compare projections of the resulting magnetic field lines with full-disk coronal images from the Atmospheric Imaging Assembly (SDO/AIA) for both models. This study has found that the NLFFF model reconstructs the magnetic configuration closer to observation than the potential field model for full-disk magnetic field extrapolation. We conclude that many of the trans-equatorial loops connecting the two solar hemispheres are current-free. 相似文献
6.
M. S. Wheatland 《Solar physics》2006,238(1):29-39
Existing methods for calculating nonlinear force-free magnetic fields are slow, and are likely to be inadequate for reconstructing
coronal magnetic fields based on high-resolution vector magnetic field data from a new generation of spectro-polarimetric
instruments. In this paper a new implementation of the current-field iteration method is presented, which is simple, fast,
and accurate. The time taken by the method scales as N
4, for a three-dimensional grid with N
3 points. The method solves the field-updating part of the iteration by exploiting a three-dimensional Fast Fourier Transform
solution of Ampere’s law with a current density field constructed to satisfy the required boundary conditions, and uses field
line tracing to solve the current-updating part of the iteration. The method is demonstrated in application to a known nonlinear
force-free field and to a bipolar test case. 相似文献
7.
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
8.
Studies of solar flares indicate that the mechanism of flares is magnetic in character and that the coronal magnetic field is a key to understanding solar high-energy phenomena. In our ongoing research we are conducting a systematic study of a large database of observations which includes both coronal structure (from the Soft X-ray Telescope on the Yohkoh spacecraft) and photospheric vector magnetic fields (from the Haleakala Stokes Polarimeter at Mees Solar Observatory). We compare the three-dimensional nonlinear force-free coronal magnetic field, computed from photospheric boundary data, to images of coronal structure. In this paper we outline our techniques and present results for active region AR 7220/7222. We show that the computed force-free coronal magnetic field agrees well with Yohkoh X-ray coronal loops, and we discuss the properties of the coronal magnetic field and the soft X-ray loops. 相似文献
9.
We present a set of cylindrically-symmetric force-free magnetic fields with non-constant scalar function scalar. We found that the kink instability of the fields can be suppressed by reducing the length of the flux tube. By using the pressure profile in coronal magnetic loops obtained on the basis of the observational data, and by neglecting the effect of gravity, these force-free fields ars modified to non-force-free ones. For the plasma of finite conductivity the time and space dependent magnetic fields are obtained, and the ohmic dissipation per unit volume per second is calculated. For the magnetic fields, presented in the investigation, it is also found that, due to the large electrical conductivity of the plasma, the ohmic dissipation is negligable in comparison to the conduction and the radiation loss. Hence, for the energy equilibrium in a coronal loop, the contribution of ohmic dissipation is insignificant. 相似文献
10.
We evaluate the performances of two newly-implemented codes for extrapolating the solar linear force-free magnetic fields,
by measuring their quantified responses to the lower boundary vector field data on a finite region using analytical models.
The codes are based on two boundary integral formulas with different mechanisms in utilizing the transverse boundary field:
the first one only utilizes the transverse boundary field to derive the value of the force-free parameter, while the other
one explicitly utilizes the whole transverse boundary field, in addition to the vertical field component. Studies on the test
cases show that both of the codes could reproduce the analytical model fields with reasonable accuracy within the valid domain,
provided a sufficient amount of data is available at the lower boundary. The code utilizing explicitly all three components
of the boundary field shows generally better performances and requires a smaller boundary-data area in order to achieve the
same degree of accuracy in the metric quantities such as the normalized vector error, vector correlation, vector angular difference,
and magnetic energy; however, the accuracy in the divergence-free metric and especially the force-free metric are less ideal. 相似文献
11.
Tilaye Tadesse T. Wiegelmann P. J. MacNeice K. Olson 《Astrophysics and Space Science》2013,347(1):21-27
The magnetic fields in the solar atmosphere structure the plasma, store free magnetic energy and produce a wide variety of active solar phenomena, like flare and coronal mass ejections (CMEs). The distribution and strength of magnetic fields are routinely measured in the solar surface (photosphere). Therefore, there is considerable interest in accurately modeling the 3D structure of the coronal magnetic field using photospheric vector magnetograms. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV images of the radiating coronal plasma. Nonlinear force-free field (NLFFF) models are thought to be viable tools for those task. Usually those models use Cartesian geometry. However, the spherical nature of the solar surface cannot be neglected when the field of view is large. In this work, we model the coronal magnetic field above multiple active regions using NLFFF extrapolation code using vector magnetograph data from the Synoptic Optical Long-term Investigations of the Sun survey (SOLIS)/Vector Spectromagnetograph (VSM) as a boundary conditions. We compare projections of the resulting magnetic field lines solutions with their respective coronal EUV-images from the Atmospheric Imaging Assembly (SDO/AIA) observed on October 15, 2011 and November 13, 2012. This study has found that the NLFFF model in spherical geometry reconstructs the magnetic configurations for several active regions which agrees to some extent with observations. During October 15, 2011 observation, there are substantial number of trans-equatorial loops carrying electric current. 相似文献
12.
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
13.
We present a novel numerical method that allows the calculation of nonlinear force-free magnetostatic solutions above a boundary
surface on which only the distribution of the normal magnetic field component is given. The method relies on the theory of
force-free electrodynamics and applies directly to the reconstruction of the solar coronal magnetic field for a given distribution
of the photospheric radial field component. The method works as follows: we start with any initial magnetostatic global field
configuration (e.g. zero, dipole), and along the boundary surface we create an evolving distribution of tangential (horizontal) electric fields
that, via Faraday’s equation, give rise to a respective normal-field distribution approaching asymptotically the target distribution.
At the same time, these electric fields are used as boundary condition to numerically evolve the resulting electromagnetic
field above the boundary surface, modeled as a thin ideal plasma with non-reflecting, perfectly absorbing outer boundaries.
The simulation relaxes to a nonlinear force-free configuration that satisfies the given normal-field distribution on the boundary.
This is different from existing methods relying on a fixed boundary condition – the boundary evolves toward the a priori given
one, at the same time evolving the three-dimensional field solution above it. Moreover, this is the first time that a nonlinear
force-free solution is reached by using only the normal field component on the boundary. This solution is not unique, but
it depends on the initial magnetic field configuration and on the evolutionary course along the boundary surface. To our knowledge,
this is the first time that the formalism of force-free electrodynamics, used very successfully in other astrophysical contexts,
is applied to the global solar magnetic field. 相似文献
14.
Nonlinear force-free magnetic field(NLFFF) extrapolation based on the observed photospheric magnetic field is the most important method to obtain the coronal magnetic field nowadays.However, raw photospheric magnetograms contain magnetic forces and small-scale noises, and fail to be consistent with the force-free assumption of NLFFF models. The procedure for removing the forces and noises in observed data is called preprocessing. In this paper, we extend the preprocessing code of Jiang Feng to spherical coordinates for a full sphere. We first smooth the observed data with Gaussian smoothing, and then split the smoothed magnetic field into a potential field and a non-potential field.The potential part is computed by a numerical potential field model, and the non-potential part is preprocessed using an optimization method to minimize the magnetic forces and magnetic torques. Applying the code to synoptic charts of the vector magnetic field from SDO/HMI, we find it can effectively reduce the noises and forces, and improve the quality of data for a better input which will be used for NLFFF extrapolations applied to the global corona. 相似文献
15.
A WKB approach, based on the method of Connor, Hastie, and Taylor (1979), is used to obtain simple estimates of the critical
conditions for the onset of ideal MHD instabilities in line-tied solar coronal loops. The method is illustrated for the constant
twist, Gold-Hoyle (1960) field, and the critical conditions are compared with previous and new numerical results. For the
force-free case, the WKB estimate for the critical loop length reduces to
. For the sufficiently non-force-free case the critical length can be expressed in the forml
0 +l
1/m. The results confirm the findings of De Bruyne and Hood (1992) that for force-free fields them = 1 mode is the first mode to become unstable but for the sufficiently strong non-force-free case this reverses with them → ∞ mode being excited first. 相似文献
16.
Force-free magnetic fields can be computed by making use of a new numerical technique, in which the fields are represented
by a boundary integral equation based on a specific Green's function. Vector magnetic fields observed on the photospheric
surface can be taken as the boundary conditions of this equation. In this numerical computation, the following two points
are emphasized: (1) A new method for data reduction is proposed, for removing uncertainties in boundary data and determining
the parameter in this Green's function, which is important for solving the boundary integral equation. In this method, the
transverse components of the observed boundary field are calibrated with a linear force-free field model without changing
their azimuth. (2) The computed 3-D fields satisfy the divergence-free and force-free conditions with high precision. The
alignment of these field lines is mostly in agreement with structures in Hα and Yohkoh soft X-ray images. Since the boundary data are calibrated with a linear force-free field model, the computed 3-D magnetic
field can be regarded as a quasi-linear force-free field approximation. The reconstruction of 3-D magnetic field in active
region NOAA 7321 was taken as an example to quantitatively exhibit the capability of our new numerical technique. 相似文献
17.
Using the boundary element method (BEM) for constant-, force-free fields, the vector magnetic field distributions in the chromosphere of a flare-productive active region. AR 6659 in June 1991, are obtained by extrapolating from the observed vector magnetograms at the photosphere. The calculated transverse magnetic fields skew highly from the photosphere to the chromosphere in the following positive polarity sunspot whereas they skew only slightly in the main preceding sunspot. This suggests that more abundant energy was stored in the former area causing flares. Those results demostrate the validity of the BEM solution and the associations between the force-free magnetic field and the structure of the AR 6659 region. It shows that the features of the active region can be revealed by the constant- force-free magnetic field approximation. 相似文献
18.
Magnetic field extrapolation is an alternative method to study chromospheric and coronal magnetic fields. In this paper, two
semi-analytical solutions of force-free fields (Low and Lou in Astrophys. J. 352:343, 1990) have been used to study the errors of nonlinear force-free (NLFF) fields based on force-free factor α. Three NLFF fields are extrapolated by approximate vertical integration (AVI) Song et al. (Astrophys. J. 649:1084, 2006), boundary integral equation (BIE) Yan and Sakurai (Sol. Phys. 195:89, 2000) and optimization (Opt.) Wiegelmann (Sol. Phys. 219:87, 2004) methods. Compared with the first semi-analytical field, it is found that the mean values of absolute relative standard deviations
(RSD) of α along field lines are about 0.96–1.19, 0.63–1.07 and 0.43–0.72 for AVI, BIE and Opt. fields, respectively. While for the
second semi-analytical field, they are about 0.80–1.02, 0.67–1.34 and 0.33–0.55 for AVI, BIE and Opt. fields, respectively.
As for the analytical field, the calculation error of 〈|RSD|〉 is about 0.1∼0.2. It is also found that RSD does not apparently depend on the length of field line. These provide the basic
estimation on the deviation of extrapolated field obtained by proposed methods from the real force-free field. 相似文献
19.
M. S. Wheatland 《Solar physics》2007,245(2):251-262
Improvements to an existing method for calculating nonlinear force-free magnetic fields (Wheatland, Solar Phys. 238, 29, 2006) are described. In particular a solution of the 3-D Poisson equation using 2-D Fourier transforms is presented. The improved
nonlinear force-free method is demonstrated in application to linear force-free test cases with localized nonzero values of
the normal component of the field in the boundary. These fields provide suitable test cases for nonlinear force-free calculations
because the boundary conditions involve localized nonzero values of the normal components of the field and of the current
density, and because (being linear force-free fields) they have more direct numerical solutions. Despite their simplicity,
fields of this kind have not been recognized as test cases for nonlinear methods before. The examples illustrate the treatment
of the boundary conditions on current in the nonlinear force-free method, and in particular the limitations imposed by field
lines that connect outside of the boundary region. 相似文献
20.
We compare the performance of two alternative algorithms which aim to construct a force-free magnetic field given suitable
boundary conditions. For this comparison, we have implemented both algorithms on the same finite element grid which uses Whitney
forms to describe the fields within the grid cells. The additional use of conjugate gradient and multigrid iterations result
in quite effective codes.
The Grad Rubin and Wheatland Sturrock Roumeliotis algorithms both perform well for the reconstruction of a known analytic
force-free field. For more arbitrary boundary conditions the Wheatland Sturrock Roumeliotis approach has some difficulties
because it requires overdetermined boundary information which may include inconsistencies. The Grad Rubin code on the other
hand loses convergence for strong current densities. For the example we have investigated, however, the maximum possible current
density seems to be not far from the limit beyond which a force-free field cannot exist anymore for a given normal magnetic
field intensity on the boundary. 相似文献