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1.
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
2.
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
3.
We developed a code for the reconstruction of nonlinear force-free and non-force-free coronal magnetic fields. The 3D magnetic
field is computed numerically with the help of an optimization principle. The force-free and non-force-free codes are compiled
in one program. The force-free approach needs photospheric vector magnetograms as input. The non-force-free code additionally
requires the line-of-sight integrated coronal density distribution in combination with a tomographic inversion code. Previously
the optimization approach has been used to compute magnetic fields using all six boundaries of a computational box. Here we
extend this method and show how the coronal magnetic field can be reconstructed only from the bottom boundary, where the boundary
conditions are measured with vector magnetographs. The program is planed for use within the Stereo mission. 相似文献
4.
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
5.
G. Allen Gary 《Solar physics》2009,257(2):271-286
The minimum dissipative rate (MDR) method for deriving a coronal non-force-free magnetic field solution is partially evaluated.
These magnetic field solutions employ a combination of three linear (constant-α) force-free-field solutions with one being a potential field (i.e., α=0). The particular case of the solutions where the other two α’s are of equal magnitude but of opposite sign is examined. This is motivated by studying the SOLIS (Synoptic Optical Long-term
Investigation of the Sun (SOLIS), a National Solar Observatory facility) vector magnetograms of AR 10987, which show a global
α value consistent with an α=0 value as evaluated by (∇×B)
z
/B
z
over the region. Typical of the current state of the observing technology, there is no definitive twist for input into the
general MDR method. This suggests that the special α case, of two α’s with equal magnitudes and opposite signs, is appropriate given the data. Only for an extensively twisted active region
does a dominant, nonzero α normally emerge from a distribution of local values. For a special set of conditions, is it found that (i) the resulting
magnetic field is a vertically inflated magnetic field resulting from the electric currents being parallel to the photosphere,
similar to the results of Gary and Alexander (Solar Phys. 186:123, 1999), and (ii) for α≈(α
max /2), the Lorentz force per unit volume normalized by the square of the magnetic field is on the order of 1.4×10−10 cm−1. The Lorentz force (F
L) is a factor of ten higher than that of the magnetic force d(B
2/8π)/dz, a component of F
L. The calculated photospheric electric current densities are an order of magnitude smaller than the maximum observed in all
active regions. Hence both the Lorentz force density and the generated electric current density seem to be physically consistent
with possible solar dynamics. The results imply that the field could be inflated with an overpressure along the neutral line.
However, the implementation of this or any other extrapolation method using the electric current density as a lower boundary
condition must be done cautiously, with the current magnetography. 相似文献
6.
We present a careful investigation of the magnetofrictional relaxation and extrapolation technique applied to the reconstruction
of two test fields. These fields are taken from the family of nonlinear force-free magnetic equilibria constructed by Low
and Lou (Astrophys. J.
352, 343, 1990), which have emerged as standard tests for extrapolation techniques in recent years. For the practically relevant case that
only the field values in the bottom plane of the considered volume (vector magnetogram) are used as input information (i.e., not including the knowledge about the test field at the side and top boundaries), the test field is reconstructed to a higher
accuracy than obtained previously. Detailed diagnostics of the reconstruction accuracy show that the implementation of fourth-order
spatial discretization was essential to reach this accuracy for the given test fields and to achieve near machine precision
in satisfying the solenoidal condition. Different variants of boundary conditions are tested, which all yield comparable accuracy.
In its present implementation, the technique yields a scaling of computing time with total number of grid points only slightly
below N
5/3, which is too steep for applications to large (≥10242) magnetograms, except on supercomputers. Directions for improvement are outlined. 相似文献
7.
A brief historical review of solar and interplanetary magnetic field modeling and analysis is presented. The modeling was initiated with the routine observation of longitudinal magnetograms and the application of current free potential magnetic fields for its interpretation. Almost simultaneously, the development of detailed H observation motivated the constant-, force-free magnetic field analysis. Subsequent development of transverse magnetograms leads not only to further refinements of the analysis and modeling but also to many physically meaningful interpretations of the observations. In this review, historical development is traced with the emphasis placed on the yet unanswered questions. 相似文献
8.
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
9.
10.
A force-free magnetic field model with constant is established, and a boundary element method is proposed to solve the problem. The procedure ensures a unique solution as well as a finite magnetic energy content. The proposed formulation is effective in solving magnetic fields above the solar surface, and the validity of our procedure is demonstrated by satisfactory agreement between calculated and observed magnetograms. 相似文献
11.
We present three-dimensional unsteady modeling and numerical simulations of a coronal active region, carried out within the
compressible single-fluid MHD approximation. We focus on AR 9077 on 14 July 2000, and the triggering of the X5.7 GOES X-ray
class “Bastille Day” flare. We simulate only the lower corona, although we include a virtual photosphere and chromosphere
below. The boundary conditions at the base of this layer are set using temperature maps from line intensities and line-of-sight
magnetograms (SOHO/MDI). From the latter, we generate vector magnetograms using the force-free approximation; these vector
magnetograms are then used to produce the boundary condition on the velocity field using a minimum energy principle (Longcope,
Astrophys. J.
612, 1181, 2004). The reconnection process is modeled through a dynamical hyper-resistivity which is activated when the current exceeds a
critical value (Klimas et al., J. Geophys. Res.
109, 2218, 2004). Comparing the time series of X-ray fluxes recorded by GOES with modeled time series of various mean physical variables
such as current density, Poynting energy flux, or radiative loss inside the active region, we can demonstrate that the model
properly captures the evolution of an active region over a day and, in particular, is able to explain the initiation of the
flare at the observed time. 相似文献
12.
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
13.
Using photospheric vector magnetograms of the Huairou Solar Observing Station and coronal X-ray images from the Yohkoh Soft X-Ray Telescope, we calculate the helicity patterns of 43 pairs of active regions and the chirality of 50 pairs of opposite
magnetic polarity regions that are connected by transequatorial loops (TLs). To make the results more convincing, two helicity
proxies including the local current helicity h
c and the force-free factor α
best are computed. The results, which are similar for both parameters, are as follows: (1) Current helicity of the active regions
pairs connected by transequatorial loops have no obvious regularity: About 50% of the active region pairs carry the same current
helicity sign and about 50% of them have the opposite. (2) If we consider the magnetic polarity pairs connected by the TLs,
the result is almost the same as that for the active region pairs, with a little more than half of them showing the same chirality.
We also make linear force-free extrapolations for 33 TLs and determine their force-free parameter α by comparing extrapolated field lines to X-ray images of the TLs. Out of the 19 cases when the footpoints of the TLs have
the same current helicity sign, we find that the sign of α of the TLs is the same as the sign of the current helicity in the footpoints in 12 cases, whereas it is of opposite sign
in 4 cases, and in 3 cases the TLs were found to be potential. 相似文献
14.
Jiangtao Su Yu Liu Jihong Liu Xinjie Mao Hongqi Zhang Hui Li Xiaofan Wang Wenbin Xie 《Solar physics》2008,252(1):55-71
Zhao and Kosovichev (Astrophys. J.
591, 446, 2003) found two opposite sub-photospheric vortical flows in the depth range of 0 – 12 Mm around a fast rotating sunspot. So far
there is no theoretical model explaining such flow motions. In this paper, we try to explain this phenomenon from the point
of view of magnetic flux tubes interacting with large-scale vortical motions of plasma. In the deeper zone under the photosphere,
the magnetic force may be less than the nonmagnetic force of plasma. The vortical flow located there twists the flux tube
and magnetic free energy is built up in the tube. In the shallower zone under the photosphere, the magnetic force may be greater
than the nonmagnetic force. Thus, part of the stored magnetic free energy is released to drive the plasma to rotate in two
opposite directions, e.g., in the depth ranges of 0 – 3(5) and 9 – 12 Mm. In addition, we also define a vector of nonpotential magnetic stress τ, which can be related to flare occurrence. It is calculated for the active region NOAA 10930 on 11 December 2006. We find
that: i) the integral of its line-of-sight (LOS) stress successively increases around the magnetic neutral line (MNL) prior to and
during the flare and decreases to a minimum after the flare; ii) the integral of its transverse stress exceeds the integral of its LOS component by one order of magnitude over the whole
field of view; iii) the transverse stress first points toward the MNL, then along it, and finally it points away from it. We need other data
to verify whether or not the magnetic energy is transported in the horizontal direction to the neutral line, and then partly
changes into the energy in LOS direction before and during the flare. 相似文献
15.
The coronal magnetic field above a particular photospheric region will vanish at a certain number of points, called null points.
These points can be found directly in a potential field extrapolation or their density can be estimated from the Fourier spectrum
of the magnetogram. The spectral estimate, in which the extrapolated field is assumed to be random and homogeneous with Gaussian
statistics, is found here to be relatively accurate for quiet Sun magnetograms from SOHO’s MDI. The majority of null points
occur at low altitudes, and their distribution is dictated by high wavenumbers in the Fourier spectrum. This portion of the
spectrum is affected by Poisson noise, and as many as five-sixths of null points identified from a direct extrapolation can
be attributed to noise. The null distribution above 1500 km is found to depend on wavelengths that are reliably measured by
MDI in either its low-resolution or high-resolution mode. After correcting the spectrum to remove white noise and compensate
for the modulation transfer function we find that a potential field extrapolation contains, on average, one magnetic null
point, with altitude greater than 1.5 Mm, above every 322 Mm2 patch of quiet Sun. Analysis of 562 quiet Sun magnetograms spanning the two latest solar minima shows that the null point
density is relatively constant with roughly 10% day-to-day variation. At heights above 1.5 Mm, the null point density decreases
approximately as the inverse cube of height. The photospheric field in the quiet Sun is well approximated as that from discrete
elements with mean flux 〈|φ|〉=1.0×1019 Mx distributed randomly with density n=0.007 Mm−2. 相似文献
16.
We present a straightforward comparison of model calculations for the α-effect, helicities, and magnetic field line twist
in the solar convection zone with magnetic field observations at atmospheric levels. The model calculations are carried out
in a mixing-length approximation for the turbulence with a profile of the solar internal rotation rate obtained from helioseismic
inversions. The magnetic field data consist of photospheric vector magnetograms of 422 active regions for which spatially-averaged
values of the force-free twist parameter and of the current helicity density are calculated, which are then used to determine
latitudinal profiles of these quantities. The comparison of the model calculations with the observations suggests that the
observed twist and helicity are generated in the bulk of the convection zone, rather than in a layer close to the bottom.
This supports two-layer dynamo models where the large-scale toroidal field is generated by differential rotation in a thin
layer at the bottom while the α-effect is operating in the bulk of the convection zone. Our previous observational finding
was that the moduli of the twist factor and of the current helicity density increase rather steeply from zero at the equator
towards higher latitudes and attain a certain saturation at about 12 – 15∘. In our dynamo model with algebraic nonlinearity, the increase continues, however, to higher latitudes and is more gradual.
This could be due to the neglect of the coupling between small-scale and large-scale current and magnetic helicities and of
the latitudinal drift of the activity belts in the model. 相似文献
17.
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
18.
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
19.
We use 270 pairs of vector magnetograms observed by Haleakala Stokes Polarimeter (HSP) and Solar Magnetic Field Telescope
(SMFT) of Huairou Solar Observing Station from 1997 to 2000 to compare current helicity derived by these two instruments.
We apply the same approach to both data sets to resolve 180∘ azimuth ambiguity and compute α coefficient of linear force-free field. After careful consideration of various aspects of
both data sets, we find that in ≈80% of cases SMFT and HSP data result in the same sign of α, and the Pearson linear correlation
coefficient between two data sets is rp = 0.64.
Operated by the Association of Universities for Research in Astronomy (AURA, Inc) under cooperative agreement with the National
Science Foundation (NSF). 相似文献
20.
We have used Stanford magnetic field maps to construct distributions of longitudinal magnetic field gradients in the neighbourhood of polarity inversion lines. The distributions were constructed with proper account of the type of the polarity inversion lines and of the existence or absence of dark filaments above them. It is shown that for polarity inversion lines that pass inside active regions or on their boundary, grad BII distributions for portions of the lines with persisting filament are shifted toward lower values of gradient as compared with grad BII distributions for portions of the lines without filaments. The influence of the spatial resolution of the magnetograms upon polarity inversion line characteristics is discussed. 相似文献