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Thomas R. Metcalf Marc L. DeRosa Carolus J. Schrijver Graham Barnes Adriaan A. van Ballegooijen Thomas Wiegelmann Michael S. Wheatland Gherardo Valori James M. McTtiernan 《Solar physics》2008,247(2):269-299
We compare a variety of nonlinear force-free field (NLFFF) extrapolation algorithms, including optimization, magneto-frictional,
and Grad – Rubin-like codes, applied to a solar-like reference model. The model used to test the algorithms includes realistic
photospheric Lorentz forces and a complex field including a weakly twisted, right helical flux bundle. The codes were applied
to both forced “photospheric” and more force-free “chromospheric” vector magnetic field boundary data derived from the model.
When applied to the chromospheric boundary data, the codes are able to recover the presence of the flux bundle and the field’s
free energy, though some details of the field connectivity are lost. When the codes are applied to the forced photospheric
boundary data, the reference model field is not well recovered, indicating that the combination of Lorentz forces and small
spatial scale structure at the photosphere severely impact the extrapolation of the field. Preprocessing of the forced photospheric
boundary does improve the extrapolations considerably for the layers above the chromosphere, but the extrapolations are sensitive
to the details of the numerical codes and neither the field connectivity nor the free magnetic energy in the full volume are
well recovered. The magnetic virial theorem gives a rapid measure of the total magnetic energy without extrapolation though,
like the NLFFF codes, it is sensitive to the Lorentz forces in the coronal volume. Both the magnetic virial theorem and the
Wiegelmann extrapolation, when applied to the preprocessed photospheric boundary, give a magnetic energy which is nearly equivalent
to the value derived from the chromospheric boundary, but both underestimate the free energy above the photosphere by at least
a factor of two. We discuss the interpretation of the preprocessed field in this context. When applying the NLFFF codes to
solar data, the problems associated with Lorentz forces present in the low solar atmosphere must be recognized: the various
codes will not necessarily converge to the correct, or even the same, solution.
On 07/07/2007, the NLFFF team was saddened by the news that Tom Metcalf had died as the result of an accident. We remain grateful
for having had the opportunity to benefit from his unwavering dedication to the problems encountered in attempting to understand
the Sun’s magnetic field; Tom had completed this paper several months before his death, leading the team through the many
steps described above. 相似文献
2.
E. Palmerio E. K. J. Kilpua A. W. James L. M. Green J. Pomoell A. Isavnin G. Valori 《Solar physics》2017,292(2):39
A key aim in space weather research is to be able to use remote-sensing observations of the solar atmosphere to extend the lead time of predicting the geoeffectiveness of a coronal mass ejection (CME). In order to achieve this, the magnetic structure of the CME as it leaves the Sun must be known. In this article we address this issue by developing a method to determine the intrinsic flux rope type of a CME solely from solar disk observations. We use several well-known proxies for the magnetic helicity sign, the axis orientation, and the axial magnetic field direction to predict the magnetic structure of the interplanetary flux rope. We present two case studies: the 2 June 2011 and the 14 June 2012 CMEs. Both of these events erupted from an active region, and despite having clear in situ counterparts, their eruption characteristics were relatively complex. The first event was associated with an active region filament that erupted in two stages, while for the other event the eruption originated from a relatively high coronal altitude and the source region did not feature a filament. Our magnetic helicity sign proxies include the analysis of magnetic tongues, soft X-ray and/or extreme-ultraviolet sigmoids, coronal arcade skew, filament emission and absorption threads, and filament rotation. Since the inclination of the post-eruption arcades was not clear, we use the tilt of the polarity inversion line to determine the flux rope axis orientation and coronal dimmings to determine the flux rope footpoints, and therefore, the direction of the axial magnetic field. The comparison of the estimated intrinsic flux rope structure to in situ observations at the Lagrangian point L1 indicated a good agreement with the predictions. Our results highlight the flux rope type determination techniques that are particularly useful for active region eruptions, where most geoeffective CMEs originate. 相似文献
3.
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
4.
Magnetic helicity is a quantity of great importance in solar studies because it is conserved in ideal magnetohydrodynamics. While many methods for computing magnetic helicity in Cartesian finite volumes exist, in spherical coordinates, the natural coordinate system for solar applications, helicity is only treated approximately. We present here a method for properly computing the relative magnetic helicity in spherical geometry. The volumes considered are finite, of shell or wedge shape, and the three-dimensional magnetic field is considered to be fully known throughout the studied domain. Testing of the method with well-known, semi-analytic, force-free magnetic-field models reveals that it has excellent accuracy. Further application to a set of nonlinear force-free reconstructions of the magnetic field of solar active regions and comparison with an approximate method used in the past indicates that the proposed method can be significantly more accurate, thus making our method a promising tool in helicity studies that employ spherical geometry. Additionally, we determine and discuss the applicability range of the approximate method. 相似文献
5.
T. Török M. Temmer G. Valori A. M. Veronig L. van Driel-Gesztelyi B. Vršnak 《Solar physics》2013,286(2):453-477
We study a filament eruption, two-ribbon flare, and coronal mass ejection (CME) that occurred in NOAA Active Region 10898 on 6 July 2006. The filament was located South of a strong sunspot that dominated the region. In the evolution leading up to the eruption, and for some time after it, a counter-clockwise rotation of the sunspot of about 30 degrees was observed. We suggest that the rotation triggered the eruption by progressively expanding the magnetic field above the filament. To test this scenario, we study the effect of twisting the initially potential field overlying a pre-existing flux-rope, using three-dimensional zero-β MHD simulations. We first consider a relatively simple and symmetric system, and then study a more complex and asymmetric magnetic configuration, whose photospheric-flux distribution and coronal structure are guided by the observations and a potential field extrapolation. In both cases, we find that the twisting leads to the expansion of the overlying field. As a consequence of the progressively reduced magnetic tension, the flux-rope quasi-statically adapts to the changed environmental field, rising slowly. Once the tension is sufficiently reduced, a distinct second phase of evolution occurs where the flux-rope enters an unstable regime characterised by a strong acceleration. Our simulations thus suggest a new mechanism for the triggering of eruptions in the vicinity of rotating sunspots. 相似文献
6.
Relative magnetic helicity, as a conserved quantity of ideal magnetohydrodynamics, has been highlighted as an important quantity
to study in plasma physics. Due to its nonlocal nature, its estimation is not straightforward in both observational and numerical
data. In this study we derive expressions for the practical computation of the gauge-independent relative magnetic helicity
in three-dimensional finite domains. The derived expressions are easy to implement and rapid to compute. They are derived
in Cartesian coordinates, but can be easily written in other coordinate systems. We apply our method to a numerical model
of a force-free equilibrium containing a flux rope, and compare the results with those obtained employing known half-space
equations. We find that our method requires a much smaller volume than half-space expressions to derive the full helicity
content. We also prove that values of relative magnetic helicity of different magnetic fields can be compared with each other
in the same sense as free-energy values can. Therefore, relative magnetic helicity can be meaningfully and directly compared
between different datasets, such as those from different active regions, but also within the same dataset at different times.
Typical applications of our formulae include the helicity computation in three-dimensional models of the solar atmosphere,
e.g., coronal-field reconstructions by force-free extrapolation and discretized magnetic fields of numerical simulations. 相似文献
7.
G. Valori L. M. Green P. Démoulin S. Vargas Domínguez L. van Driel-Gesztelyi A. Wallace D. Baker M. Fuhrmann 《Solar physics》2012,278(1):73-97
We study the flux emergence process in NOAA active region 11024, between 29 June and 7 July 2009, by means of multi-wavelength
observations and nonlinear force-free extrapolation. The main aim is to extend previous investigations by combining, as much
as possible, high spatial resolution observations to test our present understanding of small-scale (undulatory) flux emergence,
whilst putting these small-scale events in the context of the global evolution of the active region. The combination of these
techniques allows us to follow the whole process, from the first appearance of the bipolar axial field on the east limb, until
the buoyancy instability could set in and raise the main body of the twisted flux tube through the photosphere, forming magnetic
tongues and signatures of serpentine field, until the simplification of the magnetic structure into a main bipole by the time
the active region reaches the west limb. At the crucial time of the main emergence phase high spatial resolution spectropolarimetric
measurements of the photospheric field are employed to reconstruct the three-dimensional structure of the nonlinear force-free
coronal field, which is then used to test the current understanding of flux emergence processes. In particular, knowledge
of the coronal connectivity confirms the identity of the magnetic tongues as seen in their photospheric signatures, and it
exemplifies how the twisted flux, which is emerging on small scales in the form of a sea-serpent, is subsequently rearranged
by reconnection into the large-scale field of the active region. In this way, the multi-wavelength observations combined with
a nonlinear force-free extrapolation provide a coherent picture of the emergence process of small-scale magnetic bipoles,
which subsequently reconnect to form a large-scale structure in the corona. 相似文献
8.
Carolus J. Schrijver Marc L. Derosa Thomas R. Metcalf Yang Liu Jim Mctiernan Stéphane Régnier Gherardo Valori Michael S. Wheatland Thomas Wiegelmann 《Solar physics》2006,235(1-2):161-190
We compare six algorithms for the computation of nonlinear force-free (NLFF) magnetic fields (including optimization, magnetofrictional,
Grad–Rubin based, and Green's function-based methods) by evaluating their performance in blind tests on analytical force-free-field
models for which boundary conditions are specified either for the entire surface area of a cubic volume or for an extended
lower boundary only. Figures of merit are used to compare the input vector field to the resulting model fields. Based on these
merit functions, we argue that all algorithms yield NLFF fields that agree best with the input field in the lower central
region of the volume, where the field and electrical currents are strongest and the effects of boundary conditions weakest.
The NLFF vector fields in the outer domains of the volume depend sensitively on the details of the specified boundary conditions;
best agreement is found if the field outside of the model volume is incorporated as part of the model boundary, either as
potential field boundaries on the side and top surfaces, or as a potential field in a skirt around the main volume of interest.
For input field (B) and modeled field (b), the best method included in our study yields an average relative vector error En = 〈 |B−b|〉/〈 |B|〉 of only 0.02 when all sides are specified and 0.14 for the case where only the lower boundary is specified, while the total
energy in the magnetic field is approximated to within 2%. The models converge towards the central, strong input field at
speeds that differ by a factor of one million per iteration step. The fastest-converging, best-performing model for these
analytical test cases is the Wheatland, Sturrock, and Roumeliotis (2000) optimization algorithm as implemented by Wiegelmann
(2004). 相似文献
9.
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
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