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The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: First Applications  

qiang hu   Submitted: 2017-07-31 08:02

This article completes and extends a recent study of the Grad-Shafranov (GS) reconstruction in toroidal geometry, as applied to a two and a half dimensional configurations in space plasmas with rotational symmetry. A further application to the benchmark study of an analytic solution to the toroidal GS equation with added noise shows deviations in the reconstructed geometry of the flux rope configuration, characterized by the orientation of the rotation axis, the major radius, and the impact parameter. On the other hand, the physical properties of the flux rope, including the axial field strength, and the toroidal and poloidal magnetic flux, agree between the numerical and exact GS solutions. We also present a real event study of a magnetic cloud flux rope from in situ spacecraft measurements. The devised procedures for toroidal GS reconstruction are successfully executed. Various geometrical and physical parameters are obtained with associated uncertainty estimates. The overall configuration of the flux rope from the GS reconstruction is compared with the corresponding morphological reconstruction based on white-light images. The results show overall consistency, but also discrepancy in that the inclination angle of the flux rope central axis with respect to the ecliptic plane differs by about 20-30 degrees in the plane of the sky. We also compare the results with the original straight-cylinder GS reconstruction and discuss our findings.

Authors: Qiang Hu, Mark G. Linton, Brian E. Wood, Pete Riley, and Teresa Nieves-Chinchilla
Projects: ACE,SoHO-LASCO,STEREO,Wind

Publication Status: submitted to Sol. Phys.; being reviewed and revised
Last Modified: 2017-07-31 11:04
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The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies  

qiang hu   Submitted: 2017-03-10 09:51

We develop an approach of Grad-Shafranov (GS) reconstruction for toroidal structures in space plasmas, based on in-situ spacecraft measurements. The underlying theory is the GS equation that describes two-dimensional magnetohydrostatic equilibrium as widely applied in fusion plasmas. The geometry is such that the arbitrary cross section of the torus has rotational symmetry about the rotation axis Z, with a major radius r0. The magnetic field configuration is thus determined by a scalar flux function Ψ and a functional F that is a single-variable function of Ψ. The algorithm is implemented through a two-step approach: i) a trial-and-error process by minimizing the residue of the functional F(Ψ) to determine an optimal Z axis orientation, and ii) for the chosen Z, a χ^2 minimization process resulting in the range of r0. Benchmark studies of known analytic solutions to the toroidal GS equation with noise additions are presented to illustrate the two-step procedures and to demonstrate the performance of the numerical GS solver, separately. For the cases presented, the errors in Z and r0 are 9° and 22%, respectively, and the relative percent error in the numerical GS solutions is less than 10%. We also make public the computer codes for these implementations and benchmark studies.

Authors: Qiang Hu
Projects: ACE,STEREO,Wind

Publication Status: Solar Physics; under revision
Last Modified: 2017-03-14 11:47
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Magnetic field-line lengths inside interplanetary magnetic flux ropes  

qiang hu   Submitted: 2015-02-18 20:38

We report on the detailed and systematic study of field-line twist and length distributions within magnetic flux ropes embedded in Interplanetary Coronal Mass Ejections (ICMEs). The Grad-Shafranov reconstruction method is utilized together with a constant-twist nonlinear force-free (Gold-Hoyle) flux rope model to reveal the close relation between the field-line twist and length in cylindrical flux ropes, based on in-situ Wind spacecraft measurements. We show that the field-line twist distributions within interplanetary flux ropes are inconsistent with the Lundquist model. In particular we utilize the unique measurements of magnetic field-line lengths within selected ICME events as provided by Kahler et al. (2011) based on energetic electron burst observations at 1 AU and the associated type III radio emissions detected by the Wind spacecraft. These direct measurements are compared with our model calculations to help assess the flux-rope interpretation of the embedded magnetic structures. By using the different flux-rope models, we show that the in-situ direct measurements of field-line lengths are consistent with a flux-rope structure with spiral field lines of constant and low twist, largely different from that of the Lundquist model, especially for relatively large-scale flux ropes.

Authors: Qiang Hu, Jiong Qiu, and Säm Krucker
Projects: Wind

Publication Status: submitted to JGR
Last Modified: 2015-02-19 13:06
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Structures of Interplanetary Magnetic Flux Ropes and Comparison with Their Solar Sources  

qiang hu   Submitted: 2014-07-21 20:34

During the process of magnetic flux rope ejection, magnetic reconnection is essential to release the flux rope. The question remains: how does the magnetic reconnection change the flux rope structure? In this work, we continue with the original study by Qiu et al. (2007) by using a larger sample of flare-CME-ICME events to compare properties of ICME/MC flux ropes measured at 1 AU and properties of associated solar progenitors including flares, filaments, and CMEs. In particular, the magnetic field-line twist distribution within interplanetary magnetic flux ropes is systematically derived and examined. Our analysis shows that, similar to what was found before, for most of these events, the amount of twisted flux per AU in MCs is comparable with the total reconnection flux on the Sun, and the sign of the MC helicity is consistent with the sign of helicity of the solar source region judged from the geometry of postflare loops. Remarkably, we find that about one half of the 18 magnetic flux ropes, most of them being associated with erupting filaments, have a nearly uniform and relatively low twist distribution from the axis to the edge, and the majority of the other flux ropes exhibit very high twist near the axis, of up to >=5 turns per AU, which decreases toward the edge. The flux ropes are therefore not linear force free. We also conduct detailed case studies showing the contrast of two events with distinct twist distribution in MCs as well as different flare and dimming characteristics in solar source regions, and discuss how reconnection geometry reflected in flare morphology may be related to the structure of the flux rope formed on the Sun.

Authors: Qiang Hu, Jiong Qiu, B. Dasgupta, A. Khare, and G. M. Webb
Projects: ACE,GOES X-rays ,SDO-AIA,SDO-HMI,SoHO-EIT,SoHO-LASCO,STEREO,Wind

Publication Status: accepted by ApJ
Last Modified: 2014-08-08 09:08
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Klein-Gordon Equations for Transverse Oscillations in Two-dimensional Coronal Loops  

qiang hu   Submitted: 2011-06-08 20:59

This abstract was corrupted following database problems and is being recovered. It will be restored as quickly as possible. Any questions, please send them to Alisdair. Sorry for any incovenience.


Authors: Qiang Hu, J.F. McKenzie, and G.M. Webb
Projects: None

Publication Status: submitted to A&A
Last Modified: 2011-06-09 08:58
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Double Alfvén Waves  

qiang hu   Submitted: 2011-06-07 20:35

This abstract was corrupted following database problems and is being recovered. It will be restored as quickly as possible. Any questions, please send them to Alisdair. Sorry for any incovenience.


Authors: G. M. WEBB, Q. HU, B. DASGUPTA and G.P. ZANK
Projects: None

Publication Status: submitted to JPP
Last Modified: 2011-06-08 07:48
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Non-force-free extrapolation of solar coronal magnetic field using vector magnetograms  

qiang hu   Submitted: 2009-05-07 12:59

We report our recent improvement in non-force-free extrapolation of coronal magnetic field, using vector magnetograms. Based on the principle of minimum (energy) dissipation rate (MDR), a generally non-force-free magnetic field solution is expressed as the superposition of one potential field and two (constant- α ) linear force-free fields, with distinct α parameters. With a known potential field, the system is reduced to a second-order one that can be solved using one single-layer vector magnetogram. We devise an iteration procedure to determine the potential field, by achieving satisfactory agreement between the MDR-model computed and measured transverse magnetic field vectors on the bottom boundary. We illustrate this approach by applying it to real magnetograph measurement of solar active region AR10953. We show that the results are satisfactory as judged from the quantitative magnetic field measurement, and the behavior of the derived Lorentz force.

Authors: Qiang Hu, B. Dasgupta, M. DeRosa, J. Buechner, G.A. Gary
Projects: Hinode/SOT

Publication Status: submitted
Last Modified: 2009-05-07 13:31
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AN IMPROVED APPROACH TO NON-FORCE FREE CORONAL MAGNETIC FIELD EXTRAPOLATION  

qiang hu   Submitted: 2006-11-22 15:28

We develop an approach to deriving 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 superposition of one potential field, and two constant-α (linear) force free fields. Each is extrapolated from their 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 the chromospheric level, presumably. We apply it to a few analytic test cases, especially to two non-linear force free cases examined by Schrijver et al. (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 non-linear 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 due to the limitations of the linear force free field solver. As based on the Fast Fourier Transform algorithm, our method is much faster and easy to implement. We discuss the potential usefulness of our method and its limitations.

Authors: QIANG HU, and BRAHMANANDA DASGUPTA
Projects:

Publication Status: Solar Physics (submitted; under revision)
Last Modified: 2006-12-01 12:06
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Abstracts by Author
The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: First Applications
The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies
Magnetic field-line lengths inside interplanetary magnetic flux ropes
Structures of Interplanetary Magnetic Flux Ropes and Comparison with Their Solar Sources
Klein-Gordon Equations for Transverse Oscillations in Two-dimensional Coronal Loops
Double Alfvén Waves
Non-force-free extrapolation of solar coronal magnetic field using vector magnetograms
AN IMPROVED APPROACH TO NON-FORCE FREE CORONAL MAGNETIC FIELD EXTRAPOLATION

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