The GradShafranov Reconstruction of Toroidal Magnetic Flux Ropes: First Applications 

qiang hu Submitted: 20170731 08:02
This article completes and extends a recent study of the
GradShafranov (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 whitelight 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 2030 degrees in the plane of the sky. We also compare the results with the original straightcylinder GS reconstruction and discuss our findings.
Authors: Qiang Hu, Mark G. Linton, Brian E. Wood, Pete Riley, and Teresa NievesChinchilla
Projects: ACE,SoHOLASCO,STEREO,Wind

Publication Status: submitted to Sol. Phys.; being reviewed and revised
Last Modified: 20170731 11:04



The GradShafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies 

qiang hu Submitted: 20170310 09:51
We develop an approach of GradShafranov (GS) reconstruction for toroidal structures in space plasmas, based on insitu spacecraft measurements. The underlying theory is the GS equation that describes twodimensional 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 r_{0}. The magnetic field configuration is thus determined by a scalar flux function Ψ and a functional F that is a singlevariable function of Ψ. The algorithm is implemented through a twostep approach: i) a trialanderror 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 r_{0}. Benchmark studies of known analytic solutions to the toroidal GS equation with noise additions are presented to illustrate the twostep procedures and
to demonstrate the performance of the numerical GS solver, separately. For the cases presented, the errors in Z and r_{0} 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: 20170314 11:47



Structures of Interplanetary Magnetic Flux Ropes and Comparison with Their Solar Sources 

qiang hu Submitted: 20140721 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 flareCMEICME 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 fieldline 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 Xrays ,SDOAIA,SDOHMI,SoHOEIT,SoHOLASCO,STEREO,Wind

Publication Status: accepted by ApJ
Last Modified: 20140808 09:08



Nonforcefree extrapolation of solar coronal magnetic field using vector magnetograms 

qiang hu Submitted: 20090507 12:59
We report our recent improvement in nonforcefree extrapolation
of coronal magnetic field, using vector magnetograms. Based on the
principle of minimum (energy) dissipation rate (MDR), a generally
nonforcefree magnetic field solution is expressed as the
superposition of one potential field and two (constant α )
linear forcefree fields, with distinct α parameters. With
a known potential field, the system is reduced to a secondorder
one that can be solved using one singlelayer vector magnetogram.
We devise an iteration procedure to determine the potential field,
by achieving satisfactory agreement between the MDRmodel 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: 20090507 13:31



AN IMPROVED APPROACH TO NONFORCE FREE CORONAL MAGNETIC FIELD EXTRAPOLATION 

qiang hu Submitted: 20061122 15:28
We develop an approach to deriving threedimensional nonforce free coronal
magnetic field from vector magnetograms. Based on the principle of Minimum Dissipation
Rate, a general nonforce free magnetic field is expressed as superposition of one potential
field, and two constantα (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 nonlinear 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 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
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: 20061201 12:06




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