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The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies View all abstracts by submitter

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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