The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies

Abstract

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 $r_0$. The magnetic field configuration is thus determined by a scalar flux function $\Psi$ and a functional $F$ that is a single-variable function of $\Psi$. The algorithm is implemented through a two-step approach: i) a trial-and-error process by minimizing the residue of the functional $F(\Psi )$ to determine an optimal $Z$ axis orientation, and ii) for the chosen $Z$, a ${\chi }^2$ 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 two-step 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${}^{\circ }$ 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.

submitted to Sol. Phys. late Dec 2016; under review; code will be made public once review is over

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Cited by in corpus (3)

• The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: First Applications
• The properties of small magnetic flux ropes inside the solar wind come from coronal holes, active regions, and quiet Sun
• Optimal Fitting of the Freidberg Solution to In Situ Spacecraft Measurements of Magnetic Clouds