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


