3 research outputs found
The Grad-Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and Benchmark Studies
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 , with a major radius . The magnetic
field configuration is thus determined by a scalar flux function and a
functional that is a single-variable function of . The algorithm is
implemented through a two-step approach: i) a trial-and-error process by
minimizing the residue of the functional to determine an optimal
axis orientation, and ii) for the chosen , a minimization process
resulting in the range of . 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 and 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.Comment: submitted to Sol. Phys. late Dec 2016; under review; code will be
made public once review is ove