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

The Grad–Shafranov Reconstruction of Toroidal Magnetic Flux Ropes: Method Development and... We develop an approach of the 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 $Z$ , with a major radius, r 0 $r_{0}$ . The magnetic field configuration is thus determined by a scalar flux function, Ψ $\Psi$ , and a functional F $F$ that is a single-variable function of Ψ $\Psi$ . The algorithm is implemented through a two-step approach: i) a trial-and-error process by minimizing the residue of the functional F ( Ψ ) $F(\Psi)$ to determine an optimal Z $Z$ -axis orientation, and ii) for the chosen Z $Z$ , a χ 2 $\chi^{2}$ minimization process resulting in a range of r 0 $r_{0}$ . Benchmark studies of known analytic solutions to the toroidal GS equation with noise additions are presented to illustrate the two-step procedure and to demonstrate the performance of the numerical GS solver, separately. For the cases presented, the errors in Z $Z$ and r 0 $r_{0}$ are 9 ∘ $9^{\circ}$ and 22%, respectively, and the relative percent error in the numerical GS solutions is smaller than 10%. We also make public the computer codes for these implementations and benchmark studies. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Solar Physics Springer Journals

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

Solar Physics , Volume 292 (9) – Aug 15, 2017

Loading next page...
 
/lp/springer_journal/the-grad-shafranov-reconstruction-of-toroidal-magnetic-flux-ropes-K6gnXhH6Ko
Publisher
Springer Netherlands
Copyright
Copyright © 2017 by Springer Science+Business Media B.V.
Subject
Physics; Astrophysics and Astroparticles; Atmospheric Sciences; Space Sciences (including Extraterrestrial Physics, Space Exploration and Astronautics)
ISSN
0038-0938
eISSN
1573-093X
D.O.I.
10.1007/s11207-017-1134-z
Publisher site
See Article on Publisher Site

Abstract

We develop an approach of the 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 $Z$ , with a major radius, r 0 $r_{0}$ . The magnetic field configuration is thus determined by a scalar flux function, Ψ $\Psi$ , and a functional F $F$ that is a single-variable function of Ψ $\Psi$ . The algorithm is implemented through a two-step approach: i) a trial-and-error process by minimizing the residue of the functional F ( Ψ ) $F(\Psi)$ to determine an optimal Z $Z$ -axis orientation, and ii) for the chosen Z $Z$ , a χ 2 $\chi^{2}$ minimization process resulting in a range of r 0 $r_{0}$ . Benchmark studies of known analytic solutions to the toroidal GS equation with noise additions are presented to illustrate the two-step procedure and to demonstrate the performance of the numerical GS solver, separately. For the cases presented, the errors in Z $Z$ and r 0 $r_{0}$ are 9 ∘ $9^{\circ}$ and 22%, respectively, and the relative percent error in the numerical GS solutions is smaller than 10%. We also make public the computer codes for these implementations and benchmark studies.

Journal

Solar PhysicsSpringer Journals

Published: Aug 15, 2017

References

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off