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Nonlinear force-free field extrapolation calculation for inferring solar colona magnetic fields

JAXA Supercomputer System Annual Report February 2025-January 2026

Report Number: R25EU0912

Subject Category: Space and Astronautical Science

PDF (to be added)

  • Responsible Representative: Yoshifumi Saito, Institute of Space and Astronautical Science, Department of Solar System Sciences
  • Contact Information: Toshifumi Shimizu(shimizu.toshifumi@jaxa.jp)
  • Members: Toshifumi Shimizu, Kouhei Teraoka, Daiki Yamasaki

Abstract

Our study focuses on understanding of the mechanism responsible for the occurrence of the solar flares. We derive 3D magnetic field structure in the corona by performing a 3D magnetohydrodynamics simulation using vector magnetic field maps mainly acquired with the Hinode spacecraft. We investigate 3D magnetic field structure formed in the solar atmosphere responsible for the occurrence of solar flares.

Reference URL

Please refer to https://www.isas.jaxa.jp/home/solar/solarPlasma/whatsSolarPlasma_en.html .

Reasons and benefits of using JAXA Supercomputer System

The aim to use JAXA supercomputer is to estimate chromospheric and colonal 3D magnetic fields from the spatial distribution of magnetic field vectors observed at the solar surface (photosphere). We use force-free field modeling based on three-dimensional magnetohydrodynamics simulations, requiring computer resource. Usage of calculation results is to search 3D magnetic fields distribution before flare and the area where energetic magnetic fields easy to expand explosively. Thanks to high-spec supercompution resource, we can investigate a variety of magentic fields data with different time siries in a short time.

Achievements of the Year

We developed a new three-dimensional magnetic field extrapolation method that incorporates finite plasma beta effects in order to reconstruct the magnetic field structure in the solar atmosphere. The widely used nonlinear force-free field (NLFFF) extrapolation method is based on the zero-beta approximation, which neglects gas pressure and gravity, and therefore has limitations in high-beta regions such as the chromosphere and weak-field regions. To overcome this limitation, we developed a new extrapolation code based on a magnetohydrodynamic (MHD) relaxation method that considers the force balance between the Lorentz force and the gas-pressure gradient. We implemented three numerical schemes and performed large-scale three-dimensional computations using observed photospheric vector magnetic field data as the boundary condition. The results were evaluated using magnetic free energy, magnetic twist, and residual force. We found that the residual force was reduced by approximately 4% compared with the conventional NLFFF method, demonstrating that including gas pressure leads to a more force-balanced and physically consistent three-dimensional magnetic field structure (see Fig. 1). This work contributes to improving the accuracy of coronal magnetic field reconstruction, which is essential for understanding energy storage and release processes associated with solar flares and coronal mass ejections.

We also published the results of a study based on observational data using the conventional nonlinear force-free field (NLFFF) method in a peer-reviewed journal. We compared a confined flare and an eruptive flare that occurred under similar magnetic configurations in Active Region 12673 on September 6, 2017, using the twist number, decay index, and magnetic field line height. Through this comparison, we clarified the observational characteristics of flare eruptions. This study suggests that magnetic field lines in a kink-unstable state may play an important role in eruptive flares, and that taller magnetic field lines may facilitate flare eruptions.

Annual Report Figures for 2025

Fig.1: Temporal evolution of the extrapolated three-dimensional magnetic field structures. Results from the NLFFF (a-c) and the finite plasma beta extrapolation (Schemes A-C; d-l) are shown. Each column corresponds to time steps of 10000, 20000, and 30000. The color of the field lines represents the electric current density normalized by the magnetic field strength, and the grayscale at the bottom boundary shows the normal component of the photospheric magnetic field. The calculation starts from a potential field and evolves toward a force-balanced state through MHD relaxation, forming a non-potential twisted magnetic field structure.

 

Publications

- Peer-reviewed papers

Yamasaki, D., Miyoshi, T., & Inoue, S., "Finite Plasma Beta Three-dimensional Magnetic Field Extrapolation Based on Magnetohyrdodynamic Relaxation Method", ApJS, 282, 66, (2026)

Teraoka, K, Yamasaki, D., Kawabata,, Y., Imada, S., and Shimizu, T. "Observational Comparison Between Confined and Eruptive Flares: Magnetohydrodynamics Instability Parameters in a Similar Magnetic Configuration," ApJ, 983, 126. (2025)

- Poster Presentations

Daiki Yamasaki, Satoshi Inoue, Takahiro Miyoshi, "Magnetohydrostatic Three-dimensional Coronal Magnetic Field Extrapolation Based on MHD Relaxation Method", JpGU 2025

Usage of JSS

Computational Information

  • Process Parallelization Methods: MPI
  • Thread Parallelization Methods: OpenMP
  • Number of Processes: 80
  • Elapsed Time per Case: 5 Hour(s)

JSS3 Resources Used

 

Fraction of Usage in Total Resources*1(%): 0.00

 

Details

Please refer to System Configuration of JSS3 for the system configuration and major specifications of JSS3.

Computational Resources
System Name CPU Resources Used
(Core x Hours)
Fraction of Usage*2(%)
TOKI-SORA 0.00 0.00
TOKI-ST 0.00 0.00
TOKI-GP 0.00 0.00
TOKI-XM 0.00 0.00
TOKI-LM 0.00 0.00
TOKI-TST 0.00 0.00
TOKI-TGP 0.00 0.00
TOKI-TLM 0.00 0.00

 

File System Resources
File System Name Storage Assigned
(GiB)
Fraction of Usage*2(%)
/home 0.00 0.00
/data and /data2 0.00 0.00
/ssd 0.00 0.00

 

Archiver Resources
Archiver Name Storage Used
(TiB)
Fraction of Usage*2(%)
J-SPACE 0.00 0.00

*1: Fraction of Usage in Total Resources: Weighted average of three resource types (Computing, File System, and Archiver).

*2: Fraction of Usage:Percentage of usage relative to each resource used in one year.

 

ISV Software Licenses Used

ISV Software Licenses Resources
ISV Software Licenses Used
(Hours)
Fraction of Usage*2(%)
ISV Software Licenses
(Total)
0.00 0.00

*2: Fraction of Usage:Percentage of usage relative to each resource used in one year.

JAXA Supercomputer System Annual Report February 2025-January 2026