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A Unified and Very Fast Way for Computing the Global Potential and Linear Force-Free Fields

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Abstract

We present a fast solver for computing potential and linear force-free fields (LFFF) above the full solar disk with a synoptic magnetic map as input. The global potential field and the LFFF are dealt with in a unified way by solving a three-dimensional Helmholtz equation in a spherical shell and a two-dimensional Poisson equation on the solar surface. The solver is based on a combination of the spectral method and the finite-difference scheme. In the longitudinal direction the equation is transformed into the Fourier spectral space, and the resulting two-dimensional equations in the rθ plane for the Fourier coefficients are solved by finite differencing. The solver shows an extremely fast computing speed, e.g., the computation for a magnetogram with a resolution of 180(θ)×360(ϕ) is completed in less than 2 s. Even on a high-resolution 600×1200 grid, the solution can be obtained within only about one minute on a single CPU. The solver can potentially be applied directly to the original resolution of observed magnetograms from SDO/HMI for routinely analyzing daily full-disk data.

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Notes

  1. http://www.lmsal.com/~derosa/pfsspack .

  2. http://csem.engin.umich.edu/fdips/ .

  3. Generally observations do not give the radial component M but the line-of-sight component of the field (B ), and M is converted from B assuming that the field is radial at the photosphere.

  4. http://www.netlib.org/fishpack .

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Acknowledgements

The work is jointly supported by the 973 program under grant 2012CB825601, the Chinese Academy of Sciences (KZZD-EW-01-4), the National Natural Science Foundation of China (41031066, 40921063, 40890162, and 41074122), and the Specialized Research Fund for State Key Laboratories. We thank M.L. DeRosa for help on the use of the SSW/PFSS package. Special thanks go to our anonymous reviewer for valuable suggestions for the improvement of the paper.

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Correspondence to Chaowei Jiang.

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Jiang, C., Feng, X. A Unified and Very Fast Way for Computing the Global Potential and Linear Force-Free Fields. Sol Phys 281, 621–637 (2012). https://doi.org/10.1007/s11207-012-0074-x

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  • DOI: https://doi.org/10.1007/s11207-012-0074-x

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