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PFSS Magnetic Extrapolation method

This section describes the Magnetic Extrapolation algorithm steps of the IDL Solarsoft 'PFSS' package created by Dr Marc deRosa at LMSAL.

A complete list of the files in the PFSS package can be viewed at: http://orpheus.nascom.nasa.gov/~zarro/xdoc (search on 'pfss').


1. Photospheric and Heliospheric Magnetic Fields - Carolus J Schrijver and Marc L deRosa.

For a mathematical analysis of the algorithm used, refer to Appendix C. 'Source-Surface Model' of Ref 1.

Compute spherical harmonic coefficients of field potential (Phi) from input Magnetogram

  1. Read in Magnetogram
  2. Compute Spherical Harmonic Transform on 2-D input arrays
  3. Compute terms Aml and Bml, corresponding to Eqn (8) of Ref 1.

Compute the potential magnetic field components Br, Bth and Bphi.

  1. Compute Br in r,l,m space.
  2. Convert to spherical coordinates using inverse spherical transform. See Eqn (9) Ref 1.
  3. Compute Br in r,l,m space.
  4. Convert to spherical coordinates using inverse spherical transform. See Eqn (10) Ref 1.
  5. Compute Br in r,l,m space.
  6. Convert to spherical coordinates using inverse spherical transform. See Eqn (11) Ref 1.

Perform field line extrapolation and compute coronal hole footprint.

  1. Calculate gridpoints from which to start tracing magnetic field lines.
    • Compute field start coordinates - source surface inward.
      • Setup grid type [simple, random lon, random lat/lon, file, uniform, flux weighted].
      • Perform interpolation on input array.
    • Compute field start coordinates - photosphere outward.
      • Setup grid type simple, random lon, random lat/lon, file, uniform flux weighted.
      • Perform interpolation on input array to derive Br of start points.
    • Combine both sets of coordinates.
  2. Begin field tracing
    • Compute Brm Bth, Bph at current point using interpolation.
    • Determine if field is to be traced 1 way or both ways.
    • Determine position of starting point.
    • Integrate to form step size, adjusting if too big/too small.
    • Loop through previous 4 steps to form collection of field line coordinates.
  3. Map open fields (coronal hole 'footprint')
    • Compute lat/lon of each open field intersection with the photosphere and use to map coronal hole footprint.

To run the extrapolation process and create a .sav file that can be viewed by PFSS (see below) takes approximately 10-12 minutes.

The IDL Solarsoft PFSS package also includes a viewing widget that allows the user to display the extrapolated magnetic lines. The widget displays a flux density map (stored in .sav format) that allows the user to select a region of interest and specify the maximum number of lines to be plotted. Open and closed field lines are differentiated by colour.

-- MikeSmith - 07 Jun 2005

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Topic revision: r6 - 2005-06-23 - MikeSmith
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