An optimization principle for computing stationary MHD equilibria with solar wind flow

Thomas Wiegelmann*, Thomas Neukirch, Dieter Nickeler, Iulia Chifu

*Corresponding author for this work

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In this work we describe a numerical optimization method for computing stationary MHD-equilibria. The newly developed code is based on a nonlinearforce-free optimization principle. We apply our code to model the solar corona using synoptic vector magnetograms as boundary condition. Below about two solar radii the plasma β and Alfvén Mach number MA are small and the magnetic field configuration of stationary MHD is basically identical to a nonlinear force-free field, whereas higher up in the corona (where β and MA are above unity) plasma and flow effects become important and stationary MHD and force-free configuration deviate significantly. The new method allows the reconstruction of the coronal magnetic field further outwards than with potential field, nonlinear force-free or magneto-static models. This way the model might help to provide the magnetic connectivity for joint observations of remote sensing and in-situ instruments on Solar Orbiter and Parker Solar Probe.
Original languageEnglish
Article number145
Number of pages14
JournalSolar Physics
Issue number10
Early online date29 Oct 2020
Publication statusPublished - Oct 2020


  • Magnetic fields, corona
  • Magnetic fields, models
  • Magnetohydrodynamics
  • Velocity fields, solar wind


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