Solar Force-free Magnetic Fields

Abstract

The structure and dynamics of the solar corona is dominated by the magnetic field. In most areas in the corona magnetic forces are so dominant that all non-magnetic forces like plasma pressure gradient and gravity can be neglected in the lowest order. This model assumption is called the force-free field assumption, as the Lorentz force vanishes. This can be obtained by either vanishing electric currents (leading to potential fields) or the currents are co-aligned with the magnetic field lines. First we discuss a mathematically simpler approach that the magnetic field and currents are proportional with one global constant, the so-called linear force-free field approximation. In the generic case, however, the relation between magnetic fields and electric currents is nonlinear and analytic solutions have been only found for special cases, like 1D or 2D configurations. For constructing realistic nonlinear force-free coronal magnetic field models in 3D, sophisticated numerical computations are required and boundary conditions must be obtained from measurements of the magnetic field vector in the solar photosphere. This approach is currently of large interests, as accurate measurements of the photospheric field become available from ground-based (for example SOLIS) and space-born (for example Hinode and SDO) instruments. If we can obtain accurate force-free coronal magnetic field models we can calculate the free magnetic energy in the corona, a quantity which is important for the prediction of flares and coronal mass ejections. Knowledge of the 3D structure of magnetic field lines also help us to interpret other coronal observations, e.g., EUV-images of the radiating coronal plasma.

The magnetic field in the solar atmosphere

“…We will only summarize some basics about the possibilities and problems of force-free models and avoid mathematical and computational details. For a more detailed overview on the methods used to compute solar force-free fields, see Wiegelmann and Sakurai (2012). Depending on the forcefree parameter (or function), α, one distinguishes between potential (current-free) fields (α = 0), linear force-free fields (LFF; α is globally constant) and the general case that α changes in space, i.e., the non-linear force-free (NLFF) approach.…”

First observation of time variation in the solar-disk gamma-ray flux with Fermi

“…This effect is expected to be stronger for the solar-disk component than the IC component because of the much closer approach to the Sun for the parent cosmic rays. In addition, magnetic fields in the solar atmosphere [14][15][16] affect the solar-disk component. Seckel et al [10] (denoted as SSG1991 in the following) showed that solar atmospheric magnetic fields could boost gamma-ray production through the magnetic reflection of the primary cosmic rays or their showers out of the Sun.…”

A Nonlinear Force-Free Magnetic Field Approximation Suitable for Fast Forward-Fitting to Coronal Loops. III. The Free Energy

“…Alternatively, some studies show that the free energy is better estimated by the minimumenergy state above the linear force-free field with the same magnetic helicity (Woltjer, 1958;Régnier and Priest, 2007). Since NLFFF calculations are rather computing-intensive for forward-fitting tasks to coronal constraints, which requires many iterations (for an overview and discussion of different numerical methods see recent reviews by Aschwanden (2004) or Wiegelmann and Sakurai (2012)) or faster non-numerical methods are desirable. Some proxy of the active region's free magnetic energy has been defined based on the twist and magnetic field orientation near the neutral line (e.g., Falconer et al, 2006Falconer et al, , 2011.…”