Linear force-free fields are characterized by
For computing the solar magnetic field in the corona with the linear force-free model one needs only measurements of the LOS photospheric magnetic field. The force-free parameter is a priori unknown and we will discuss later how can be approximated from observations. Seehafer (1978) derived solutions of the linear force-free equations (local Cartesian geometry with in the photosphere and is the height from the Sun’s surface) in the form:
As the boundary condition, the method uses the distribution of on the photosphere . The coefficients can be obtained by comparing Equation (20) for with the magnetogram data. In practice, Seehafer’s (1978) method is used for calculating the linear force-free field (or potential field for ) for a given magnetogram (e.g., MDI on SOHO) and a given value of as follows. The observed magnetogram which covers a rectangular region extending from 0 to in and 0 to in is artificially extended onto a rectangular region covering to and to by taking an antisymmetric mirror image of the original magnetogram in the extended region, i.e.,
Usually, is normalized by the harmonic mean of and defined by
For we have . With this normalization the values of fall into the range .
Living Rev. Solar Phys. 9, (2012), 5
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