Astronomy and Astrophysics – Astrophysics
Scientific paper
Jun 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992apj...392..722g&link_type=abstract
Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 392, no. 2, June 20, 1992, p. 722-735.
Astronomy and Astrophysics
Astrophysics
5
Extrapolation, Magnetohydrodynamics, Plasma Potentials, Solar Corona, Solar Magnetic Field, Cauchy Problem, Chromosphere, Data Smoothing, Partial Differential Equations, Solar Activity
Scientific paper
The mathematical basis of a Tikhonov regularization method for extrapolating the chromospheric-coronal magnetic field using photospheric vector magnetograms is discussed. The basic techniques show that the Cauchy initial value problem can be formulated for potential magnetic fields. The potential field analysis considers a set of linear, elliptic partial differential equations. It is found that, by introducing an appropriate smoothing of the initial data of the Cauchy potential problem, an approximate Fourier integral solution is found, and an upper bound to the error in the solution is derived. This specific regularization technique, which is a function of magnetograph measurement sensitivities, provides a method to extrapolate the potential magnetic field above an active region into the chromosphere and low corona.
Gary Gilmer A.
Musielak Zdzislaw E.
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