A Regularization Method for Extrapolation of Solar Potential Magnetic Fields
Abstract
The mathematical basis of a Tikhonov regularization method for extrapolating the chromosphericcoronal 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.
 Publication:

The Astrophysical Journal
 Pub Date:
 June 1992
 DOI:
 10.1086/171475
 Bibcode:
 1992ApJ...392..722G
 Keywords:

 Extrapolation;
 Magnetohydrodynamics;
 Plasma Potentials;
 Solar Corona;
 Solar Magnetic Field;
 Cauchy Problem;
 Chromosphere;
 Data Smoothing;
 Partial Differential Equations;
 Solar Activity;
 Solar Physics;
 MAGNETOHYDRODYNAMICS: MHD;
 SUN: CORONA;
 SUN: MAGNETIC FIELDS