Removal of singularities in the Cauchy problem for the extrapolation of solar force-free magnetic fields

Details Removal of singularities in the Cauchy problem for the extrapolation of solar force-free magnetic fields Removal of singularities in the Cauchy problem for the extrapolation of solar force-free magnetic fields

May 1991

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991a%26a...245..285c&link_type=abstract

Astronomy and Astrophysics (ISSN 0004-6361), vol. 245, no. 1, May 1991, p. 285-288.

Mathematics

17

Cauchy Problem, Force-Free Magnetic Fields, Photosphere, Singularity (Mathematics), Solar Corona, Solar Magnetic Field, Mathematical Models, Maxwell Equation, Taylor Series

Scientific paper

The singularities occurring in the Cauchy problem for the extrapolation of solar nonlinear force-free magnetic fields at positions of vanishing normal component, B(z), are removed. This is based on the observation that the constancy of the quantity alpha(r), characterizing the force-free magnetic fields, along a given magnetic field line, implies that the singularity in Maxwell's equation is of mathematical rather than of physical origin. Thus, requiring also the vanishing of the numerator at P(0) leads to an undetermined form for alpha. By using Taylor's expansions in two variables (x and y) about P(0) for both numerator and denominator, the actual value for alpha, namely alpha (P(0), is obtained. The procedure is tested on the case of the analytical model proposed by Low (1982).

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