Mathematics
Scientific paper
Jan 1992
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1992phdt........12w&link_type=abstract
Ph.D. Thesis Alabama Univ., Huntsville.
Mathematics
Electric Current, Force-Free Magnetic Fields, Magnetic Flux, Magnetic Measurement, Magnetohydrodynamic Stability, Photosphere, Solar Atmosphere, Solar Magnetic Field, Current Density, Free Energy, Mathematical Models, Noise Intensity, Solar Flares, Stellar Structure
Scientific paper
The threads of magnetic flux which permeate the solar atmosphere are known to play several important roles in the activity of the Sun. Most notably, it is the excess energy stored in these magnetic fields which powers the violent eruptions known as flares. The presence of free energy in active regions of magnetic flux is evidenced by observations of 'magnetic shear' and of electric currents present in the regions. This dissertation considers several topics related to the structure of active region magnetic fields, observations of magnetic shear, and measurements of electric currents flowing in the magnetic fields of active regions. First, we consider the problem of modeling the structure of the loops of magnetic flux. We find solutions to the force-free equation for slightly bent, thin flux tubes and evidence that the effects of curvature on force-free flux tubes may in fact contribute to their stability. The implication is that the critical twist of flux tubes may be higher than previously thought and thus that greater amounts of energy may be stored within these loops. Our second endeavor is to find reasonable limits under which the evaluation of magnetic shear may be made using the observed photospheric magnetic field of active regions. The calculation of magnetic shear relies upon simplifying assumptions to overcome the problem of noise in magnetic field data. Under these assumptions, the calculation of magnetic shear is subject to projection effects which become significant for regions located away from the center of the solar disk. We demonstrate, using an analytical force-free field model, that the calculation of shear is valid only for regions within 15 deg of disk center. Lastly, we concern ourselves with the measurement of electric currents flowing in active regions. We demonstrate that previously used methods of measuring current densities from magnetic field measurements using the differential form of Ampere's law are highly vulnerable to the high noise levels of magnetic field data. We propose, instead, an integral method, arguing that it is less susceptible to the noise levels. Our aim is to demonstrate the great need for reliable measurements of the electric currents flowing in active region magnetic fields.
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