Analytical Treatment Of Static Magnetic Field Strucures In The Corona From Boundary Conditions On The Photosphere

Details Analytical Treatment Of Static Magnetic Field Strucures In The Corona From Boundary Conditions On The Photosphere Analytical Treatment Of Static Magnetic Field Strucures In The Corona From Boundary Conditions On The Photosphere

Oct 1999

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1999esasp.446..213c&link_type=abstract

8th SOHO Workshop: Plasma Dynamics and Diagnostics in the Solar Transition Region and Corona. Proceedings of the Conference hel

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Magnetic fields of the solar corona may have very complex structures depending on the solar activity cycle. Often, however, they take more regular shapes like those of arcades and loops emerging from the photosphere, penetrating through the coronal medium and then sinking back into the photosphere. Observational data, such as those obtained by the UVCS and LASCO experiments on board SOHO, indicate large spatial scales of such magnetic features and their stationarity over comparatively long time intervals. Typically, the magnetic fields and the ambient plasma are characterized by magnetic Raynolds numbers much bigger than unity, when the frozen-in magnetic field approximation may be applied. Furthermore, as the thermal pressure of the coronal plasma is generally found much smaller than the magnetic pressure, the low plasma-beta approximation is applicable too. In this case, the magnetic forces are dominant and the hydrostatic balance condition is practically achieved by the equilibrium of magnetic forces only. Other forces, like the gas pressure gradient and gravitational force, have therefore a minor effect on the topology of magnetic field in the corona. Consequently, the coronal magnetic structures can be modelled by force-free fields that are either current-free, i.e. potential, or have electric currents aligned along the field lines. In this work, we present an analytical treatment of the basic magneto-hydrostatic equation and its solutions for particular force-free and axially symmetric magnetic field configurations in cylindrical geometry. The corresponding boundary conditions are given by prescribed distributions of magnetic flux function and its vertical derivative on the photospheric plane. As these two quantities determine the vertical and horizontal component of magnetic field on the photosphere, they can be estimated from observational data. The expression of the solution contains several parameters such as integration constants and expansion coefficients that can be chosen as to provide the optimal model characteristics. This analytical treatment is a complemetary means to analyze data and model the observed coronal magnetic structures.

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