Hydraulic Concentration of Magnetic Fields in the Solar Photosphere. I. Turbulent Pumping

Observations suggest that most of the magnetic flux through the solar photosphere is concentrated in vertical filaments in the supergranule boundaries. Each filament appears to contain about 3 x 10' maxwells, in the form of a field of 500 gauss or more, over a diameter of 700 km or less. The magnetic energy density in the filaments is 100 times the observed kinetic energy density of the observed supergranule motions, but comparable to the kinetic energy density of the granules. Force-free field configurations cannot duplicate the observational numbers, nor can such cooling effects as are believed responsible for the intense fields in sunspot umbrae. We point out a simple hydraulic mechanism- turbulent pumping that appears to account for the observed concentration of fields. The mechanism is treated by using the simple mixing-length theory of convection and turbulence. Subject headings: atmospheres, solar - granules and supergranules, solar hydromagnetics - turbulence