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M.L. Goodman (Catholic University of America, and NASA Goddard Space Flight Center)
In thin magnetic flux tubes in the photospheric and lower chromospheric network, the product \omega \tau of the proton cyclotron frequency with the proton-hydrogen collision time increases with height. Near the photosphere (\omega \tau)2 << 1 in strong magnetic flux tubes. Near the height of the temperature minimum, which is different for flux tubes with different photospheric field strengths, (\omega \tau)2 ~1. When (\omega \tau)2 increases through unity the protons are said to become magnetized: at this height control of the proton dynamics switches from collisions with hydrogen to the magnetic field. This causes a rapid increase in the rate of Pedersen current dissipation, determined by the rapid change in the anisotropic conductivity tensor for a weakly ionized plasma of hydrogen, electrons, protons, and singly ionized heavy ions. The rapid increase of heating rate with height just above the temperature minimum in a flux tube is due to the continuing increase of proton magnetization with height, and to the following feedback mechanism: heating by Pedersen current dissipation ---> increase in hydrogen ionization ---> increase in ratio of proton number density to heavy ion number density ---> increase in heating by Pedersen current dissipation. Above the temperature minimum the heating rate increases by one order of magnitude over one pressure scale height. The classical concept of a single temperature minimum about 500 km above the photosphere is interpreted as an average over the heights of the different temperature minima of different flux tubes. Ranges of hydrogen density and magnetic field strength for the lower chromospheric network are predicted. The current density is driven by slow, longitudinal, magnetoacoustic waves that have their source in the dynamic interaction between the photospheric granulation and the magnetic flux tubes concentrated at the granulation boundaries.
The author gratefully acknowledges support by NSF grant ATM-9816335 to the Catholic University of America.