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Dynamic Hydrogen Ionization

We investigate the ionization of hydrogen in a dynamic Solar atmosphere. We show that the time scale for ionization/recombination can be estimated from the eigenvalues of a modified rate matrix where the optically thick Lyman transitions that are in detailed balance have been excluded. We find that the time scale for ionization/recombination is dominated by the slow collisional leakage from the ground state to the first excited state. Throughout the chromosphere the time scale is long ($10^3$-$10^5$ s), except in shocks where the increased temperature and density shorten the time scale for ionization/recombination, especially in the upper chromosphere. Because the relaxation time scale is much longer than dynamic time scales, hydrogen ionization does not have time to reach its equilibrium value and its fluctuations are much smaller than the variation of its statistical equilibrium value appropriate for the instantaneous conditions. The ionization state tends to represent the higher temperature of the shocks, and the mean electron density is up to a factor of six higher than the electron density calculated in statistical equilibrium from the mean atmosphere. The simulations show tha