Chromospheric heating by electric currents induced by fluctuating magnetic elements

We refer to two papers by Goodman (1995, 1996) on the heating of the chromosphere by large-scale electric currents, and to our paper (Lorrain and Koutchmy, 1993) on magnetic elements. Goodman assumes that the dynamo that runs a magnetic element stops operating at t = 0. From then on, the magnetic field decays exponentially, and the induced currents heat the chromosphere. The time constants calculated by Goodman disagree with the observed values, possibly because he disregards the driving dynamo. Also, he assumes static conditions, but his magnetic force density appears suddenly when the dynamo stops, and it is about equal to the gravitational force density. The magnetic force acts downward and fluctuations in the current flowing through the magnetic element should induce vertical oscillations at the photosphere. This point should be investigated further.