Cross-field Current Closure Below the Solar Photosphere

Abstract

A simple model is developed to describe how an externally imposed current closes as a function of time below the photosphere. A vertical current density is assumed to turn on at the photospheric boundary. The model implies that the subsequent closure of the current in the sub-photosphere depends only on the ratio RA/ R, where RA = /-LaVA is the Alfvenic impedance of the photosphere and = I/o-pI is the resistance corresponding to the conductivity O-p and a characteristic length 1. For RA/R » 1, current closure occurs at a front, propagating with the Alfven speed. For RA/ R 1, current closure is a diffusive process ahead and behind a slowly propagating Alfvenic front. The first case is the relevant one for the Sun, where RA/ R /VA, for VA in kilometres per second.