Heating in the solar atmosphere at a fin current sheet driven by magnetic flux cancellation

Magnetic reconnection before flux cancellation in the solar photosphere when two opposite-polarity photospheric magnetic fragments are approaching one another is usually modelled by assuming that a small so-called 'floating current sheet' forms about a null point or separator that is situated in the overlying atmosphere. Here, instead we consider the reconnection that is initiated as soon as the fragments become close enough that their magnetic fields interact. The resulting current sheet, which we term a 'fin sheet' extends up from the null point or separator that is initially located in the solar surface. We develop here non-linear analyses for finite-length models of both fin and floating current sheets that extend the previous models that were limited to short floating current sheets. These enable the length of the current sheet and the rate of heating to be calculated in both cases as functions of the separation distance of the sources and the reconnection rate. Usually, the fin current sheet liberates more energy than a floating current sheet.