Context. Recent observations have shown that magnetic flux cancellation occurs at the photosphere more frequently than previously thought. Aims. In order to understand the energy release by reconnection driven by flux cancellation, we previously studied a simple model of two cancelling polarities of equal flux. Here, we further develop our analysis to achieve a more general setup where the two cancelling polarities have unequal magnetic fluxes and where many new features are revealed. Methods. We carried out an analytical study of the cancellation of two magnetic fragments of unequal and opposite flux that approach one another and are located in an overlying horizontal magnetic field. Results. The energy release as microflares and nanoflares occurs in two main phases. During phase 1a, a separator is formed and reconnection is driven at it as it rises to a maximum height and then moves back down to the photosphere, heating the plasma and accelerating plasma jets in the process. During phase 1b, once the separator moves back to the photosphere, it bifurcates into two null points. Reconnection is no longer driven at the separator and an isolated magnetic domain connecting the two polarities is formed. During phase 2, the polarities cancel out at the photosphere as magnetic flux submerges below the photosphere and as reconnection occurs at and above the photosphere and plasma jets and a mini-filament eruption can be produced.
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