Context. The recent discovery of much greater magnetic flux cancellation taking place at the photosphere than previously realised has led us in our previous works to suggest magnetic reconnection driven by flux cancellation as the cause of a wide range of dynamic phenomena, including jets of various kinds and solar atmospheric heating. Aims. Previously, the theory considered energy release at a two-dimensional current sheet. Here we develop the theory further by extending it to an axisymmetric current sheet in three dimensions without resorting to complex variable theory. Methods. We analytically study reconnection and treat the current sheet as a three-dimensional structure. We apply the theory to the cancellation of two fragments of equal but opposite flux that approach each another and are located in an overlying horizontal magnetic field. Results. The energy release occurs in two phases. During Phase 1, 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 a plasma jet as it does so. During Phase 2 the fluxes cancel in the photosphere and accelerate a mixture of cool and hot plasma upwards.
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