MAGNETIC NULLS AND TOPOLOGY IN A CLASS OF SOLAR-FLARE MODELS

We study the magnetic field-line topology in a class of solar flare models with four magnetic dipoles. By introducing a series of symmetry-breaking perturbations to a fully symmetric potential field model, we show that isolated magnetic nulls generally exist above the photosphere. These nuns are physically important because they determine the magnetic topology above the photosphere. In some special cases, there may be a single null above the photosphere with quasi two-dimensional properties. For such a model, a quasi null line connects the null to the photosphere. In the limit of small non-ideal effects, boundary layers and current sheets may develop along the quasi null line and the associated separatrix surfaces. Field lines can then reconect across the quasi null line, as in two-dimensional reconnection. In a more general force-free case, the field contains a pair of nulls above the photosphere, with a field line (the separator) connecting the two nulls. In the limit of small non-ideal effects, boundary layers and current sheets develop along the separator and the associated separatrix surfaces. The system exhibits three-dimensional reconnection across the separator, over which field lines exchange identity. The separatrices are related to preferable sites of energy release during solar flares.