Dimensionality of solar magnetic reconnection

Solar flares are the best examples of astrophysical magnetic reconnection in which the reconnection structure can be studied in detail. The structure is manifested through flare ribbons, intense optical and EUV emissions in footpoints of field lines attached to the coronal reconnection region. In the most common type of solar flares, two parallel ribbons appear and move away from each other, which could be related to the reconnection electric field under the theory of two-dimensional (2D) X-point reconnection, opening up a wide field of solar research. Another breakthrough came upon the discovery of circular ribbons, which implies a dome-shaped spine-fan structure capable of truly three dimensional (3D) null point reconnection. The variability of circular ribbons could also shed light on the reconnection electric field in the corona, but was relatively less attended. In this paper, we review selective topics in both types of flares with emphasis on the dimensionality of magnetic reconnection. Three types of reconnection: 2D X-point, 3D torsional, and 3D spine-fan reconnection are studied and associated with translational, rotational, and vibrational degrees of freedom. It is demonstrated that the dimensionality-based analysis of the observed dynamics of circular and parallel ribbons can facilitate a better understanding of the nature of solar magnetic reconnection.