A comparison of analytical and numerical models for steadily driven magnetic reconnection

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Abstract
In this review we consider the role of boundary conditions in both analytical and numerical solutions of steadily driven reconnection. Recently, we developed a unified formulation for steady state reconnection in which different types of reconnection are produced by varying the inflow boundary conditions. Three families of solutions occur, namely, the slow‐mode compression, the hybrid expansion, and the flux pile up. The Petschek solution and a Sonneruplike solution occur as special cases separating the new regimes. We use this unified formulation to reinterpret the main numerical experiments of steadily driven reconnection and find that many previous contradictory features of the experiments are caused by the use of different boundary conditions. For example, the 1986 Biskamp experiment did not produce a Petschek‐like solution owing to the particular boundary conditions that were adopted rather than to any basic failure of the Petschek solution. The new solutions are used to derive conditions for the onset of impulsive, bursty reconnection in which a steady state regime goes unstable to secondary tearing and coalescence and which may be a prelude to fully turbulent reconnection. Our analysis suggests that the flux pileup solutions, which are relevant to magnetopause reconnection, are the ones most likely to be unstable in this way.