Computer studies on the spontaneous fast reconnection model as a nonlinear instability

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Abstract
The spontaneous fast reconnection model is examined for a current-driven anomalous resistivity model where the threshold for resistivity occurrence is assumed to increase with the temperature (thermal velocity). It is demonstrated that the fast reconnection mechanism can effectively evolve even if the threshold notably increases with the temperature increase near an X neutral point. The evolutionary process can be characterized by two distinct phases. In the initial phase, coupled to the anomalous resistivity, the reconnection process grows rather slowly. In the subsequent explosive phase, as soon as the plasma and the reconnected magnetic flux are effectively ejected from near the X point, it drastically grows due to the powerful positive feedback between the localized enhancement of anomalous resistivity and the growth of reconnection flow. For the larger resistivity threshold, the localization of anomalous resistivity near the X point becomes more effective, so that the fast reconnection development becomes more drastic. On the nonlinear saturation level, the (quasi-steady) fast reconnection mechanism is set up, where the peak fast reconnection rate is sustained, and standing slow shocks, attached to the localized diffusion region, are extended outwards with time. On the other hand, for uniform resistivity, the explosive phase does not occur, so that the fast reconnection mechanism cannot build up. Hence, it is concluded that the spontaneous fast reconnection model describes a new-type nonlinear instability in a long current sheet system, leading to drastic collapse of the overall magnetic field system.