Scalings of plasmoid-instability-mediated current sheet disruption

A phenomenological model that describes the process of current sheet disruption mediated by the plasmoid instability in an evolving background has been proposed. The model incorporates the effects of the linear growth of tearing instability as well as mode stretching and advective losses due to reconnection outflow. Numerically obtained scalings of disruption conditions from the model are in good agreement with the results from direct numerical simulations [1]. In this work, we derive analytical scalings from the model in the asymptotic regime of high Lundquist number $S$. The scalings take the form of a power law multiplied by a factor that, to the leading order, is logarithmic on $S$ and the noise level of the environment. The analytic scalings agree with the predictions of previous calculations based on a principle of least time [2,3] up to the leading order expansion of the multiplication factor if the effect of outflow is neglected. Our model predicts a critical Lundquist number for disruption, which is not a constant value but weakly depends on the noise level.

[1] Huang et al., ApJ 849, 75 (2017)

[2] Comisso et al., PoP 23, 100702 (2016)

[3] Comisso et al., ApJ 850, 142 (2017)