Fast Recursive Reconnection and the Hall Effect: Hall-MHD Simulations

Abstract

Magnetohydrodynamic (MHD) theory and simulations have shown that reconnection is triggered via a fast "ideal" tearing instability in current sheets whose inverse aspect ratio decreases to a/L ∼ S −1/3 , with S is the Lundquist number defined by the half-length L of the current sheet (of thickness 2a). Ideal tearing, in 2D sheets, triggers a hierarchical collapse via stretching of X-points and recursive instability. At each step, the local Lundquist number decreases, until the subsequent sheet thickness either approaches kinetic scales or the Lundquist number becomes sufficiently small. Here we carry out a series of Hall-MHD simulations to show how the Hall effect modifies recursive reconnection once the ion inertial scale is approached. We show that as the ion inertial length becomes of the order of the inner, singular layer thickness at some step of the recursive collapse, reconnection transits from the plasmoid-dominant regime to an intermediate plasmoid+Hall regime and then to the Hall-dominant regime. The structure around the X-point, the reconnection rate, the dissipation property and the power spectra are also modified significantly by the Hall effect.

Onset of fast magnetic reconnection and particle energization in laboratory and space plasmas

“…They numerically showed in this case the asymptotic growth rate of the tearing instability is Alfvénic, independent of the Lundquist number and the ion inertial length itself. Shi et al (2019) performed a series of Hall-MHD simulations, testing the results for the primary reconnection site onset discussed in Pucci et al (2017). Shi et al (2019) focused on how the Hall effect modifies the recursive collapse trigger of reconnection.…”

“…Shi et al (2019) performed a series of Hall-MHD simulations, testing the results for the primary reconnection site onset discussed in Pucci et al (2017). Shi et al (2019) focused on how the Hall effect modifies the recursive collapse trigger of reconnection. They showed that the reconnection rate, the dissipation property and the power spectra are modified significantly.…”

“…Transition from one domain to the other mainly depends on the trigger condition for reconnection and the relative physics of the plasma of interest. For example, the purple region in figure 9 represents the study of the IT in the resistive reconnection regime (Pucci & Velli 2014) and the white region is the Hall-MHD regime (Pucci et al 2017;Shi et al 2019), whereas the orange region has been investigated in Del Sarto et al (2016) (the latter actually neglects the Hall effect). The green region cannot be investigated with a single-nor two-fluid model, but requires a kinetic treatment.…”

“…2016; Pucci, Velli & Tenerani 2017), leading to different conclusions (Shi et al. 2019) than those of Cassak et al. (2006).…”

“…Such a treatment, based on one-dimensional systems with antiparallel field lines and a collisional resistivity described by a single global parameter, the Lundquist number, does not capture the totality of potentially dynamic situations, nor the complexity, for example, of collisionless dissipation mechanisms, that may offer new onset and/or stabilization scenarios, see, e.g., Cassak, Shay & Drake (2006) and Swisdak et al (2003). Note, however, that the 'ideal' tearing has been generalized to small-scale kinetic effects (Del Sarto et al 2016;Pucci, Velli & Tenerani 2017), leading to different conclusions (Shi et al 2019) than those of Cassak et al (2006).…”