“Ideal” tearing and the transition to fast reconnection in the weakly collisional MHD and EMHD regimes

Abstract

This paper discusses the transition to fast growth of the tearing instability in thin current sheets in the collisionless limit where electron inertia drives the reconnection process. It has been previously suggested that in resistive MHD there is a natural maximum aspect ratio (ratio of sheet length and breadth to thickness) which may be reached for current sheets with a macroscopic length L, the limit being provided by the fact that the tearing mode growth time becomes of the same order as the Alfvén time calculated on the macroscopic scale. For current sheets with a smaller aspect ratio than critical the normalized growth rate tends to zero with increasing Lundquist number S, while for current sheets with an aspect ratio greater than critical the growth rate diverges with S. Here we carry out a similar analysis but with electron inertia as the term violating magnetic flux conservation: previously found scalings of critical current sheet aspect ratios with the Lundquist number are generalized to include the dependence on the ratio de2/L2, where de is the electron skin depth, and it is shown that there are limiting scalings which, as in the resistive case, result in reconnecting modes growing on ideal time scales. Finite Larmor radius effects are then included, and the rescaling argument at the basis of “ideal” reconnection is proposed to explain secondary fast reconnection regimes naturally appearing in numerical simulations of current sheet evolution.

Reconnection and small-scale fields in 2D-3V hybrid-kinetic driven turbulence simulations

“…In other words, once the jet-structure along the CS1 has been formed, reconnection starts to generate the islands more or less simultaneously. We argue that the velocity shear at the edge of the magnetic field reversal, by possibly introducing KH-like magnetic fluctuations or by dynamically squeezing/elongating the CS (i.e., lowering the ratio a/L), could be responsible for accelerating the development of reconnection [65,66]. Transition to fast magnetic reconnection is a fundamental aspect for the understanding of its connection to the turbulent cascade across the ion break: the turbulent cascade proceeds in the standard way, setting up the -5 3 spectrum accordingly to the nonlinear timescale up to…”

“…In our case, although the dynamics and the parameters range might be similar to the one driven by the plasmoid instability, we reach an aspect ratio L/a much smaller than the expected one. This could be due to the fact that fast reconnection already proceeds on ideal timescales before a very large L/a value can be dynamically reached [64][65][66]. Moreover, it is worth stressing that the parameter space illustrated in figure 1 of [63] is mainly limited to a qualitative validity, as stated by the authors, since in large part still unexplored.…”

Fast Magnetic Reconnection: “Ideal” Tearing and the Hall Effect

“…7 summarizes the results obtained using the IT criterion, in the absence of a guide field (in the figure, λ = 1/h). The (S, λ) parameter space has an extension on the left due to the fact that we also take into account the effect of finite electron skin depth in the RMHD case discussed in Del Sarto et al (2016), where d i = m i /m e d e ∼ 42d e . Indeed the Hall effect on its own can not break the frozen in conditions, i.e.…”

“…In this form, Ohm's law includes the Hall effect and collisional resistivity but neglects electron pressure and electron inertia: the effect of these terms on"ideal" reconnection regimes has been discussed in Del Sarto et al (2016). Upon linearization, the equations are nondimensionalized using the magnetic field intensity B 0 (the perturbed magnetic field b = b/B 0 ), the magnetic field gradient scale a (essentially the Harris sheet thickness), and the Alfvén time τ A = a/v A where the Alfvén speed v A = B 0 / √ 4πρ.…”

“…We have investigated the purple region in Pucci and Velli (2014) and the white region within this work. While the orange region has been investigated in Del Sarto et al (2016) (even if the Hall effect is negligible in the adopted frame), the green one still has to be explored and with that, a possible critical value of d e for which collisionless reconnection can present single or multiple x-points. These are useful to understand the ongoing process regime in astrophysical plasmas as well as in laboratory plasmas, and in the latter case to visualize the parameter space of an experimental facility, and in particular can be applied to the multi-point observations of MMS, to compare theoretical predictions the spatial structure of the Hall magnetic and electric fields surrounding the diffusion region.…”