Fast Magnetic Reconnection: Secondary Tearing Instability and Role of the Hall Term

Abstract

Magnetic reconnection provides the primary source for explosive energy release, plasma heating and particle acceleration in many astrophysical environments. The last years witnessed a revival of interest in the MHD tearing instability as a driver for efficient reconnection. It has been established that, provided the current sheet aspect ratio becomes small enough (a/L ∼ S −1/3 for a given Lundquist number S ≫ 1), reconnection occurs on ideal Alfvén timescales and becomes independent on S . Here we investigate, by means of two-dimensional simulations, the ideal tearing instability in the Hall-MHD regime, which is appropriate when the width of the resistive layer δ becomes comparable to the ion inertial length d i . Moreover, we study in detail the spontaneous development and reconnection of secondary current sheets, which for high S naturally adjust to the ideal aspect ratio and hence their evolution proceeds very rapidly. For moderate low S , the aspect ratio tends to the Sweet-Parker scaling (a/L ∼ S −1/2 ), in order to fulfill the condition δ ≪ a necessary for the onset of a tearing instability. When the Hall term is included, the reconnection rate of this secondary nonlinear phase is enhanced and, depending on the ratio d i /δ, can be twice with respect to the pure MHD case, and up to ten times larger than the linear phase. Therefore, the evolution of the tearing instability in thin current sheets in the Hall-MHD regime naturally leads to an explosive disruption of the reconnecting site and to energy release on super-Alfvénic timescales, as required to explain astrophysical observations.

Three-dimensional magnetic reconnection in particle-in-cell simulations of anisotropic plasma turbulence

“…The critical-balance theory of Alfvénic turbulence has been tested using gyrokinetic simulations (Howes et al 2008a;) and 3-D PIC simulations (Grošelj et al 2018). The evolution and morphology of 3-D reconnection events, starting from a Harris current-sheet configuration, have been studied at kinetic scales (Hesse et al 2001;Pritchett & Coroniti 2001;Wiegelmann & Büchner 2001;Lapenta et al 2006;Liu et al 2013;Vapirev et al 2013;Muñoz & Büchner 2018;Lapenta et al 2020), as has been the effect of turbulence on the development of reconnection events (Daughton et al 2014;Lapenta et al 2015;Pucci et al 2017;Papini et al 2019b). However, little attention has been given to the occurrence of small-scale reconnection as a product of the turbulent cascade in a fully 3-D geometry.…”

“…It is unclear how turbulence and reconnection affect each other and how the energy is partitioned between particles and fields through both processes. For instance, although the role of reconnection in the small-scale turbulent cascade has been studied previously (Franci et al 2017;Boldyrev & Loureiro 2017;Papini, Landi & Del Zanna 2019b), it is still unclear how 3-D reconnection proceeds in the turbulent solar wind. It is not well understood whether 3-D reconnection disrupts current sheets and coherent magnetic-field structures associated with intermittency at small scales in the same way as it disrupts these structures at large scales (Boldyrev et al 2013;Mallet, Schekochihin & Chandran 2017).…”

Multidimensional Iterative Filtering: a new approach for investigating plasma turbulence in numerical simulations

“…Equations (2.1)-(2.4) are numerically solved by using a pseudospectral code we developed, already employed for studies of magnetic reconnection (Landi et al 2015;Papini, Landi & Del Zanna 2018, 2019c and plasma turbulence (Papini et al 2019a,b). We consider a two-dimensional (x, y) periodic domain and use Fourier decomposition to calculate the spatial derivatives.…”

“…Equations (2.1)–(2.4) are numerically solved by using a pseudospectral code we developed, already employed for studies of magnetic reconnection (Landi et al. 2015; Papini, Landi & Del Zanna 2018, 2019 c ) and plasma turbulence (Papini et al. 2019 a , b ).…”

Systematic construction of upwind constrained transport schemes for MHD

“…This choice of parameters makes the test particularly severe since the configuration is only weakly unstable. The maximum growth rate that can fit in the computational box, indeed, has been found by repeating the linear analysis of Miura & Pritchett (1982) [55] yielding Im(ωa/c s ) ≈ 0.395 × 10 −2 , where ω is the growth rate. Computations are repeated using two different grid resolutions, N x = 128 and N x = 256 (N y = 2N x ) so that the shear width is resolved on ∼ 4 and ∼ 8 zones, respectively.…”