Spectral signatures of recursive magnetic field reconnection

Abstract

We use 2.5D viscoresistive Magnetohydrodynamic simulations to investigate the spectral signatures of the nonlinear disruption of a tearing unstable current sheet via the generation of multiple secondary current sheets and magnetic islands. During the nonlinear phase of tearing mode evolution, there develops a regime in which the magnetic energy density shows a spectrum with a power-law close to B(k) 2 ∼ k −0.8 . Such an energy spectrum is found in correspondence of the neutral line, within the diffusion region of the primary current sheet, where energy is conveyed towards smaller scales via a "recursive" process of fast tearing-type instabilities. Far from the neutral line we find that magnetic energy spectra evolve towards slopes compatible with the "standard" Kolmogorov spectrum. Starting from a selfsimilar description of the nonlinear stage at the neutral line, we provide a model that predicts a reconnecting magnetic field energy spectrum scaling as k −4/5 , in good agreement with numerical results. An extension of the predicted power-law to generic current sheet profiles is also given and possible implications for turbulence phenomenology are discussed.

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

“…Below the break point, the spectral index (defined as the absolute value of the slope) is smaller than 1, while above the break point the spectral index is very close to 2. Especially, in Run 0 the slope of B y spectrum below the break point is approximately −4/5, the value estimated by [26], indicating that in the low-k x range the spectra are controlled by the recursive plasmoid generation. In high-k x range the −2 slope is mainly due to the discontinuities near the boundaries of the plasmoids.…”

“…The development of turbulence with an extended inertial range is important both to energization [15] and scattering of particles [9]. In the MHD case, a phenomenological model based on the recursive tearing mode developed by [26] leads to a spectrum |B y (k x )| 2 ∝ k −4/5 x . In the kinetic regime, i.e.…”

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

“…(2017) and Loureiro & Boldyrev (2020) (and references therein) the anisotropy of cascading eddies increases as the energy transfer marches to smaller scales, until current sheets form, whose tearing growth rate might be comparable to the nonlinear cascade time: the effects of the tearing of turbulent eddies alters the slope of turbulence inertial range spectra at higher wave numbers. On the other hand, the turbulence consequences of the self-similar current sheet collapse starting from a laminar configuration have been presented in Uzdensky, Loureiro & Schekochihin (2010) and Tenerani & Velli (2020).…”

Probing Current Sheet Instabilities from Flare Ribbon Dynamics

“…Or, an alternative turbulence model is a better fit for these conditions. Tenerani & Velli (2020), for example, predict a power-law index of 2.2, when introducing a model of intermittency (Frisch et al 1978) to the collapsing magnetic islands and beginning from a Kolmogorov state. Dong et al (2018) also find an index of 2.2, in their simulation of a plasmoid-mediated regime.…”

“…These magnetic islands form at a preferred spatial scale, and continue to collapse further to produce islands at progressively smaller scales. Larger islands are also produced via the reconnection and coalescence at island boundaries (Tenerani & Velli 2020). This critical aspect ratio and spatial scales are dependent on the local magnetic conditions, in particular the Lunduist number.…”