# Spectral signatures of recursive magnetic field reconnection

## TL;DR

This paper uses MHD simulations to analyze the spectral signatures of magnetic reconnection, revealing a recursive process that generates a specific power-law spectrum near the neutral line, with implications for astrophysical plasma turbulence.

## Contribution

It introduces a self-similar model predicting a magnetic energy spectrum scaling as k^{-4/5} during recursive tearing instabilities, supported by numerical simulations.

## Key findings

- Magnetic energy spectrum near the neutral line follows a k^{-0.8} power-law.
- The model predicts a k^{-4/5} scaling for the reconnecting magnetic field energy spectrum.
- Results suggest a recursive process of magnetic island formation influences turbulence in astrophysical plasmas.

## Abstract

We use 2.5D 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 $B(k)^2\sim k^{-0.8}$. 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 self-similar 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. These results provide a step forward to understand the ``recursive'' generation of magnetic islands (plasmoids), which has been proposed as a possible explanation for the energy release during flares, but which, more in general, can have an impact on the subsequent turbulent evolution of unstable sheets that naturally form in the high-Lundquist number and collisionless plasmas found in most of the astrophysical environments.