Spectral signatures of recursive magnetic field reconnection

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 $k^{-4\mathrm{/}5}$, 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.