Understanding the Magnetic Power Spectra in Plasmoid-mediated Magnetic Reconnection

Reconnection driven turbulence is a frontier of research in plasma physics. Some theoretical studies and MMS observations in the plasmoid reconnection regime found some power spectral indices around 5/3 to indicate Goldreich–Sridhar turbulence vortex cascade. But the Goldreich–Sridhar theory is not strictly applicable to plasmoid reconnection with order-unity magnetic field change in the inertial range. Using 2D and 3D kinetic and MHD simulations, we find that while the power spectra in the x direction or the x-y plane (with x the reconnecting field and y the guide field direction) have indices close to 5/3, the spectra in the x-z plane (the k_⟂ spectra perpendicular to the guide field) have indices around 2.7, differing by 1 from 5/3. Surprisingly, 2D and 3D simulations have similar spectral indices even though 2D simulations only have magnetic islands without the 3D turbulence.  These results suggest that the power spectra may not indicate turbulence vortex cascade but may instead reflect the size distribution of magnetic islands/flux ropes. We use a theoretical model to predict the island-size (w) distribution (∝w^-1) and the corresponding various power spectra, which roughly agree with the simulation and observation results particularly the large 2D MHD simulation with clear island distributions. These findings are essential to understanding the nature of magnetic fluctuations driven by reconnection.