Plasmoid-mediated inverse energy transfer driven by coalescing magnetic islands*

The dynamics of a large ensemble of magnetic islands in a turbulent environment are relevant to a wide range of heliospheric and astrophysical phenomena. We investigate such dynamics using high-resolution, two-dimensional magnetohydrodynamic (MHD) simulations. The coalescence of magnetic islands, enabled by magnetic reconnection, leads to both an inverse energy transfer to large spatial scales and a direct turbulent cascade to smaller scales. The successive island mergers dictate the decay of magnetic energy and formation of progressive larger-scale structures of magnetic fields, the time evolution of which can be explained by the conservation of the (ideal) invariants such as the magnetic potential. With a sufficiently high magnetic Reynolds number, the elongated reconnecting current sheets between the merging islands break into chains of small plasmoids. The mediation of plasmoids causes the magnetic energy spectrum to steepen to a spectral index of -2.2, as predicted by previous studies when the rate of energy cascade is controlled by that of the growth of plasmoids. This transition scale of spectra is time-dependent, collectively determined by the merging dynamics of energy-containing islands and that of small-scale plasmoids. The complex dynamics introduced by the dynamics of omnipresent plasmoids result in a new regime for the inverse and direct energy cascade of turbulence and thus have important implications for various long-standing problems such as corona heating and magnetogenesis.