Electron-only reconnection and inverse magnetic-energy transfer at sub-ion scales

Electron-only reconnection is a form of magnetic reconnection that occurs within sufficiently small spatial regions, where ions are effectively decoupled from the reconnection dynamics. In this study, we derive and numerically validate an analytical model for electron-only magnetic reconnection in a merging island configuration. The model predicts reconnection rates at sub-ion scales that are significantly higher than those associated with magnetohydrodynamic (MHD) scale reconnection, in agreement with recent observations and kinetic simulations. We further apply this model to investigate inverse magnetic energy transfer at sub-ion scales, deriving time-dependent scaling laws for magnetic energy decay that diverge from those found in the MHD regime. These scaling laws are validated through two- and three-dimensional numerical simulations, demonstrating that sub-ion scale magnetic structures can grow to system-scale via successive island coalescence. We also characterize the resulting plasma turbulence, examining the energy spectrum and the typical spatial dimensions of magnetic structures.