Asymptotic scalings of fluid, incompressible “electron-only” reconnection instabilities: Electron-magnetohydrodynamics tearing modes

Abstract

We perform a numerical study of the scaling laws of tearing modes in different parameter regimes of incompressible fluid electron magnetohydrodynamics, both in the small and large wavelength limits, as well as for the fastest growing mode that can be destabilized in a large aspect ratio current sheet. We discuss the relevance of these results, also for the interpretation of the “electron-only reconnection regime,” recently identified in spacecraft measures and in numerical simulations of solar wind turbulence. We restrict here to a single parameter study, in which we selectively consider only one non-ideal effect among electron inertia, perpendicular resistivity, and perpendicular electron viscosity, and we also consider the cases in which a proportionality exists between the parallel and the perpendicular dissipative coefficients. While some known theoretical results are thus confirmed, in other regimes and/or wavelength limits, corrections are proposed with respect to some theoretical estimates already available in the literature. In other cases, the scalings are provided for the first time. All numerical results are justified in terms of heuristic arguments based on the measurement of the scaling laws of some new microscopic scales associated with the gradients of the eigenfunctions. The alternative scalings we have found are consistent with this interpretation.