Quantitative analytical model for magnetic reconnection in Hall magnetohydrodynamics

Magnetic reconnection is of fundamental importance for laboratory and naturally occurring plasmas. Reconnection usually develops on time scales which are much shorter than those associated with classical collisional dissipation processes, and which are not fully understood. While such dissipation-independent (or “fast”) reconnection rates have been observed in particle and Hall magnetohydrodynamics (MHD) simulations and predicted analytically in electron MHD, a quantitative analytical theory of fast reconnection valid for arbitrary ion inertial lengths di has been lacking. Here we propose such a theory without a guide field. The theory describes two-dimensional magnetic field diffusion regions, provides expressions for the reconnection rates, and derives a formal criterion for fast reconnection in terms of dissipation parameters and di. It also demonstrates that both open X-point and elongated diffusion regions allow dissipation-independent reconnection and reveals a possibility of strong dependence of the reconnection rates on di.