Quantitative, comprehensive, analytical model for magnetic reconnection in hall magnetohydrodynamics

Dissipation-independent, or fast, magnetic reconnection has been observed computationally in Hall magnetohydrodynamics (MHD) and predicted analytically in electron MHD. However, a quantitative analytical theory of reconnection valid for arbitrary ion inertial lengths, d(i), has been lacking and is proposed here for the first time. The theory describes a two-dimensional reconnection diffusion region, provides expressions for reconnection rates, and derives a formal criterion for fast reconnection in terms of dissipation parameters and d(i). It also confirms the electron MHD prediction that both open and elongated diffusion regions allow fast reconnection, and reveals strong dependence of the reconnection rates on d(i).