Relating reconnection rate, exhaust structure and effective resistivity
The magnetic reconnection structure consists of a central diffusion region (CDR) and a cone or wedge shaped reconnection exhaust containing accelerated plasma flows and electromagnetic fluctuations. We predict here the relationship among the exhaust half-cone angle (θ{sub e}), the half width (w) of the CDR, the outflow velocity V{sub o}, and the effective resistivity (η{sub eff}), which includes the effects of all the nonideal terms in the generalized Ohm's law. The effective resistivity is defined as the ratio of reconnection electric field E{sub rec} to the current density J{sub y} at the X point and it essentially represents the loss of momentum from the current-carrying plasma particles due to scattering by waves, their inertia or outflux from the CDR. The relation is checked against relevant results previously reported from laboratory experiments, space observations, and simulations, showing excellent agreement. The relation can be used for estimating the ad-hoc effective resistivity often used in magnetohydrodynamic modeling of reconnection.