The current dynamo effect and its statistical description during 3-D time-dependent reconnection

Time-dependent magnetic reconnection is not only a dissipation process (J·E > 0), but also a dynamo process (J·E < 0). The current dynamo effect during (and after) 3-D magnetic reconnection corresponds to the formation of the field-aligned current for the geomagnetic flux tubes, which can be described as result of injection of twist helicity. The self-organization process of the local turbulent magnetofluids is used to explain the initial formation of the twisted flux tubes (i.e. the formation of the holes at the magntopause and the diversion and disruption of the magnetopause current). The theory of the conversion and conservation of the magnetic helicity during reconnection is used to estimate the average dynamo effect. The torques which come from the volume integral of the curl of Lorentz force and/or the drag force by the magnetosheath flow can also provide the source of twist helicity during (and after) reconnection. The average input rate of the electromagnetic energy during reconnection is formulated in terms of the input rate of the total twist helicity or an equivalent inductance. For a turbulent reconnection region, the induced electric field is formulated in terms of the α and β effect, where α corresponds to the current dynamo effect and β provides the MHD turbulent diffusivity required for reconnection.