Frozen-in condition for ions and electrons: implication on magnetic flux transport by dipolarizing flux bundles

The ability of dipolarizing flux bundles (DFBs) in transporting magnetic flux from the mid-tail reconnection site for near-Earth dipolarization is evaluated by two methods: the generalized Ohm's law and the concept of flux preserving and line preserving. From the generalized Ohm's law, the breakdown of the frozen-in condition (FIC) for ions is shown to be intimately related to that for electrons. When FIC is not satisfied for the ion fluid associated with energy conversion, it also implies the same for the electron fluid. When FIC holds, the plasma has the flux preserving property. It further guarantees that charged particles on a given magnetic field line will stay together on a magnetic field line at later times, i.e., line preserving. Conversely, when line preserving does not hold, flux preserving does not hold also. Previous detailed examination on the FIC for DFBs revealed that the majority of DFBs associated with energy conversion violate the FIC for the ion fluid. This implies that FIC does not hold for the electron fluid also. Furthermore, plasmas in substorm injections come from vastly different locations, violating the line preserving property and implying that FIC is broken for the magnetic flux tubes associated with substorm injection and dipolarization. These observations indicate that DFBs are not an effective agent to transport magnetic flux within the magnetosphere and further imply that mid-tail magnetic reconnection is rather ineffective in transporting magnetic flux for near-Earth dipolarization.