We formulate the evolution of ionospheric conductivity in the framework of 3-D M-I coupling. Two important physical processes are taken into account. One is the ionization process by precipitating mono-energetic particles, which are accelerated by parallel-potential drops in the auroral acceleration region. The other process reflects the fact that part of field-aligned current (FAC) carried by electrons is closed with a perpendicular ionic current. Here, whereas the electric current is divergence-free, the divergence of electron current is finite. Therefore, the ionospheric electron density changes, and so does the conductivity. If the energy of electron precipitation is below ∼10 eV, this second process plays an important role in plasma transportation, production, and evacuation processes. In this case the density variation does not extend in space at the perpendicular electron velocity, but it rather moves at the ion perpendicular velocity. If the energy of electron precipitation is above ∼1 keV, in contrast, the precipitation has a nonlinear effect on plasma evolution. That is, the propagation speed of the density variation increases with increasing upward-FAC density, and the propagation takes place in the direction of the converging current into the upward FAC region. The Cowling effect on the plasma evolution process is crucially important. Our formulation is more general than the previous studies and is not limited to certain geometries, current component or interaction modes between the ionosphere and magnetosphere. It is therefore better-suited for describing the self-organized M-I coupling system, which evolves with current systems, conductivity, and magnetospheric processes interacting with each other.
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