In ̄uence of the ®nite ionospheric conductivity on dispersive, nonradiative ®eld line resonances

The in ̄uence of the ®nite ionospheric conductivity on the structure of dispersive, nonradiative ®eld line resonances (FLRs) is investigated for the ®rst four odd harmonics. The results are based on a linear, magnetically incompressible, reduced, twōuid MHD model. The model includes e€ects of ®nite electron inertia (at low altitude) and ®nite electron pressure (at high altitude). The ionosphere is treated as a highintegrated conducting substrate. The results show that even very low ionospheric conductivity (RP ˆ 2 mho) is not sucient to prevent the formation of a largeamplitude, small-scale, nonradiative FLR for the third and higher harmonics when the background transverse plasma inhomogeneity is strong enough. At the same time, the fundamental FLR is strongly a€ected by a state of low conductivity, and when RP ˆ 2 mho, this resonance forms only small-amplitude, relatively broad electromagnetic disturbance. The di€erence in conductivities of northern and southern ionospheres does not produce signi®cant asymmetry in the distribution of electric and magnetic ®elds along the resonant ®eld line. The transverse gradient of the background Alfve n speed plays an important role in structure of the FLR when the ionospheric conductivity is ®nite. In cases where the transverse inhomogeneity of the plasma is not strong enough, the low ionospheric conductivity can prevent even higher-harmonic FLRs from contracting to small scales where dispersive e€ects are important. The application of these results to the formation and temporal evolution of small-scale, active auroral arc forms is discussed.