Feedback instability analysis for dipole configuration with ionospheric and magnetospheric cavities

Linear eigenmodes of ionospheric feedback instability in the dipole magnetic field geometry are investigated by considering the ionospheric and magnetospheric resonant cavities with inhomogeneous Alfven velocity profiles. The two-field reduced magnetohydrodynamic model is used to describe shear Alfven wave dynamics, associated with auroral arcs, in a strongly nonuniform magnetic flux tube. Linear properties of ionospheric cavity modes (eigenfrequency and eigenfunctions) are examined for a wider parameter range than the previous works. It is found that several harmonics, denoted by the mode numbers of n = 3, 6-7, 10-11, ... , are trapped in the cavity region, and their magnetic fluctuations have a large amplitude at the ionosphere, leading to a high growth rate. By steepening a gradient of the Alfven velocity on the magnetospheric side, the properties of ionospheric cavity modes are fully dismissed from these low n harmonics, although their growth rates remain small positive values. On the other hand, the fundamental field line resonant mode (n = 0) has a high growth rate with a large amplitude of magnetic fluctuations at the ionosphere owing to the magnetospheric cavity. Possible spatial and temporal scales of auroral arcs and ULF wave resonances in a realistic situation are discussed.