Limitation of Height-Integrated Conductivity Boundary Condition on the Ionospheric Feedback Instability

The often-used height-integrated conductivity (HIC) boundary condition replaces a slab of plasma at the bottom of the ionosphere by a sheet with conducting properties obtained by integration of the transverse plasma conductivity over the slab thickness. This HIC replaces the E-layer but does not capture collision frequencies and horizontal ion flow velocities that vary rapidly with altitude. An altitude-averaged conductivity can be justified for a Pc5-range Alfven wave because its electric field barely changes with altitude at long wavelengths. The wave electric current, however, depends on both the electric field and the density perturbation, and the latter may be strongly nonuniform. A linear analysis of the ionospheric feedback instability is performed in a system similar to [Watanabe and Maeyama, 2018], except that (a) the parallel electric field of the wave and electron-neutral collisions are accounted for, and (b) the collisional ionosphere is represented by a 300 km layer with realistic collision profiles. The collisional region is adjoined to a 50000 km region of collisionless plasma. Instability parameters are determined numerically for HIC slabs of thickness varying from 2 km to 300 km and compared to those obtained when the collisional region is fully resolved. Only with the thinnest integrated layers are the maximal growth rate and corresponding transverse wavenumber close to the values obtained with the fully resolved collisional region. For example, the 30 km integrated layer gives the maximal growth rate at a transverse wavenumber that is three times smaller, while the 100 km integrated layer gives the growth rate about three times higher than required. Therefore, the HIC boundary condition is very limited in its validity even for low frequency field-line resonances. Previously, a similar conclusion was reached for higher frequency waves by [Cosgrove and Doe, 2010].

Cosgrove R. and Doe R. (2010). Ann. Geophys., 28, 1777-1794.

Watanabe, T.-H., and Maeyama, S. (2018). Geophys. Res. Lett., 45, 10,043-10,049.