Symmetry considerations in the two-fluid theory of the gradient drift instability in the lower ionosphere

Abstract

A general dispersion relation for the gradient drift instability (GDI) in the lower ionosphere is derived and solved analytically for the oscillation frequency and growth rate of unstable GDI waves. The approach presented is applicable in the broad range of altitudes, both within the E region and the lower F region, and for an arbitrary background density gradient. The ion and electron fluids are treated in the same way, and linearized system of fluid equations is solved exactly, with no geometry- or altitude-specific approximations required. It is demonstrated that, in the short-wavelength limit, the GDI growth rate is maximized along the bisector between the electric current and the cross product of the gradient vector and magnetic field. This result holds at all considered altitudes, including a transitional region between the E and F regions. Symmetries of the resulting expression for the growth rate are discussed, and numerical calculations for representative gradient and current configurations are presented to illustrate and validate analytical results. Key PointsApproach with no species-, geometry-, or altitude-specific approximationsSame gradient drift instability processes throughout the lower ionosphereGrowth rate maximized on bisector between current and rotated density gradient