Toward an integrated view of ionospheric plasma instabilities: 2. Three inertial modes of a cubic dispersion relation

Abstract

The cubic dispersion relation describing inertial modes of fundamental ionospheric instabilities at arbitrary altitude is demonstrated to yield three distinct solutions, and their stability is analyzed using a combination of numerical and analytic techniques. A robust numerical method is developed for obtaining all three solutions for arbitrary altitude, and analytic expressions are developed for two solutions. In the E region, one unstable and two stable modes are found for strong electric fields, with the unstable mode being the Farley-Buneman instability. In the F region, zero, one, or two unstable modes are found depending on the plasma density gradient. The first unstable mode represents a finite-temperature generalization of the inertial mode of the gradient drift instability (GDI) in the F region that has been previously considered for cold-plasma case. The instability cone width and the gradient strength cutoff values are analyzed analytically and inertial effects are shown to drastically alter their behavior for decameter-scale waves. In particular, progressively stronger gradients are required to excite the instability with an increasing electric field. Another strongly unstable mode is found at high altitudes and for sufficiently sharp gradients, although the applicability of this solution is limited due to its high-frequency nature. The results strengthen the case for analyzing different ionospheric instabilities within the same formalism and provide an additional framework for interpreting the experimentally observed irregularity formation times that are inconsistent with those predicted by the standard GDI theory.