Linear theory of the <b>E×B</b> instability with an inhomogeneous electric field

Abstract

A general linear theory of the E×B instability is developed which considers an ambient electric field that is at an arbitrary angle to the density gradient and allows the electric field component parallel to the density gradient to be inhomogeneous. A differential equation is derived which describes the mode structure of the unstable waves in the direction of the inhomogeneities. The theory (1) includes ion inertia effects, (2) allows for arbitrary density and electric field profiles, and (3) is valid in the long‐wavelength regime, i.e., k y L &lt; 1, where L is the width of the boundary layer. The main results of the analysis are as follows. First, the inhomogeneous velocity flow caused by the inhomogeneous electric field can stabilize the instability. Second, short‐wavelength modes are preferentially stabilized over longer‐wavelength modes. Third, the stabilization mechanism is associated with the velocity shear due to an x ‐dependent resonance [ω − k y V y ( x )] −1 , where V y ( x ) = − cE x ( x )/ B , and not velocity shear terms explicitly proportional to ∂ V y /∂ x or ∂² V y /∂ x ². Fourth, the marginal stability criterion is weakly dependent on the magnitude of ν in /ω. Applications of these results to ionospheric phenomena are discussed, viz., barium cloud striations and high‐latitude F region irregularities.