Three‐Dimensional Analysis of the Cross‐Field Instability in the Ionosphere

A three‐dimensional linear analysis is made of the cross‐field instability for a geometry in which the magnetic field lines make an arbitrary angle with the direction of density gradient. A general formula of the growth rate is obtained for a perturbation over whose scale the background quantities do not change appreciably. Applying the formula to the lower ionosphere, we find that the results of an earlier analysis [ Tsuda et al. , 1966] are recovered as a special case; that is, the present instability is a potential source of small‐scale irregularities in temperate latitude E region, as well as in the equatorial E region.