A linear theory is presented of the current convective instability in the long wavelength limit, i.e., kL≪1 where k is the wave number and L is the scale length of the density inhomogeneity A relatively simple dispersion equation is derived that describes the modes in this limit. Analytical solutions are presented in both the collisional (&ngr;in≫&ohgr;) and inertial (&ngr;in≫&ohgr;) limits where &ohgr; is the wave frequency and &ngr;in is the ion-neutral collision frequency. It is shown that the growth rate scales as k in the collisional limit and as k2/3 in the inertial limit. The analytical solutions are compared to exact numerical solutions, and very good agreement is found. Applications to the auroral ionosphere are discussed.