On the nonlinear motion of a small barium cloud in the ionosphere

The nonlinear behavior of a barium ion cloud whose integrated Pedersen conductivity is small (of order ϵ) in comparison with the background ionospheric Pedersen conductivity is studied in terms of fluid equations governing the motion of the barium plasma and the ionospheric plasma, which are both approximated by uniform layers. The barium cloud drives images in the ionospheric conductivity that are of order ϵ1/2 relative to the undisturbed ionosphere. These then produce motion of the barium cloud and the ionospheric image cloud on a time scale of LB/(cE0ϵ1/2), where L is a linear dimension of the cloud perpendicular to the earth's magnetic field B and E0 is the ambient transverse electric field in the ionosphere. In the limit of zero diffusion, numerical solution of the equations shows that at long times the contours of constant barium ion density for relatively high density values are thin sheets making a definite angle θ≡tan−1 (νi/ωci with the direction of the E × B cloud velocity (νi and ωci are the ion-neutral collision frequency and the ion cyclotron frequency, respectively, for E region ions). These results are consistent with observations of an F region release of a small barium cloud. Also at long times, large image cloud densities coincide, in the plane transverse to B with regions of the barium cloud that are relatively far from the initial position of the barium cloud. Modifications for small diffusion, which include back side steepening, are also given.