By using a general expression for the ponderomotive wave force, we have evaluated the action of ion cyclotron Alfv¿n waves on the plasma density in a longitudinal waveguide. The main effect is the condensation of the plasma in the vicinity of the waveguide equator. According to observations onboard the GEOS 1 and Viking satellites, the amplitudes of such geomagnetic pulsations can reach up to several nanoteslas. This is sufficient to cause a strong modification of the cold plasma density in the magnetosphere under the action of ion cyclotron Alfv¿n pulsations. Furthermore, we have also speculated on the possible effects of the pondermotive wave force on the problems connected with the so called ''wave-induced substorms'' in the neutral sheet of the geomagnetic tail as well as with the phenomenon of ''ponderomotive plasma fil1ing'' which determines the relaxation of the plasmasphere after the geomagnetic perturbations. ¿American Geophysical University 1995