The second-order force generated by standing Alfv¿n waves in a dipolar magnetospheric geometry is rederived in a more straightforward and accurate way than previously done. The spatial structure of the resulting ponderomotive acceleration consists of regions in which plasma can be trapped between ''diverging'' nodes of the acceleration field (where the acceleration vector points away from the node). The ''specific parallel energy'' (parallel energy per proton mass) of accelerated plasma particles is derived. This quantity maximizes at ''converging'' nodes of the acceleration field (where the acceleration vector points toward the node). For the fundamental standing mode the converging node is at the equatorial plane, and the maximum specific energy there increases rapidly with L (where L is the McIlwain parameter), becoming significant above L=5 for typical wave amplitudes. At L~10, H+ ions should reach energies of ~100 eV and O+ ions energies of ~2 keV. Gravity has little effect on the energization, other than to define the magnetic latitude from which acceleration begins. At reasonably high L, almost all the energization occurs at magnetic latitudes above ¿45¿. For the second harmonic the converging nodes are situated away from the equatorial plane, and accelerated particles starting from rest do not reach that plane. The third harmonic has a converging node at the equatorial plane, and specific energies there are the same as for the fundamental mode. However, the accelerated particles originate from above the diverging nodes at latitudes of about ¿18¿, passing through a larger acceleration field than for the fundamental mode in that region. Particles having initial energies of a few electron volts near the ionosphere may be able to traverse the diverging nodes of the third harmonic and reach the equatorial plane. ¿ American Geophysical Union 1993