Observations by Topaz 3 show ionospheric O+ and H+ ions, with ambient energies of around 0.3 eV, to be transversely (to the geomagnetic field) energized, to around 10 eV, within lower hybrid structures composed of broadband large-amplitude (100--200 mV/m) electrostatic waves. In this paper we show that the energization of O+ ions can be explained by a new nonlinear coherent interaction mechanism involving multiple electrostatic waves propagating across the magnetic field. Low-energy ions, whose velocities are well below the phase velocities of the waves, are shown to gain energy monotonically increasing in time when averaged over a cyclotron orbit. We examine the properties of this coherent energization mechanism numerically and by an analytical, multiple timescale, analysis. We find, in accordance with observations, that the tail of the O+ distribution is most likely to be energized. The analysis provides the spatial extent, along the geomagnetic field, of the lower hybrid structures needed for the observed energization. ¿ 1998 American Geophysical Union