Observations by Topaz 3 show ionospheric O+ and H+ ions; with ambient
energies of around 0.3 eV, to be transversely (to the geomagnetic fiel
d) energized, to around 10 eV, within lower hybrid structures composed
of broadband large-amplitude (100-200 mV/m) electrostatic waves. In t
his paper we show that the energization of O+ ions can be explained by
a new nonlinear coherent interaction mechanism involving multiple ele
ctrostatic waves propagating across the magnetic field. Low-energy ion
s, whose velocities are well below the phase velocities of the waves,
are shown to gain energy monotonically increasing in time when average
d over a cyclotron orbit. We examine the properties of this coherent e
nergization mechanism numerically and by an analytical, multiple times
cale, analysis. We find, in accordance with observations, that the tai
l 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.