The dynamics of electrons in a low‐frequency wave propagating perpendicular to a uniform magnetic field are studied and the implications of these results for transport and heating by the lower hybrid drift instability are explored. Below a thresholde&fgr;/Ti≊ 0.25–1.0, all electron energy exchange with the wave is reversible and no plasma transport is possible. Above this threshold, trapping of electrons by the wave potentials takes place and causes irreversible electron heating and diffusion. These results imply that anomolous transport in inhomogeneous plasma with weak drifts (diamagnetic velocity less than the ion thermal velocity) may be substantially less than previously predicted.