Direct numerical simulations of electron dynamics in externally driven electrostatic waves have been carried out using a relativistic two-fluid one-dimensional Vlasov–Poisson code. When the driver wave has sufficiently large amplitude, ion density holes ( cavitons ) form. The interaction between these cavitons and other incoming Langmuir waves gives rise to substantial local acceleration of groups of electrons, and fine jetlike structures arise in electron phase space.We show that these jets are caused by wave breaking when finite amplitude Langmuir waves experience the ion density gradient at the leading edge of the holes, and are not caused by caviton burnout. An analytical two-fluid model gives the critical density gradient and caviton depth for which this process can occur. In particular, the density gradient critically affects the rate at which a Langmuir wave, moving into the caviton, undergoes Landau damping. This treatment also enables us to derive analytical estimates for the maximum energy of accelerated electrons, and for the energy spectrum along a phase-space jet. These are confirmed by direct numerical simulations.