  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 jet-like 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 burn-out. 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.
