  Non-thermal electron populations are observed throughout the heliosphere. The
relaxation of an electron beam is known to produce Langmuir waves which, in
turn, may substantially modify the electron distribution function. As the
Langmuir waves are refracted by background density gradients and as the solar
and heliospheric plasma density is naturally perturbed with various levels of
inhomogeneity, the interaction of Langmuir waves with non-thermal electrons in
inhomogeneous plasmas is an important topic. We investigate the role played by
ambient density fluctuations on the beam-plasma relaxation, focusing on the
effect of acceleration of beam electrons. The scattering of Langmuir waves off
turbulent density fluctuations is modeled as a wavenumber diffusion process
which is implemented in numerical simulations of the one-dimensional
quasilinear kinetic equations describing the beam relaxation. The results show
that a substantial number of beam electrons are accelerated when the diffusive
time scale in wavenumber space \tau_D is of the order of the quasilinear time
scale \tau_ql, while when \tau_D << \tau_ql, the beam relaxation is suppressed.
Plasma inhomogeneities are therefore an important means of energy
redistribution for waves and hence electrons, and so must be taken into account
when interpreting, for example, hard X-ray or Type III emission from
flare-accelerated electrons.
