  Previous theoretical considerations of electron beam relaxation in
inhomogeneous plasmas have indicated that the effects of the irregular solar
wind may account for the poor agreement of homogeneous modelling with the
observations. Quasi-linear theory and Hamiltonian models based on Zakharov's
equations have indicated that when a level of density fluctuations is above a
given threshold, density irregularities act to de-resonate the beam-plasma
interaction, restricting Langmuir wave growth on the expense of beam energy.
This work presents the first fully kinetic particle-in-cell (PIC) simulations
of beam relaxation under the influence of density irregularities. We aim to
independently determine the influence of background inhomogeneity on the
beam-plasma system, and to test theoretical predictions and alternative models
using a fully kinetic treatment. We carry out 1D PIC simulations of a
bump-on-tail unstable electron beam in the presence of increasing levels of
background inhomogeneity using the fully electromagnetic, relativistic EPOCH
PIC code. We find that in the case of homogeneous background plasma density,
Langmuir wave packets are generated at the resonant condition and then
quasi-liear relaxation leads to a dynamic increase of wavenumbers generated. No
electron acceleration is seen - unlike in the inhomogeneous experiments, all of
which produce high-energy electrons. For the inhomogeneous experiments we also
observe the generation of backwards propagating Langmuir waves, which is shown
directly to be due to the refraction of the packets off the density gradients.
Our fully kinetic PIC simulations broadly confirm the findings of quasi-linear
theory and the Hamiltonian model based on Zakharov's equations. Strong density
fluctuations modify properties of excited Langmuir waves altering their
dispersion properties.
