  Solar flare hard X-ray spectra from RHESSI are normally interpreted in terms
of purely collisional electron beam propagation, ignoring spatial evolution and
collective effects. In this paper we present self-consistent numerical
simulations of the spatial and temporal evolution of an electron beam subject
to collisional transport and beam-driven Langmuir wave turbulence. These
wave-particle interactions represent the background plasma's response to the
electron beam propagating from the corona to chromosphere and occur on a far
faster timescale than coulomb collisions. From these simulations we derive the
mean electron flux spectrum, comparable to such spectra recovered from high
resolution hard X-rays observations of solar flares with RHESSI. We find that a
negative spectral index (i.e. a spectrum that increases with energy), or local
minima when including the expected thermal spectral component at low energies,
occurs in the standard thick-target model, when coulomb collisions are only
considered. The inclusion of wave-particle interactions does not produce a
local minimum, maintaining a positive spectral index. These simulations are a
step towards a more complete treatment of electron transport in solar flares
and suggest that a flat spectrum (spectral index of 0 to 1) down to thermal
energies maybe a better approximation instead of a sharp cut-off in the
injected electron spectrum.
