  Most theoretical descriptions of the production of solar flare bremsstrahlung
radiation assume the collision of dilute accelerated particles with a cold,
dense target plasma, neglecting interactions of the fast particles with each
other. This is inadequate for situations where collisions with this background
plasma are not completely dominant, as may be the case in, for example,
low-density coronal sources. We aim to formulate a model of a self-interacting,
entirely fast electron population in the absence of a dense background plasma,
to investigate its implications for observed bremsstrahlung spectra and the
flare energy budget. We derive approximate expressions for the time-dependent
distribution function of the fast electrons using a Fokker-Planck approach. We
use these expressions to generate synthetic bremsstrahlung X-ray spectra as
would be seen from a corresponding coronal source. We find that our model
qualitatively reproduces the observed behaviour of some flares. As the flare
progresses, the model's initial power-law spectrum is joined by a lower energy,
thermal component. The power-law component diminishes, and the growing thermal
component proceeds to dominate the total emission over timescales consistent
with flare observations. The power-law exhibits progressive spectral hardening,
as is seen in some flare coronal sources. We also find that our model requires
a factor of 7 - 10 fewer accelerated electrons than the cold, thick target
model to generate an equivalent hard X-ray flux. This model forms the basis of
a treatment of self-interactions among flare fast electrons, a process which
affords a more efficient means to produce bremsstrahlung photons and so may
reduce the efficiency requirements placed on the particle acceleration
mechanism. It also provides a useful description of the thermalisation of fast
electrons in coronal sources.
