  In solar flares, inverse Compton scattering (ICS) of photospheric photons
might give rise to detectable hard X-ray photon fluxes from the corona where
ambient densities are too low for significant bremsstrahlung or recombination.
Gamma-ray lines and continuum in some large flares imply the presence of the
necessary ~100 MeV electrons and positrons, the latter as by-products of GeV
energy ions. Recent observations of coronal hard X-ray sources in particular
prompt us to reconsider here the possible contribution of ICS. We aim to
evaluate the ICS X-ray fluxes to be expected from prescribed populations of
relativistic electrons and positrons in the solar corona. The ultimate aim is
to determine if ICS coronal X-ray sources might offer a new diagnostic window
on relativistic electrons and ions in flares. We use the complete formalism of
ICS to calculate X-ray fluxes from possible populations of flare primary
electrons and secondary positrons, paying attention to the incident photon
angular distribution near the solar surface and thus improving on the
assumption of isotropy made in previous solar discussions. Both primary
electrons and secondary positrons produce very hard ICS X-ray spectra. The
anisotropic primary radiation field results in pronounced centre-to-limb
variation in predicted fluxes and spectra, with the most intense spectra,
extending to the highest photon energies, expected from limb flares. Acceptable
numbers of electrons or positrons could account for RHESSI coronal X/gamma-ray
sources. Some coronal X-ray sources at least might be interpreted in terms of
ICS by relativistic electrons or positrons, particularly when sources appear at
such low ambient densities that bremsstrahlung appears implausible.
