  In recent work we suggested that photons of energy >100 MeV detected from
GRBs by the Fermi Satellite are produced via synchrotron emission in the
external forward shock with a weak magnetic field - consistent with shock
compressed upstream magnetic field of a few tens of micro-Gauss. Here we
investigate whether electrons can be accelerated to energies such that they
radiate synchrotron photons with energy up to about 10 GeV in this particular
scenario. We do this using two methods: (i) we check if these electrons can be
confined to the shock front; and (ii) we calculate radiative losses while they
are being accelerated. We find that these electrons remain confined to the
shock front, as long as the upstream magnetic field is >~ 10 micro-Gauss, and
don't suffer substantial radiative losses, the only condition required is that
the external reverse shock emission be not too bright: peak flux less than 1 Jy
in order to produce photons of 100 MeV, and less than ~100 mJy for producing
1-GeV photons. We also find that the acceleration time for electrons radiating
at 100 MeV is a few seconds (in observer frame), and the acceleration time is
somewhat longer for electrons radiating at a few GeV. This could explain the
lack of >100 MeV photons for the first few seconds after the trigger time for
long GRBs reported by the Fermi Satellite, and also the slight lag between
photons of GeV and 100 MeV energies. We model the onset of the external forward
shock light curve in this scenario and find it consistent with the sharp rise
observed in the 100-MeV light curve of GRB080916C and similar bursts.
