  Linear acceleration in free space is a topic that has been studied for over
20 years, and its ability to eventually produce high-quality, high energy
multi-particle bunches has remained a subject of great interest. Arguments can
certainly be made that such an ability is very doubtful. Nevertheless, we chose
to develop an accurate and truly predictive theoretical formalism to explore
this remote possibility in a computational experiment. The formalism includes
exact treatment of Maxwell's equations, exact relativistic treatment of the
interaction among the multiple individual particles, and exact treatment of the
interaction at near and far field. Several surprising results emerged. For
example, we find that 30 keV electrons (2.5% energy spread) can be accelerated
to 7.7 MeV (2.5% spread) and to 205 MeV (0.25% spread) using 25 mJ and 2.5 J
lasers respectively. These findings should hopefully guide and help develop
compact, high-quality, ultra-relativistic electron sources, avoiding
conventional limits imposed by material breakdown or structural constraints.
