  We hypothesize that a charged particle in unbounded vacuum can be
substantially accelerated by a force linear in the electric field of a
propagating electromagnetic wave only if the accelerating field is capable of
bringing the particle to a relativistic energy in its initial rest frame during
the interaction. We consequently derive a general formula for the acceleration
threshold of such schemes and support our conclusion with the results of
numerical simulations over a broad range of parameters for different kinds of
pulsed laser beams.
