A Threshold for Laser-Driven Linear Particle Acceleration in Unbounded Vacuum

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.