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We hypothesize that a charged particle in unbounded vacuum can besubstantially accelerated by a force linear in the electric field of apropagating electromagnetic wave only if the accelerating field is capable ofbringing the particle to a relativistic energy in its initial rest frame duringthe interaction. We consequently derive a general formula for the accelerationthreshold of such schemes and support our conclusion with the results ofnumerical simulations over a broad range of parameters for different kinds ofpulsed laser beams.

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