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.Energetic particle beams are crucial to the progress of fields across the spectrum of science and technology, from cancer treatment [1] to particle physics [2] to inertial confinement fusion [3], nanolithography [4] and radioactive waste management [5].High-intensity laser systems, made possible by chirped-pulsed amplification [6], can provide accelerating gradients that surpass those of conventional accelerators by as much as six orders of magnitude [7], paving the way to an era of table-top particle accelerators and table-top x-ray laser systems. Although plasma-based acceleration schemes [8] have had much experimental success, the possibility of accelerating particles in vacuum [9,10] remains of great interest since the absence of plasma would preclude problems associated with the inherent instability of laser-plasma interactions.
2Among the many vacuum-based acceleration schemes proposed is the acceleration of particles (primarily) by a force linear in the electric field of the laser [11][12][13][14][15][16][17][18][19]. This scheme may be realized with an electromagnetic wave that vanishes completely on the beam axis except for its longitudinal electric field component. As a result, an on-axis charged particle experiences only a force along the axis. Particles that are slightly off-axis will experience some ponderomotive acceleration due to non-zero transverse field components, but the longitudinal linear force should dominate.In this Letter, we obtain a formula for the threshold power of net linear acceleration (a.k.a. direct acceleration) in unbounded vacuum. We hypothesize that a charged particle (regardless of initial energy) 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. By "substantial acceleration" we mean the ratio of final to initial particle energy 1 0 f . Based on our hypothesis, we derive a formula for the threshold power and compare the formula with the results of exact numerical simulations over a broad range of parameters for different kinds of pulsed laser beams.The accuracy with which the formula matches our numerical simulations lends credence to our hypothesis and sheds light on the physical mechanism that enables net linear acceleration in unbounded vacuum: namely, that the ability of the accelerating field to bring the parti...