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Linear-field particle acceleration in free space (which is distinct from geometries like the linac that requires components in the vicinity of the particle) 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 linear-field particle acceleration in free space is very doubtful given that first-order electron-photon interactions are forbidden in free space. Nevertheless, we chose to develop an accurate and truly predictive theoretical formalism to explore this remote possibility when intense, few-cycle electromagnetic pulses are used in a computational experiment. The formalism includes exact treatment of Maxwell's equations and exact treatment of the interaction among the multiple individual particles at near and far field. Several surprising results emerge. We find that electrons interacting with intense laser pulses in free space are capable of gaining substantial amounts of energy that scale linearly with the field amplitude. For example, 30 keV electrons (2.5% energy spread) are accelerated to 61 MeV (0.5% spread) and to 205 MeV (0.25% spread) using 250 mJ and 2.5 J lasers respectively. These findings carry important implications for our understanding of ultrafast electron-photon interactions in strong fields., Singapore. Agency for Science, Technology and Research (Grant No. 1426500054), European Commission. Framework Programme for Research and Innovation (Grant Agreement No. 328853−MC−BSiCS), United States. Department of Energy. Laboratory Technology Research Program (contract DE-AC02-76SF00515), United States. Army Research Office (contract no. W911NF-13-D0001)

We propose an all-optical, three-dimensional electron pulse compression scheme in which Hermite–Gaussian optical modes are used to fashion a three-dimensional optical trap in the electron pulse's rest frame. We show that the correct choices of optical incidence angles are necessary for optimal compression. We obtain analytical expressions for the net impulse imparted by Hermite–Gaussian free-space modes of arbitrary order. Although we focus on electrons, our theory applies to any charged particle and any particle with non-zero polarizability in the Rayleigh regime. We verify our theory numerically using exact solutions to Maxwell's equations for first-order Hermite–Gaussian beams, demonstrating single-electron pulse compression factors of >10[superscript 2] in both longitudinal and transverse dimensions with experimentally realizable optical pulses. The proposed scheme is useful in ultrafast electron imaging for both single- and multi-electron pulse compression, and as a means of circumventing temporal distortions in magnetic lenses when focusing ultrashort electron pulses. Other applications include the creation of flat electron beams and ultrashort electron bunches for coherent terahertz emission., United States. Army Research Office (Contract No. W911NF-13-D-0001), United States. Defense Advanced Research Projects Agency (DARPA Young Faculty Award, Grant No. D13AP00050), Alexander von Humboldt-Stiftung, Singapore. Agency for Science, Technology and Research

We propose a direct electron acceleration scheme that uses a two-color pulsed radially polarized laser beam. The two-color scheme achieves electron acceleration exceeding 90% of the theoretical energy gain limit, over twice of what is possible with a one-color pulsed beam of equal total energy and pulse duration. The scheme succeeds by exploiting the Gouy phase shift to cause an acceleration-favoring interference of fields only as the electron enters its effectively final accelerating cycle. Optimization conditions and power scaling characteristics are discussed., National Science Foundation (U.S.) (NSF grant NSF-018899-001), Singapore. Agency for Science, Technology and Research

We derive an asymptotically accurate formula for the beam waist of ultrashort, tightly-focused fundamental linearly-polarized, radially-polarized, and azimuthally-polarized modes in free space. We compute the exact beam waist via numerical cubature to ascertain the accuracy with which our formula approximates the exact beam waist over a broad range of parameters of practical interest. Based on this, we describe a method of choosing parameters in the model given the beam waist and pulse duration of a laser pulse., Comment: 5 pages, 3 figures. Liang Jie Wong, Franz X. K\"artner, and Steven G. Johnson, "Improved beam waist formula for ultrashort, tightly focused linearly, radially, and azimuthally polarized laser pulses in free space,"

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., Singapore. Agency for Science, Technology and Research, National Science Foundation (U.S.) (NSF grant NSF-018899-001)