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Acceleration of a relativistic electron beam by the longitudinal field component of a focused laser beam is optimal when the laser beam is radially polarized. A variational calculation shows that the electron energy gain in a laser beam of given power cannot greatly exceed that available from a Gaussian beam. Particle trajectories calculated in a radially polarized Gaussian beam indicate that transverse forces focus and recollimate appropriately phased off- axis electrons over the acceleration length.
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Gerald T. Moore, Erik J. Bochove, Marlan O. Scully, "Laser linac in vacuum: assessment of a high-energy particle accelerator," Proc. SPIE 1497, Nonlinear Optics and Materials, (1 September 1991); https://doi.org/10.1117/12.46789