Abstract
Collective methods of charged particle acceleration provide an approach towards achieving high-energy particle beams with relatively compact accelerator facilities. Among the collective acceleration methods, one of the central places belong to the electron Laser Wakefield Acceleration concept, when the regular accelerating structure in the form of longitudinal electrostatic wave propagating with the phase speed close to speed of light in vacuum is generated by ultrashort laser pulse in collisionless plasma. The review article contains theoretical description of charged particle (electron) interaction with various configurations of the electromagnetic field and with the longitudinal plasma waves. The radiation dominated regimes of the electron interaction with strong electromagnetic waves, when the radiation friction force effects play the key role, are also discussed.
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