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Universal scalings for laser acceleration of electrons in ion channels

Direct laser acceleration of electrons in ion channels is investigated in a general case when the laser phase velocity is greater than (or equal to) the speed of light. Using the similarity of the equations of motion for ultra-relativistic electrons, we develop a universal scaling theory that gives the maximum possible energy that can be attained by an electron for given laser and plasma parameters. The theory predicts appearance of forbidden zones in the phase space of the particle, which manifests itself as an energy gain threshold. We apply the developed theory to find the conditions needed for an energy enhancement via a resonant interaction between the third harmonic of betatron oscillations and the laser wave. The theory is also used to analyze electron dynamics in a circularly polarized laser.