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

Universal scalings for laser acceleration of electrons in ion channels