Universal scalings for laser acceleration of electrons in ion channels

Abstract

We analytically investigate the acceleration of electrons undergoing betatron oscillations in an ion channel, driven by a laser beam propagating with superluminal (or luminal) phase velocity. The universal scalings for the maximum attainable electron energy are found for arbitrary laser and plasma parameters by deriving a set of dimensionless equations for paraxial ultra-relativistic electron motion. One of our analytic predictions is the emergence of forbidden zones in the electrons' phase space. For an individual electron, these give rise to a threshold-type dependence of the final energy gain on the laser intensity. The universal scalings are also generalized to the resonant laser interaction with the third harmonic of betatron motion and to the case when the laser beam is circularly polarized.