Direct laser acceleration of electrons in the plasma bubble by tightly focused laser pulses

We present an analytical theory that reveals the importance of the longitudinal laser electric field in the course of the resonant acceleration of relativistic electrons by a tightly confined laser beam. It is shown that this laser field component always counteracts the transverse one and effectively decreases the final energy gain of electrons via the direct laser acceleration (DLA) mechanism. This effect is demonstrated by carrying out particle-in-cell simulations of the DLA of the electrons injected into the accelerating phase of the plasma wake. It is shown that the electron energy gain from the wakefield is substantially compensated by the quasiresonant energy loss to the longitudinal laser field component. The analytically obtained scalings and estimates are in good agreement with the results of the numerical simulations.