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Electron acceleration by transversely echelon phase-modulated (EPM) circularly polarized (CP) intense laser pulse is investigated. Solution of the relativistic electron equations of motion shows that the CP EPM light wave structure can disrupt the harmonic response of a trapped electron not only in the transverse direction but also in the direction of laser propagation. In each laser cycle, there can be a net gain in the electron's transverse momentum, which is promptly converted into the forward direction by the Lorentz force. As a result, the electron can be trapped and accelerated in the favorable phase of the laser for a rather long time. Its momentum gain then accumulates and can eventually reach high levels. It is also found that with the CP EPM laser, the net acceleration of the electron is not sensitive to its initial position and velocity relative to the phase of the laser fields, so that such a laser can also be useful for accelerating thermal electron bunches to high energies.


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