The trapping and acceleration of nonmonoenergetic electron bunches in a wake field wave excited by a laser pulse in a plasma channel is studied. Electrons are injected into the region of the wake wave potential maximum at a velocity lower than the phase velocity of the wave. The paper analyzes the grouping of bunch electrons in the energy space emerging in the course of acceleration under certain conditions of their injection into the wake wave and minimizing the energy spread for such electrons. The factors determining the minimal energy spread between bunch electrons are analyzed. The possibility of monoenergetic acceleration of electron bunches generated by modern injectors in a wake wave is analyzed.
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