We propose a new approach to high-intensity laser-driven electron acceleration in a plasma. Here, we demonstrate that a plasma wave generated by a stimulated forward-scattering of an incident laser pulse can be in a longest acceleration phase with an incident laser wave. This is why the plasma wave has the maximum amplification coefficient which is determined by the breakdown (overturn) electric field in which the acceleration of injected relativistic beam electrons occurs. We estimate qualitatively the acceleration parameters of relativistic electrons in the field of a plasma wave generated at the stimulated forward scattering of a high-intensity laser pulse in a plasma.
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