The achievable energy and the stability of accelerated electron beams have been the most critical issues in laser wakefield acceleration. As laser propagation, plasma wave formation and electron acceleration are highly nonlinear processes, the laser wakefield acceleration (LWFA) is extremely sensitive to initial experimental conditions. We propose a simple and elegant waveform control method for the LWFA process to enhance the performance of a laser electron accelerator by applying a fully optical and programmable technique to control the chirp of PW laser pulses. We found sensitive dependence of energy and stability of electron beams on the spectral phase of laser pulses and obtained stable 2-GeV electron beams from a 1-cm gas cell of helium. The waveform control technique for LWFA would prompt practical applications of centimeter-scale GeV-electron accelerators to a compact radiation sources in the x-ray and γ-ray regions.
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