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A laser plasma accelerator (LPA) has the potential to realize compact free-electron laser (FEL) radiation at the regular laboratory scale. However, large initial angular divergence and energy spread dramatically hinder ways to transport the beam and realize FEL radiation. Although methods have been proposed to solve these problems, the relatively large jitter, including transverse position jitter and energy jitter, still limits the advance of these experiments. In this paper a simple method to realize coherent harmonic generation based on a LPA beam is proposed. The scheme is very compact, adopting a high-power laser split from the driver laser, a short modulator and a short radiator which has a great tolerance to these typical types of jitter. Numerical simulations indicate that coherent third-harmonic radiation with gigawatt-level power and single spike spectra can be obtained, verifying the feasibility of the scheme and indicating the capability to generate ultrashort fully coherent radiation.

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