A novel regime of self-compression is proposed for plasma-based backward Raman amplification(BRA) upon flying focus. By using a pumping focus moving with a speed equal to the group velocity of stimulated Raman backscattering(SRBS), only a short part of SRBS which does always synchronize with the flying focus can be amplified. Due to the asymmetrical amplification, the pulse can be directly compressed in the linear stage of BRA. Therefore, instead of a short pulse, the Raman spontaneous or a long pulse can seed the BRA amplifiers. The regime is supported by the 2D particle-in-cell(PIC) simulation without a seed, presenting that the pump pulse is compressed from 26ps to 116fs, with an output amplitude comparable with the case of a well-synchronized short seed. This method provides a significant way to simplify the Raman amplifiers and overcome the issue of synchronization jitter between the pump and the seed.
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