  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.
