  We present the analytical and simulated results concerning the influences of
the acceleration gradient in the velocity bunching process, which is a bunch
compression scheme that uses a traveling wave accelerating structure as a
compressor. Our study shows that the bunch compression application with low
acceleration gradient is more tolerant to phase jitter and more successful to
obtain compressed electron beam with symmetrical longitudinal distribution and
low energy spread. We also present a transverse emittance compensation scheme
to compensate the emittance growth caused by the increasing of the space charge
force in the compressing process that is easy to be adjusted for different
compressing factors.
