  A scheme of laser wakefield acceleration, when a relatively rare and long
bunch of non-relativistic or weakly-relativistic electrons is initially in
front of the laser pulse, is suggested and considered. The motion of test
electrons is studied both in the one-dimensional case (1D wakefield) and in the
three-dimensional laser wakefield excited in a plasma channel. It is shown that
the bunch is trapped, effectively compressed both in longitudinal and
transverse directions and accelerated to ultra-relativistic energies in the
region of first accelerating maximum of the wakefield. The accelerated bunch
has sizes much less than the plasma wavelength and relatively small energy
spread.
