Trapping, compression, and acceleration of an electron bunch in the nonlinear laser wakefield

A scheme of laser wakefield acceleration, when a relatively rare and long bunch of nonrelativistic 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 (1D) case (1D wakefield) and in the case of three-dimensional laser wakefield excited in a plasma channel. It is shown that for definite parameters of the problem the bunch can be 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.