The invention provides a novel laser-plasma-based source of relativistic electrons; and a method to use laser-driven plasma waves as the basis for the source of electrons. The technique involves a combination of laser beams, which are focused in a plasma. One beam creates a wakefield plasma wave. In one embodiment, the one beam creates a wakefield plasma wave and the other beam alters the trajectory of background electrons, such that they become trapped in the plasma wave and are then accelerated to relativistic velocities, preferably in a distance less than a millimeter. In another embodiment, the second beam removes electrons from atomic ions previously generated by the first beam thereby providing electrons which become trapped in the plasma wave and then accelerated to relativistic velocities.