Wake field excitation by a train of the laser pulses is an attractive branch of the laser wake field acceleration (LWFA). In this paper, we first discuss analytical formalism for constructing uniform and non-uniform train of laser pulses from a chirped laser pulse in the Michelson interferometer. Afterward, special criteria for resonance generation of wake field with the laser multi-pulses (MPLWFA) are discussed numerically.Weshow that in the nonlinear regime of the laser wake field, a nonuniform train of laser pulse can be attractive in maintaining the resonance condition. For large laser amplitudes, 3
30% increase in the acceleration gradient compared to the uniform train of laser pulses.
