  Particle energy chirp is shown to be a useful instrument in the staging laser
wake field acceleration directed to generation of high-quality dense electron
beams. The chirp is a necessary tool to compensate non-uniformity of
acceleration field in longitudinal direction and achieve essential reduction of
energy dispersion. This is demonstrated via particle-in-cell simulations
exploiting the splitting technique for plasma and beam electrons. Properly
chosen beam chirps allow decrease in the energy dispersion of order of
magnitude in every single stage during acceleration to the GeV energy range.
