  The multi-stage technique for laser driven acceleration of electrons become a
critical part of full-optical, jitter-free accelerators. Use of several
independent laser drivers and shorter length plasma targets allows the stable
and reproducible acceleration of electron bunches (or beam) in the GeV energies
with lower energy spreads. At the same time the charge coupling, necessary for
efficient acceleration in the consecutive acceleration stage(s), depends
collectively on the parameters of the injected electron beam, the booster
stage, and the non-linear transverse dynamics of the electron beam in the laser
pulse wake. An unmatched electron beam injected in the booster stage(s), and
its non-linear transverse evolution may result in perturbation and even
reduction of the field strength in the acceleration phase of the wakefield.
Analysis and characterization of charge coupling in multi-stage laser wakefield
acceleration (LWFA) become ultimately important. Here, we investigate two-stage
LWFA via fully relativistic multi-dimensional particle-in-cell simulations, and
underlying the most critical parameters, which affect the efficient coupling
and acceleration of the electron beam in the booster stage.
