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.
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