Despite considerable progress in multi-stage laser wakefield acceleration (MSLWFA), efficient coupling between stages and the impact of laser–beam injection delay remains open challenges. A two-stage LWFA scheme is demonstrated using particle-in-cell (PIC) simulations, capable of producing multi-GeV electron beams over millimeter-scale propagation lengths. In the first stage, a high-intensity laser pulse (with \(\:{a}_{0}=7.7,\:{\:w}_{0}=20\:\mu m,\:\tau\:=30\:fs,\:\) \(\:E=30\:J\) , \(\:\:{\lambda\:}_{0}\:\) = 800 \(\:nm\) and \(\:{I}_{0}=1.2\:\times\:{10}^{20}\:{W/cm}^{2}\) ) propagates through a neutral helium (He) gas target inside a gas cell, with ionization modeled self-consistently to produce a fully ionized plasma at a plateau density \(\:7\:\times\:{10}^{18}\:{cm}^{-3}\) , generating a high-quality 1 GeV electron beam. This beam is then injected into a second stage inside the same gas cell, where systematically varying the injection delay enhances the injected bunch energy to 2.5 GeV and boosts background trapped electrons to 3 GeV, while reducing energy spread and preserving charge. These findings underscore the critical role of synchronization and plasma tailoring strategies relevant for future multi-pulse and flying-focus LWFA configurations.
