This paper presents a comprehensive numerical study of vacuum electron acceleration driven by Hermite–cosh–Gaussian (HcG) laser pulses, emphasizing beam structure control as a route to enhance the efficiency and scalability of direct laser acceleration (DLA). The combined influence of the Hermite index ( \(\:s\) ), cosh–Gaussian decentered parameter ( \(\:b\) ), linear chirp parameter ( \(\:C\) ), and polarization state is systematically analyzed. The simulations reveal three distinct acceleration stages governed by a phase synchronization process, with the quasi-static phase identified as the regime of maximal energy transfer. Importantly, it is demonstrated that an optimally tailored linear chirp can dramatically enhance energy gain, and tuning the parameter \(\:b\) leads to improved field localization and extended synchronism, yielding peak energies up to \(\:\approx\:8\:\text{GeV}\) . A decisive role of polarization is revealed: circular polarization not only maximizes energy transfer but also suppresses sensitivity to the initial phase, thereby ensuring stable and reproducible acceleration. Furthermore, higher-order HcG modes are shown to expand the effective injection window, allowing even off-axis electrons to reach substantial energies. These findings demonstrate that chirped HcG beams, through polarization- and chirp-controlled beam structure, offer a versatile and efficient driver for compact next-generation laser-based accelerators.
