Excitation of Wakefields in Graphene Layers: PIC Simulations vs. Hydrodynamic Model

The interaction between charged particles and graphene layers can lead to the collective oscillation of free electrons within the graphene shell, resulting in electromagnetic modes. These plasmonic modes offer strong potential for enabling ultra-high acceleration gradients in particle acceleration systems. Their behavior can be effectively explored using both particle-based simulations and analytical modeling approaches. This chapter begins by introducing the linearized hydrodynamic model, which provides an analytical framework for describing the plasmonic modes excited by a point-like charge interacting with graphene layers. In this model, the free electron gas at the layers is treated as a plasma, governed by the linearized continuity and momentum equations with different solid-state properties such as the interactions with acoustic modes, a quantum correction, and the scattering due to ionic-lattice charges. Subsequently, the plasmonic excitations obtained from the hydrodynamic model are compared with those derived from PIC simulations performed with the WarpX code. While the hydrodynamic model offers analytical insight into the excitation of plasmonic modes, the PIC simulations provide a more comprehensive treatment of nonlinear and collective effects. The comparison reveals consistent trends in mode structure but highlights differences in amplitude and spatial results. The analysis highlights key similarities, distinctions, and constraints between the two approaches. Overall, the study provides meaningful insight into how graphene layers could be harnessed to improve particle acceleration methods, potentially driving future innovations in high-energy physics and related disciplines.