Theoretical Analysis and PIC Simulations of Electromagnetic Wakefields Excited by Relativistic Beams in Magnetized Plasmas

Abstract

This study presents theoretical and numerical investigation of the coupled longitudinal and radial wakefields excited by ultrarelativistic electron beams propagating through a cold plasma channel subjected to an external axial magnetic field. A fully causal three dimensional Green function formalism is developed directly from the linearized Maxwell fluid equations in the presence of the magnetized plasma dielectric tensor. This unified framework captures the complete electromagnetic response, including the induction of a transverse plasma current and the resulting hybridization of longitudinal charge separation dynamics with cyclotron driven transverse motion. The analytical treatment reveals how magnetization modifies the effective restoring forces, enhances wake amplitudes, and reshapes the radial focusing defocusing structure of the wake. To validate the theoretical predictions and explore realistic parameter regimes, extensive three dimensional particle in cell simulations are performed using the EPOCH code across wide ranges of plasma density, magnetic field strength, beam Lorentz factor, transverse beam radius, and longitudinal current profiles. The simulations demonstrate excellent quantitative agreement with the analytical Green function solutions, confirming that increasing plasma density substantially amplifies the initial wake amplitude while accelerating the damping of higher order oscillations. Application of an external magnetic field induces coherent high frequency radial oscillations, strengthens focusing forces, and produces a hybrid eigenmode whose properties are absent in the unmagnetized limit. Variations in the driver Lorentz factor lead to rapid convergence toward a universal ultrarelativistic wake structure, while the transverse beam profile controls the radial extent and balance between longitudinal acceleration and transverse focusing.