Electron trapping and acceleration by drift electric fields in plasma two-stream instability

We investigated electron acceleration during the nonlinear stage of the two-stream instability, combining one-dimensional particle-in-cell simulations with Hamiltonian analysis. The simulations show that a drift electric field emerges from mode coupling, facilitating stepwise, ‘hopping’–type acceleration of electrons across successive wave packets. By tracking particle trajectories in phase space, we identify two distinct populations: trapped electrons that comove with electron holes and high-energy electrons that gain energy through repeated interactions with drifting potential wells. Using a sawtooth electric field model and a harmonic oscillator approximation, we derive the maximum attainable electron energy and show that it is independent of plasma density but scales quadratically with the initial beam momentum. These findings elucidate the role of drift fields in shaping electron energy spectra during beam-driven instabilities and provide a theoretical framework for understanding kinetic processes in plasma microturbulence and astrophysical environments.