Electron kinetic effects in the neutralization process of a longitudinally focused ion beam

This paper investigates electron kinetic effects during the neutralization of a longitudinally focused ion beam pulse, using two-dimensional electrostatic particle-in-cell simulations. A velocity-tilted ion beam pulse compresses as it propagates, capturing electrons from a localized electron source. Results reveal that injected electrons excite large-amplitude electrostatic solitary waves (ESWs) through two-stream instability. These ESWs, manifesting as phase-space electron holes, create deep density depressions and undergo pulsed acceleration during beam compression, significantly reducing neutralization degree. Unlike one-dimensional Bernstein–Greene–Kruskal modes, the two-dimensional ESWs are inherently unstable with finite lifetimes, dissipating more rapidly under compression and causing partial electron loss. Subsequently, compression of the ion beam’s potential well heats the remaining neutralizing electrons non-adiabatically, with temperature scaling as (Formula presented) (Formula presented). Although the total electron number remains nearly constant, this heating elevates the beam’s residual potential, leading to a substantial decline in neutralization degree when evaluated by potential reduction ( (Formula presented) (Formula presented) ) compared to density ratio methods. These findings demonstrate that ESW excitation and electron compression heating critically degrade neutralization in focused beams, highlighting the necessity of kinetic treatments for accurate neutralization assessment.