Abstract
A numerical simulation concerning the spatial evolution of electron plasma waves and electron distributions in collisionless plasmas is performed. Only those particles in and around the resonant region are followed numerically, while the bulk plasma is treated analytically. Our results are in good agreement with existing theoretical results as well as experimental observations. The method introduced here is valid for waves with arbitrary amplitude. It does not depend on either a large-amplitude asymptotic expansion or a small-amplitude perturbation scheme.