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A disk model is developed to simulate the propagation of a cylindrical relativistic electron beam through plasma into vacuum via collective acceleration of positive ions from the plasma. Simulation results show dynamic details of electron and ion flow not noticed previously. The high‐energy tail in the ion distribution is attributed to motion of the virtual cathode early in time when the ions enter the system. A comparison between the computer simulation and our analytical model published earlier shows good agreement for the time average behavior of the particles.