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A predicted effect of current shot-noise suppression at optical-frequencies in a drifting charged-particle-beam and the corresponding process of particles self-ordering are analyzed in a one-dimensional (1D) model and verified by three-dimensional numerical simulations. The analysis confirms the prediction of a 1D single mode Langmuir plasma wave model of longitudinal plasma oscillation in the beam, and it defines the regime of beam parameters in which this effect takes place. The suppression of relativistic beam shot noise can be utilized to enhance the coherence of free electron lasers and of any coherent radiation device using an electron beam.