In this paper, an economical low-noise plasma simulation model originated by Denair is applied to a series of problems associated with electrostatic wave propagation in a one-dimensional, collisionless, Maxwelllan plasma, in the absence of magnetic field. In Part I, the model is described and tested, first in the absence of an applied signal, and then with a small amplitude perturbation. These tests serve to establish the low-noise features of the model, and to verify the theoretical linear dispersion relation at wave energy levels as low as 10 of the plasma thermal energy: better quantitative results are obtained, for comparable computing time, than can be obtained by conventional particle simulation models, or direct solution of the Vlassov equation. The method is then used to study propagation of an essentially monochromatic plane wave. Results on amplitude oscillation and nonlinear frequency shift are compared with available theories. The additional phenomena of sideband instability and satellite growth, stimulated by large amplitude wave propagation and the resulting particle trapping, are described in Part II.
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