Multiple water-bag model and nonlinear plasma oscillations: appearance of a new pole

The complete second-order theory of the multiple water-bag model is developed for one-dimensional collisionless electrostatic waves, in terms of the initial value problem. Nonlinear frequency spectra are obtained in Van Kampen's formulation, and a new pole, already predicted by R. W. B. Best, appears for hot plasmas. This theory is successfully checked by a full numerical experiment of the Vlasov-Poisson system.