Nonlinear oscillations in warm plasmas with initial velocity perturbations

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Abstract
The Vlasov equation is solved by a phase-space boundary integration method in order to investigate the nonlinear frequency of an electron plasma mode. Unlike the familiar discrete particle simulation codes in which a limited number of particles may be considered, the present model represents a more realistic plasma case in which a very large number (practically unlimited) of plasma particles evolving in their self-consistent collective field is investigated. The unperturbed collisionless one-dimensional plasma system consists of warm electrons having a water-bag distribution to simulate equilibrium, and of static ions. The initial perturbation is introduced by changing the boundaries of the electron plasma such that υu = υ0 (1 + α.sin kx) and υl = − υ0(1 − α sin kx), υu and υl representing the upper and the lower boundaries, respectively. This corresponds to a standing wave perturbation. The results obtained for different wavelength perturbations λ ≡ 2π/k, and for several perturbation amplitudes α, are presented and discussed.