Nonlinear oscillations in warm plasmas with initial velocity perturbations

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 υ_u = υ₀ (1 + α.sin kx) and υ_l = - υ₀(1 - α sin kx), υ_u and υ_l 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.