الفهرس 
NONLINEAR THEORY OF TWO - STREAMOnly 14 pages are availabe for public view
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Abstract
A multiple timescales perturbation theory has been applied to investigate some nonlinear plasma physics problems. For nonlinear electron plasma oscillations, an expression for the frequency shift due to the thermal motion of the electron is obtained. The frequency shift is found to be proportional to the square of the amplitude of the electric field, which agrees with that obtained by other perturbation methods. For cold nonlinear electron plasma oscillations, the perturbation theory gives a solution which agrees, for small values of amplitude of the electric field, with well known exact results. The problem of the nonlinear time evolution of the warm beam-plasrna instability near the marginally stable state is investigated. The perturbation theory leads to a nonlinear Schrödinger equation governing the finite amplitude of the wave. The coefficients of this equation show that, only if the beam is compressed isothermally, does there exist a range of wavenumbers for which stabilization might occur. This range decreases with an increase of temperature. However, for cold beam-plasma instability, the coefficients of the Schrödinger equation show that the nonlinearity enhances the instability. It is found that the inclusion of higher order terms than third leads to a periodic bounded-type solution which means that a saturation mechanism has been identified. This has been confirmed numerically. The results of perturbation theory has been used in conjunction with a Lagrangian interpolation scheme, suggested by the results of a treatment of a cold nonlinear electron plasma oscillation, to give a theory valid for large amplitudes. In particular, the theory now shows the main qualitative feature of the exact solution obtained by numerical simulation namely the phenomenon of overtaking.