Theory of Excited Plasma Waves

Abstract

The excitation of oscillations in a uniform plasma by an injected electron beam is considered. The dispersion relation for this system is derived by means of Fourier-Laplace transform method. The solutions of the dispersion relation are obtained which yield the characteristics of excited waves; the frequency, the phase velocity and the time-rate of wave-growth as functions of the wave number. It is demonstrated that the wave characteristics are varied by the influence of thermal velocity of electrons in the main plasma and by taking the ratio of electron density in the beam to that in the main plasma over a wide range of values. It is then examined that both the velocity spread in the beam and collisions in the medium have the decaying effect on the growing wave. By the use of the above results the case is also discussed where the main plasma is bounded by ideally thin sheaths.