Av. Kovalenko et Vp. Kovalenko, LANGMUIR OSCILLATIONS IN A COLD INHOMOGENEOUS-PLASMA, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 53(4), 1996, pp. 4046-4050
One-dimensional nonlinear Langmuir oscillations in a cold inhomogeneou
s plasma are considered. The spatial distribution of the amplitude of
oscillations is set by the initial disturbance and can be arbitrary, i
.e., it is not in any way connected with the inhomogeneity of the plas
ma. Taking place at small spatial gradients of the initial disturbance
because of a growing with time phase shift of oscillations of differe
nt electrons, the effect of formation of narrow density peaks is illus
trated. The density peaks always move in the direction of a decrease o
f ion concentration. In this movement their amplitude can grow or decr
ease depending on the direction of the initial disturbance gradient. A
number of electrons, forming density peaks, reduce with a diminution
of plasma inhomogeneity but the peak amplitudes always increase unlimi
tedly with time up to the self-intersection of electron trajectories.
An equation, making it possible to determine the instant of trajectory
intersection in case of small plasma inhomogeneity of arbitrary kind
and arbitrary gradients of the initial disturbance, is obtained. It is
shown by a numerical calculation that the analytical relations obtain
ed are not essentially changed if one takes into account the nonlinear
ity of corresponding differential equations.