Abstract
We study stationary waves of envelopes in a nonrelativistic electron stream on a fixed ion background. It is shown that the velocity of the stationary wave of an envelope is always equal to the velocity of the unperturbed electron stream. In the adiabatic approximation it is found that each perturbation of the envelopes propagates with velocity of the unperturbed stream. The result is of interest for the theory of nonlinear waves in dispersive media.
Similar content being viewed by others
Literature cited
S. A. Akhmanov and R. V. Khokhlov, “New developments in nonlinear optics,” Usp. Fiz. Nauk,95, No. 1, 231–247 (1968).
G. A. Askar'yan, “Action of the gradient of the field on an intense electromagnetic beam on electrons and atoms,” Zh. Éksp. i Teor. Fiz.,42, No. 6, 1567 (1962).
L. A. Ostrovskii, “Electromagnetic waves in nonlinear media with dispersion,” Zh. Tekh. Fiz.,33, No. 8, 905 (1963).
G. B. Whitham, “Nonlinear dispersive waves,” Proc. Roy. Soc.,283 A, No. 1393, 238 (1965).
A. G. Litvak, “Self-focusing of electromagnetic waves in a plasma,” Izv. VUZ. Radiofiz.,9, No. 5, 900 (1965).
L. A. Ostrovskii, “Propagation of wave packets and space-time self-focusing in a nonlinear medium,” Zh. Éksp. i Teor. Fiz.,51, No. 4, 1189 (1966).
L. A. Cstrovskii, “Shock waves of envelopes,” Zh. Éksp. i Teor. Fiz.,54, No. 4, 1236 (1965).
A. D. Gladun, “Quasishock waves in electron streams,” Zh. Éksp. i Teor. Fiz.,55, No. 2, 499 (1968).
V. I. Petviashvili, “Self-focusing of an ion-sound wave in a plasma,” Zh. Éksp. i Teor. Fiz.,55, No. 3, 917 (1968).
V. I. Petviashvili, “Oscillations of a periodic ion-sound wave,” Zh. Tekh. Fiz.,38, No. 2, 205 (1968).
N. N. Bogolyubov and Yu. A. Mitropol'skii, Asymptotic Methods in the Theory of Nonlinear Oscillations, Gordon and Breach (1962).
G. B. Whitham, “Variational methods and application to water waves,” Proc. Roy. Soc.,299, No. 1456, 6–25 (1967).
J. M. Dowson, “Nonlinear electron oscillations in cold plasma,” Phys. Rev.,113, No. 2, 383 (1959).
R. W. C. Davidson and P. P. J. M. Schram, “Nonlinear osculations in a cold plasma,” Nucl. Fusion,8, No. 3, 183–195 (1968).
Author information
Authors and Affiliations
Additional information
Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 3, pp. 16–23, May–June, 1972.
Rights and permissions
About this article
Cite this article
Gladun, A.D., Korshunov, S.M. Waves of envelopes in electron streams. J Appl Mech Tech Phys 13, 273–280 (1972). https://doi.org/10.1007/BF00850414
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00850414