Engineering Physics Annotation << Back NONLINEAR LANGMUIR WAVES IN A COLD COLLISIONLESS PLASMA D.N. GABYSHEV, A.A. RUKHADZE Nonlinear one-dimensional electron oscillations in a cold collisionless plasma in the absence of a magnetic fi eld are considered. The solution of the motion equations of the electron is obtained in terms of the dimensionless momentum and time by using the elliptic integrals. The analytical expressions for the dependence of the momentum of the oscillating electron on time are found as well as for the period of its oscillations. Particular attention is paid to the case of ultrarelativistic oscillations. There is obtained a corresponding limit function that can be expanded into a Fourier series exactly. A possibility of taking into account the heat losses is mentioned. Keywords: nonlinear Langmuir waves, plasma waves, relativistic oscillations, elliptic integrals. Contacts: E-mail: gabyshev-dmitrij@rambler.ru Pp. 53-58.