Abstract
It is shown that stochastic instability can arise in the amplification of a real multifrequency signal in resonant amplifiers with distributed interaction that are stable under the influence of a harmonic oscillation. Necessary conditions for the onset of chaos are determined analytically by means of running Lyapunov exponents. Specific results of numerical and analytic studies of the stability or orotron amplifiers are presented.
Similar content being viewed by others
Literature Cited
M. Chodorov and B. Kulke, IEEE Trans.,ED-13, No. 4, 439 (1966).
V. G. Borodenko, N. Ya. Mal'kova, and A. S. Pobedonostsev, Élektron. Tekh., Ser. 1, No. 6, 3 (1968).
V. K. Kornienko and V. S. Miroshnichenko, Izv. Vyssh. Uchebn. Zaved., Radioélektron.,26, No. 3, 93 (1983).
D. M. Vavriv, Élektron. Tekh., Ser. 1, No. 5, 3 (1986).
A. B. Belogortsev, D. M. Vavriv, B. A. Kalugin, and O. A. Tret'yakov, Radiotekhnika, No. 5, 33 (1988).
D. M. Vavriv, Radiotekh. Élektron.,30, No. 7, 1391 (1985).
D. M. Vavriv, O. A. Tret'yakov, and S. A. Sharapov, Élektron. Tekh., Ser. 1, No. 4, 10 (1988).
T. C. Marshall, Free-Electron Lasers, Macmillan, New York (1985).
E. Garate, R. Cherry, A. Fisher, and P. Phillips, J. Appl. Phys.,62, No. 12, 6618 (1988).
D. M. Vavriv and O. A. Tret'yakov, Izv. Vyssh. Uchebn. Zaved., Radiofiz.,27, No. 2, 238 (1984);28, No. 1, 107 (1985).
D. M. Vavriv, Yu. A. Romantsov, and O. A. Tret'yakov, Élektron. Tekh., Ser. 1, No. 10, 3 (1984).
D. M. Vavriv and V. B. Ryabov, Dokl. Akad. Nauk UkrSSR, No. 2, 50 (1990).
J. M. Guckenheimer and Ph. Holmes, Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields, Springer-Verlag, New York (1986).
S. Novak and R. G. Frehlich, Phys. Rev. A,26, No. 6, 3660 (1982).
Yu. D. Kalafati and B. A. Malakhov, Pis'ma Zh. Éksp. Teor. Fiz.,37, No. 10, 486 (1985).
D. M. Vavriv, O. A. Tret'yakov, and I. Yu. Chernyshev, Ratiotekh. Élektron.,34, No. 8, 1698 (1989).
Additional information
Radio-Astronomy Institute, Academy of Sciences of Ukraine. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 35, Nos, 3, 4, pp. 285–294, March–April, 1992.
Rights and permissions
About this article
Cite this article
Vavriv, D.M., Sharapov, S.A. Toward a theory of stability of resonant amplifiers with distributed interaction. Radiophys Quantum Electron 35, 193–198 (1992). https://doi.org/10.1007/BF01038026
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01038026