Abstract
The nonlinear interaction of oscillation modes is investigated on the basis of Lagrangian formalism. Equations describing the changes of the bound mode amplitudes versus time, are obtained. It is shown that the energy transformation between different modes is of a periodic nature: if in the initial moment of time an appreciable part of the energy is contained, for example, in them-th mode, then after a period of timeTt (called a time of nonlinear interaction) the energy will be transformed to then-th mode. Expressions forT t for cases with the interaction of two and three modes are obtained. As a particular case the process of nonlinear interaction of the electron “transverse” and “longitudinal” oscillations in the highfrequency hybrid resonance region of a “weakly” inhomogeneous plasma was investigated.
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On leave from the Atomic Energy State Committee, USSR.
The authors are obliged to Prof. Dr. M. El-Nadi and Dr. T. El-Khalafawy for encouragement and support. They also wish to thank Mr. V. A. Utenock for his aid in preparation of this manuscript for publication.
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Demchenko, V.V., El-Naggar, I.A. & Hussein, A.M. To the theory of nonlinear mode coupling in dynamic stabilization of MHD modes. Z. Physik 264, 85–94 (1973). https://doi.org/10.1007/BF01392419
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DOI: https://doi.org/10.1007/BF01392419