|Source||United States Department of Energy Office of Scientific and Technical Information|
|Subject Keyword||PLASMA PHYSICS AND FUSION TECHNOLOGY ♦ BOLTZMANN-VLASOV EQUATION ♦ ASYMPTOTIC SOLUTIONS ♦ PLASMA WAVES ♦ NONLINEAR PROBLEMS ♦ AMPLITUDES ♦ DISTRIBUTION FUNCTIONS ♦ DIFFERENTIAL EQUATIONS ♦ EQUATIONS ♦ Fusion Energy- Plasma Research- Wave Phenomena|
|Abstract||A weakly nonlinear analysis of the Vlasov equation is made in the case of small amplitude Langmuir waves. The nonlinear terms are treated as a small perturbation in the framework of the asymptotic theory of Krylov and Bogoliubov. In order to apply this method, the Vlasov system of equations is transformed by taking as new unknown functions a complete system of constants of the motions of the linearized equations. Such a system can be found with the help of essentially Van Kampen's and Case's expansion in normal modes. Resonant wave particle interaction is avoided by cutting off the distribution functions in velocity space and by considering waves of phase velocities larger than the cutoff. In this case, the main physical effect is mode coupling and Davidson's nonlinear system of equations on the wave amplitudes is recovered. The main point is that the derivation is made without neglecting the free streaming portions of the distribution functions. A discussion of the validity of the approximation and of the relevant time scales is presented.|
|Learning Resource Type||Article|
|Publisher Department||Association Euratom-CEA Sur la Fusion, Departement de Physique du Plasma et de la Fusion Controlee, Centre d'Etudes Nuclaires, Boite Postale n 6, 92260 Fontenay-Aux-Roses, France|
|Publisher Place||United States|
|Journal||J. Math. Phys.|
|Organization||Association Euratom-CEA Sur la Fusion, Departement de Physique du Plasma et de la Fusion Controlee, Centre d'Etudes Nuclaires, Boite Postale n 6, 92260 Fontenay-Aux-Roses, France|
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