First Principles Justification of a ``Single Wave Model'' for Electrostatic Instabilities

Details First Principles Justification of a ``Single Wave Model'' for Electrostatic Instabilities First Principles Justification of a ``Single Wave Model'' for Electrostatic Instabilities

1998-04-14

arxiv.org/abs/physics/9804014v1

Physics

Plasma Physics

13 pages (LaTeX/RevTeX), no figures

Scientific paper

10.1063/1.873302

The nonlinear evolution of a unstable electrostatic wave is considered for a multi-species Vlasov plasma. From the singularity structure of the associated amplitude expansions, the asymptotic features of the electric field and distribution functions are determined in the limit of weak instability, i.e. $\gamma\to 0^+$ where $\gamma$ is the linear growth rate. The asymptotic electric field is monochromatic at the wavelength of the linear mode with a nonlinear time dependence. The structure of the distibutions outside the resonant region is given by the linear eigenfunction but in the resonant region the distribution is nonlinear. The details depend on whether the ions are fixed or mobile; in either case the physical picture corresponds to the single wave model originally proposed by O"Neil, Winfrey, and Malmberg for the interaction of a cold weak beam with a plasma of fixed ions.

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