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

Abstract

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.

13 pages (LaTeX/RevTeX), no figures

References in corpus (4)

• Scaling and singularities in the entrainment of globally-coupled oscillators
• Amplitude Equations for Electrostatic Waves: universal singular behavior in the limit of weak instability
• Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling
• Amplitude Equations for Electrostatic Waves: multiple species

Cited by in corpus (5)

• Long-time discrete particle effects versus kinetic theory in the self-consistent single-wave model
• Contributions of plasma physics to chaos and nonlinear dynamics
• Towards a classification of bifurcations in Vlasov equations
• Nonlinear Density Waves in the Single-Wave Model
• Low-dimensional chaos in the single wave model for self-consistent wave-particle Hamiltonian