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- W3100971258 abstract "The amplitude equation for an unstable electrostatic wave is analyzed using an expansion in the mode amplitude $A(t)$. In the limit of weak instability, i.e. $gammato 0^+$ where $gamma$ is the linear growth rate, the nonlinear coefficients are singular and their singularities predict the dependence of $A(t)$ on $gamma$. Generically the scaling $|A(t)|=gamma^{5/2}r(gamma t)$ as $gammato 0^+$ is required to cancel the coefficient singularities to all orders. This result predicts the electric field scaling $|E_k|simgamma^{5/2}$ will hold universally for these instabilities (including beam-plasma and two-stream configurations) throughout the dynamical evolution and in the time-asymptotic state. In exceptional cases, such as infinitely massive ions, the coefficients are less singular and the more familiar trapping scaling $|E_k|simgamma^2$ is recovered." @default.
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- W3100971258 date "1998-09-01" @default.
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- W3100971258 title "Amplitude equations for electrostatic waves: Multiple species" @default.
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- W3100971258 doi "https://doi.org/10.1063/1.532635" @default.
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