Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling

Abstract

The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $\rho (t)$ is studied using an expansion in $\rho$; in particular, in the limit $\gamma \to 0^{+}$, the singularities in the expansion coefficients are analyzed to predict the asymptotic dependence of the electric field on the linear growth rate $\gamma$. Generically $|E_k|\sim {\gamma }^{5/2}$, as $\gamma \to 0^{+}$, but in the limit of infinite ion mass or for instabilities in reflection-symmetric systems due to real eigenvalues the more familiar trapping scaling $|E_k|\sim {\gamma }^2$ is predicted.

13 pages (Latex/RevTex), 4 postscript encapsulated figures which are included using the utility "uufiles". They should be automatically included with the text when it is downloaded. Figures also available in hard copy from the authors ([email protected])

References in corpus (1)

• Amplitude Equations for Electrostatic Waves: universal singular behavior in the limit of weak instability

Cited by in corpus (5)

• First Principles Justification of a ``Single Wave Model'' for Electrostatic Instabilities
• Towards a classification of bifurcations in Vlasov equations
• Amplitude equations for coupled electrostatic waves in the limit of weak instability
• Amplitude Equations for Electrostatic Waves: multiple species
• Synchronization of globally-coupled phase oscillators: singularities and scaling for general couplings