Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling

Details Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling

1996-06-24

arxiv.org/abs/patt-sol/9606005v1

Phys. Rev. Lett. 77 (1996) 3549.

Nonlinear Sciences

Pattern Formation and Solitons

13 pages (Latex/RevTex), 4 postscript encapsulated figures which are included using the utility "uufiles". They should be auto

Scientific paper

10.1103/PhysRevLett.77.3549

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 $\gamma\rightarrow0^+$, 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 $\gamma\rightarrow0^+$, 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.

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