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Nonlinear Saturation of an Electrostatic Wave: Mobile Ions Modify Trapping Scaling
Physical Review Letters
The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude ρ(t) is studied using an expansion in ρ; in particular, in the limit γ→0^+, the singularities in the expansion coefficients are analyzed to predict the asymptotic dependence of the electric field on the linear growth rate γ. Generically |E_k|∼γ^5/2, as γ→0^+, but in the limit of infinite ion mass or for instabilities in reflection-symmetric systems duedoi:10.1103/physrevlett.77.3549 pmid:10062248 fatcat:4mwsmqgswjgorlwmhujfcctwc4