dorsal/arxiv
View SchemaNonlinear saturation of electrostatic waves: mobile ions modify trapping scaling
| Authors | John David Crawford, Anandhan Jayaraman |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9606005 |
| URL | https://arxiv.org/abs/patt-sol/9606005 |
| DOI | 10.1103/PhysRevLett.77.3549 |
| Journal | Phys. Rev. Lett. 77 (1996) 3549. |
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 $\gamma\rightarrow0^+$, 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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"abstract": "The amplitude equation for an unstable electrostatic wave in a multi-species\nVlasov plasma has been derived. The dynamics of the mode amplitude $\\rho(t)$ is\nstudied using an expansion in $\\rho$; in particular, in the limit\n$\\gamma\\rightarrow0^+$, the singularities in the expansion coefficients are\nanalyzed to predict the asymptotic dependence of the electric field on the\nlinear growth rate $\\gamma$. Generically $|E_k|\\sim \\gamma^{5/2}$, as\n$\\gamma\\rightarrow0^+$, but in the limit of infinite ion mass or for\ninstabilities in reflection-symmetric systems due to real eigenvalues the more\nfamiliar trapping scaling $|E_k|\\sim \\gamma^{2}$ is predicted.",
"arxiv_id": "patt-sol/9606005",
"authors": [
"John David Crawford",
"Anandhan Jayaraman"
],
"categories": [
"patt-sol",
"nlin.PS",
"plasm-ph"
],
"doi": "10.1103/PhysRevLett.77.3549",
"journal_ref": "Phys. Rev. Lett. 77 (1996) 3549.",
"title": "Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling",
"url": "https://arxiv.org/abs/patt-sol/9606005"
},
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