dorsal/arxiv
View SchemaAmplitude Equations for Electrostatic Waves: multiple species
| Authors | John David Crawford, Anandhan Jayaraman |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9706001 |
| URL | https://arxiv.org/abs/patt-sol/9706001 |
| DOI | 10.1063/1.532635 |
| Journal | J. Math. Phys., 39 (1998) 4546 |
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. $\gamma\to 0^+$ 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 $\gamma\to 0^+$ is required to cancel the coefficient singularities to all orders. This result predicts the electric field scaling $|E_k|\sim\gamma^{5/2}$ 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 $|E_k|\sim\gamma^2$ is recovered.
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"abstract": "The amplitude equation for an unstable electrostatic wave is analyzed using\nan expansion in the mode amplitude $A(t)$. In the limit of weak instability,\ni.e. $\\gamma\\to 0^+$ where $\\gamma$ is the linear growth rate, the nonlinear\ncoefficients are singular and their singularities predict the dependence of\n$A(t)$ on $\\gamma$. Generically the scaling $|A(t)|=\\gamma^{5/2}r(\\gamma t)$ as\n$\\gamma\\to 0^+$ is required to cancel the coefficient singularities to all\norders. This result predicts the electric field scaling $|E_k|\\sim\\gamma^{5/2}$\nwill hold universally for these instabilities (including beam-plasma and\ntwo-stream configurations) throughout the dynamical evolution and in the\ntime-asymptotic state. In exceptional cases, such as infinitely massive ions,\nthe coefficients are less singular and the more familiar trapping scaling\n$|E_k|\\sim\\gamma^2$ is recovered.",
"arxiv_id": "patt-sol/9706001",
"authors": [
"John David Crawford",
"Anandhan Jayaraman"
],
"categories": [
"patt-sol",
"cond-mat",
"nlin.PS",
"physics.plasm-ph"
],
"doi": "10.1063/1.532635",
"journal_ref": "J. Math. Phys., 39 (1998) 4546",
"title": "Amplitude Equations for Electrostatic Waves: multiple species",
"url": "https://arxiv.org/abs/patt-sol/9706001"
},
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