Title: Approximation scheme for strongly coupled plasmas: Dynamical theory
Abstract: The authors present a self-consistent approximation scheme for the calculation of the dynamical polarizability $\ensuremath{\alpha}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega})$ at long wavelengths in strongly coupled one-component plasmas. Development of the scheme is carried out in two stages. The first stage follows the earlier Golden-Kalman-Silevitch (GKS) velocity-average approximation approach, but goes much further in its application of the nonlinear fluctuation-dissipation theorem to dynamical calculations. The result is the simple expression for $\ensuremath{\alpha}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega})$, ${\ensuremath{\alpha}}_{\mathrm{GKS}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega})={\ensuremath{\alpha}}_{\mathrm{RPA}}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega})[1+v(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega})]$, where the dynamical screening function $v(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega})$ is expressed in terms of quadratic polarizabilities, and RPA stands for random-phase approximation. Its zero-frequency limit $v(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},0)$ has already been established and analyzed in the earlier GKS work. At high frequency, ${\ensuremath{\alpha}}_{\mathrm{GKS}} (\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\infty})$ exactly satisfies the $\frac{1}{{\ensuremath{\omega}}^{4}}$ moment sum rule. In the second stage, the above dynamical expression is made self-consistent at long wavelengths by postulating that a decomposition of the quadratic polarizabilities in terms of linear ones, which prevails in the $k\ensuremath{\rightarrow}0$ limit for weak coupling, can be relied upon as a paradigm for arbitrary coupling. The result is a relatively simple quadratic integral equation for $\ensuremath{\alpha}$. Its evaluation in the weak-coupling limit and its comparison with known exact results in that limit reveal that almost all important correlational and long-time effects are reproduced by our theory with very good numerical accuracy over the entire frequency range; the only significant defect of the approximation seems to be the absence of the "dominant" $\ensuremath{\gamma}\mathrm{ln}{\ensuremath{\gamma}}^{\ensuremath{-}1}$ ($\ensuremath{\gamma}$ is the plasma parameter) contribution to $\mathrm{Im} \ensuremath{\alpha}(\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}},\ensuremath{\omega})$.
Publication Year: 1979
Publication Date: 1979-05-01
Language: en
Type: article
Indexed In: ['crossref']
Access and Citation
Cited By Count: 46
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