Abstract
Using field-theoretic methods, we calculate the internal energy for the One-Component Plasma (OCP). We go beyond the recent calculation by Brilliantov [N. Brilliantov, Contrib. Plasma Phys. 38, 489 (1998)] by including non-Gaussian terms. We show that, for the whole range of the plasma parameter Γ, the effect of the higher-order terms is small and that the final result is not improved relative to the Gaussian theory when compared to simulations.
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Although the deviations are small, we should notice that they are statistically significant since the numerical error given by simulations in this range of Γ is below ±0:02% [11].
X XXX, As a side remark, we note that the application of the cut-off k o to the Two-Component Plasma (TCP) leads to unphysical results. At the Debye-Hückel level, the excess free energy per volume goes for small c ≡ (n + +n −)/V as f ex ∼ −(4πℓB q 2 c 3/2/12π (the already discussed Debye-Hückel limiting law) and as f ex ∼ −(9/π)1/3ℓB q 2 c 4/3 for large c; at this limit total free energy per volume is unbounded from below and non-convex. At finite temperatures, the Maxwell construction leads to the coexistence between states with a zero and an infinite density, which is clearly unphysical and signals that this approach is not appropriate for the TCP. This difference between the OCP and the TCP becomes more transparent in a recent systematic low-density expansion of the free energy, where the TCP expansion coefficients are shown to be dominated by ion-pair formation [18].
R.R. Netz, H. Orland, to be published.
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Moreira, A.G., Netz, R.R. One-component-plasma: Going beyond Debye-Hückel. Eur. Phys. J. D 8, 145–149 (2000). https://doi.org/10.1007/s10053-000-9076-6
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DOI: https://doi.org/10.1007/s10053-000-9076-6