Excess pressure and electric fields in nonideal plasma hydrodynamics

Nonideal plasmas have nontrivial space and time correlations, which simultaneously impact both the excess thermodynamic quantities as well as the collision processes. However, hydrodynamics models for designing and interpreting nonideal plasma experiments, such as inertial-confinement fusion experiments, typically neglect electrodynamics, although some models include electric fields indirectly through a generalized Fick's law. However, because most transport models are not computed self-consistently with the equation of state, there is double counting of the forces in the excess thermodynamic quantities and the collision terms. Here we employ the statistical mechanical hydrodynamic theory of Irving and Kirkwood [J. Chem. Phys. 18, 817 (1950)] to examine inhomogeneous, nonideal plasmas that contain electric fields. We show that it is not possible to simultaneously separate terms that correspond to electric fields and excess pressure; rather, these quantities arise from the same interparticle Coulomb forces. Moreover, new terms associated with nonlocality appear in the presence of strong inhomogeneities.

Figure 1

Ionization and pair correlations for a binary-ionic mixture. (a) The top panel shows the mean ionization state (MIS) for a model system of plastic composed of equal densities of hydrogen and carbon (a CH plastic) with densities $n_H=n_C=1\times {10}^{23}{\mathrm{cm}}^{-3}$ and nuclear charges $Z=1$ and $Z=6$. (b)–(e) The various contributions of the total correlation functions $h_{\alpha \beta }\left(r\right)$ to the total pressure are shown for a model system of CH plastic, with $n_H=n_C=1\times {10}^{23}{\mathrm{cm}}^{-3}$, heated to different temperatures: (b) 10 eV, (c) 21 eV, (d) 127 eV, and (e) 545 eV. The MD results are shown with solid lines, and the Debye-Hückel results (8) are shown with dashed lines. We see that the cross-correlation functions cannot be neglected because they are of the order of the mutual terms. Also, it is well known that the Debye-Hückel model does not capture the different peaks of the correlation functions, in contrast with MD.

Figure 2

The ionic pressure, in units of $nT$, as a function of temperature, from MD (dots) and the Debye-Hückel (dashed curve) prediction from (10). We see that the Debye-Hückel model is in good agreement with the MD results in the high-temperature limit but differs from the MD results in the low-temperature limit (i.e., in the strongly coupled regime).