Integral equation model for warm and hot dense mixtures

In a previous work [C. E. Starrett and D. Saumon, Phys. Rev. E 87, 013104 (2013)] a model for the calculation of electronic and ionic structures of warm and hot dense matter was described and validated. In that model the electronic structure of one atom in a plasma is determined using a density-functional-theory-based average-atom (AA) model and the ionic structure is determined by coupling the AA model to integral equations governing the fluid structure. That model was for plasmas with one nuclear species only. Here we extend it to treat plasmas with many nuclear species, i.e., mixtures, and apply it to a carbon-hydrogen mixture relevant to inertial confinement fusion experiments. Comparison of the predicted electronic and ionic structures with orbital-free and Kohn-Sham molecular dynamics simulations reveals excellent agreement wherever chemical bonding is not significant.

Figure 1

Ion-ion pair distribution functions for ${\mathrm{CH}}_{1.36}$. Comparison of the IS-TF (solid lines) and OFMD simulation results (dashed lines) in the TF approximation for C-C (black, rightmost lines), C-H (red, middle lines), and H-H (green, leftmost lines).

Figure 2

Comparison of the IS-TF ion-electron pair distribution functions for ${\mathrm{CH}}_{1.36}$ at $2.94{\mathrm{g}/\mathrm{cm}}^3$ and the OFMD simulation results in the TF approximation for carbon (black, rightmost lines), hydrogen (red, leftmost lines). Solid lines are the IS-TF model and dashed lines are the OFMD. Also shown (dotted lines) is the contribution to $g_{ie}\left(r\right)$ from $n_e^{\mathrm{PA}}\left(r\right)$ alone. The thin vertical lines indicate the cutoff radius $r_c$ used to generate the pseudopotentials for H (left) and C (right) in the OFMD simulations.

Figure 3

Ion-ion pair distribution functions for ${\mathrm{CH}}_{1.36}$. Comparison of the IS-QM (solid lines) and the QMD simulations (dashed lines) for C-C (black, rightmost lines), C-H (red, middle lines), and H-H (green, leftmost lines). For panels with only IS-QM curves, corresponding QMD results were not available.

Figure 4

Ion-ion pair distribution functions for pure C. Comparison of the IS-QM (solid lines) and the QMD simulations (dashed lines).