Ionic Transport Coefficients of Dense Plasmas without Molecular Dynamics

We present a theoretical model that allows a fast and accurate evaluation of ionic transport properties of realistic plasmas spanning from warm and dense to hot and dilute conditions, including mixtures. This is achieved by combining a recent kinetic theory based on effective interaction potentials with a model for the equilibrium radial density distribution based on an average atom model and the integral equations theory of fluids. The model should find broad use in applications where nonideal plasma conditions are traversed, including inertial confinement fusion, compact astrophysical objects, solar and extrasolar planets, and numerous present-day high energy density laboratory experiments.

Figure 1

Coefficient of self-diffusion of deuterium plasmas at $4.04\mathrm{g}{\mathrm{cm}}^{-3}$ and temperatures in the range 1–80 eV. The EPT results, which were here evaluated using the pair-distribution functions $g(r)$ calculated with the QOFMD simulations, are in excellent agreement with the latter, while the traditional weak-coupling (Landau-Spitzer; red dotted line) plasma theory breaks down at low temperatures. The model of Paquette et al. [27] (blue dashed line) is widely used in stellar astrophysics.

Figure 2

Self-diffusion coefficient of aluminum plasmas at solid density ($2.7\mathrm{g}{\mathrm{cm}}^{-3}$ upper curves) and 10 times compressed ($2.7\mathrm{g}{\mathrm{cm}}^{-3}$; lower curves). The PAMD results agree very well with the ab initio simulations (QOFMD and TFMD at higher temperatures), which shows that the pair potential from the AA-TCP model is accurate. Using this same potential, the EPT reproduces the PAMD very closely except for very strong plasma coupling.

Figure 3

Coefficients of self-diffusion $D$ (upper blue curves) and shear viscosity $\eta$ (lower red curves) of hydrogen plasmas at $8\mathrm{g}{\mathrm{cm}}^{-3}$. Both the PAMD and EPT results are in very good agreement with the ab initio QOFMD values. The larger deviations occur at low temperatures where the plasma is very strongly coupled.

Figure 4

Coefficient of self-diffusion $D$ (upper blue curves) and of shear viscosity $\eta$ (lower red curves) of iron plasmas at $7.87\mathrm{g}{\mathrm{cm}}^{-3}$. These calculations are based on the Thomas-Fermi model of the electrons.

Figure 5

Interdiffusion coefficient $D_{12}$ of $\mathrm{C}/\mathrm{He}$ mixtures (60% C, 40% He by number) at $10\mathrm{g}{\mathrm{cm}}^{-3}$. The agreement between $\mathrm{EPT}+\mathrm{AA}$ and PAMD is excellent, especially considering the level of noise in the latter calculations ($\pm 3\%$).