Extremely Low Electron-ion Temperature Relaxation Rates in Warm Dense Hydrogen: Interplay between Quantum Electrons and Coupled Ions

Theoretical and computational modeling of nonequilibrium processes in warm dense matter represents a significant challenge. The electron-ion relaxation process in warm dense hydrogen is investigated here by nonequilibrium molecular dynamics using the constrained electron force field (CEFF) method. CEFF evolves wave packets that incorporate dynamic quantum diffraction that obviates the Coulomb catastrophe. Predictions from this model reveal temperature relaxation times as much as three times longer than prior molecular dynamics results based on quantum statistical potentials. Through analyses of energy distributions and mean free paths, this result can be traced to delocalization. Finally, an improved GMS [Gericke, Murillo, and Schlanges, Phys. Rev. E 78, 025401 (2008)] model is proposed, in which the Coulomb logarithms are in good agreement with CEFF results.

Figure 1

The radius of wave packets of the temperature relaxation of warm dense hydrogen with initial electronic temperature $T_{e0}=10\mathrm{eV}$ and ionic temperature $T_{i0}=1\mathrm{eV}$ (left column), $T_{e0}=20\mathrm{eV}$ and $T_{i0}=10\mathrm{eV}$ (right column) with different densities $n_e$. Green dotted lines represent the radii from original EFF using boundary of half box size, red square lines are our CEFF results.

Figure 2

The temporal evolution of ionic and electronic temperatures at different densities. The initial electronic temperature $T_{e0}=10\mathrm{eV}$ and ionic temperature $T_{i0}=1\mathrm{eV}$ [(d)–(f)], $T_{e0}=20\mathrm{eV}$ and $T_{i0}=10\mathrm{eV}$ [(a)–(c)]. The red curves are results from the CEFF method while the blue curves are from CMD with QSP. The related parameters are ${\mathrm{\Gamma }}_{\mathrm{ii}}=8.63$, 19.55, 29.25, 0.86, 1.96, 2.92 and $\mathrm{\Theta }=1.98$, 0.39, 0.17, 3.97, 0.77, 0.35 corresponding to the initial temperature, respectively.

Figure 3

RDFs calculated from EFF, CEFF, CMD with QSP, and PIMC in equilibrium conditions. Here, the temperature is 125 000 K and the Wigner radius is 1.5 Bohr. The ion-ion (ii) distribution $g_{\mathrm{ii}}$, electron-electron (ee) distribution $g_{\mathrm{ee}}$, and ion-electron (ie) distribution $g_{\mathrm{ie}}$ are shown. For PIMC, the spin-resolved RDFs are shown.

Figure 4

The diffusion coefficients $D$ [(a),(b), and (c)] are at the electron number density of $2.0\times {10}^{24}{\mathrm{cm}}^{-3}$ and the temperature of 20 eV. The dimensionless self-diffusion coefficients $D^{*}$ versus ${\mathrm{\Gamma }}_{\mathrm{ii}}$ are shown in (d), in which data points indicated with circles are at 10 eV, and data points indicated with squares are at 20 eV.

Figure 5

Coulomb logarithm calculated from theoretical methods [LS (black dotted), BPS (black dashed), GMS (black dotted dash line), coupled GMS (CGMS, black solid line)] and molecular dynamics simulations [CMD (blue square), EFF (green circle), and CEFF (red diamond)]. Initial temperatures are $T_{e0}=10\mathrm{eV}$ and $T_{i0}=1\mathrm{eV}$ in (a), $T_{e0}=20\mathrm{eV}$ and $T_{i0}=10\mathrm{eV}$ in (b). Electron number density is chosen from $n_e=5.1\times {10}^{22}{\mathrm{cm}}^{-3}$ to $n_e=6.0\times {10}^{24}{\mathrm{cm}}^{-3}$.