Molecular dynamics simulations of temperature equilibration in dense hydrogen

The temperature equilibration rate between electrons and protons in dense hydrogen has been calculated with molecular dynamics simulations for temperatures between 10 and $600\mathrm{eV}$ and densities between ${10}^{20}{\mathrm{cm}}^{-3}\text{to}{10}^{24}{\mathrm{cm}}^{-3}$. Careful attention has been devoted to convergence of the simulations, including the role of semiclassical potentials. We find that for Coulomb logarithms $\mathcal{L}\gtrsim 1$, a model by Gericke-Murillo-Schlanges (GMS) [D. O. Gericke et al., Phys. Rev. E 65, 036418 (2002)] based on a $T$-matrix method and the approach by Brown-Preston-Singleton [L. S. Brown et al., Phys. Rep. 410, 237 (2005)] agrees with the simulation data to within the error bars of the simulation. For smaller Coulomb logarithms, the GMS model is consistent with the simulation results. Landau-Spitzer models are consistent with the simulation data for $\mathcal{L}>4$.

Figure 1

(Color) Electron (top curves) and proton (bottom curves) temperature relaxation is shown based on MD, GMS, LS, and BPS for case $K$. The MD results are shown by points from several simulations, with a line through the average. Note that all approaches relax slower than LS.

Figure 2

(Color) Theoretical (GMS [solid], BPS [dashed], and LS [dotted]) and MD calculations of $\mathcal{L}$ as a function of initial $T_e$ for densities ${10}^{20}{\mathrm{cm}}^{-3}$, ${10}^{22}{\mathrm{cm}}^{-3}$, and ${10}^{24}{\mathrm{cm}}^{-3}$ (blue, red, and black, respectively). Diamond symbols indicate results obtained from like-charge MD simulations. Additional detail is in the text.