Assessment of the electron-proton energy relaxation rates extracted from molecular dynamics simulations in weakly-coupled hydrogen plasmas

Electron-proton energy relaxation rates are assessed using molecular dynamics (MD) simulations in weakly-coupled hydrogen plasmas. To this end, we use various approaches to extract the energy relaxation rate from MD-simulated temperatures, and we find that existing extracting approaches may yield results with a sizable discrepancy larger than the variance between analytical models, which is further verified by well-known case studies. Present results show that two of the extracting approaches can produce identical results, which is attributed to a proper treatment of relaxation evolution. To discriminate the use of various methods, an empirical criterion with respect to initial plasma temperatures is proposed, which can self-consistently explain the cases considered. In addition, for a transient electron-proton plasma, we show that it is possible to extrapolate the Coulomb logarithm from that derived by initial plasma parameters in a single MD calculation, which is reasonably consistent with previous MD data. Our results are helpful to obtain accurate MD-based energy relaxation rates.

Figure 1

Comparison of MD simulation results with fitted results by various schemes. (a) Full relaxation dynamics, (b) partial relaxation dynamics, (c) optimal fitting procedure. Note that (b) employs a logarithmic y axis. In order to facilitate the comparison between fitted and MD results, (c1) shows their difference. More details can be found in the main text.

Figure 2

Time evolution of the electron and ion temperature for MD simulations (solid square symbols), together with the fitting results of full relaxation dynamics (S1, red curves) and optimal fitting procedure (S3, green curves). For comparison, the analytical LS (blue curves), GMS (pink curves), BPS (purple curves), and DD (orange curves) results are shown. This illustration corresponds to case F in Table 1

Figure 3

Plasma parameters $g$ as a function of time for cases A–F analyzed in Table 1. For a better comparison, $g$ is normalized by its value at $t=0$ and the time is scaled to unity. The gray dashed line indicates the normalized plasma parameter equal to 1 at any times.

Figure 4

The Coulomb logarithm $(ln\mathrm{\Lambda })$ vs the plasma parameter $\left(g\right)$. The solid curve is computed by a single MD simulation with $n_i=n_e=3.35\times {10}^{22}{\mathrm{cm}}^{-3}$, $T_e^0=50$ eV, and $T_i^0=1000$ eV (case F in Table 1). Symbols are independent MD results reported in Ref. [37].

Figure 5

The Coulomb logarithm ($ln\mathrm{\Lambda }$) vs the number of electrons used in the MD simulations.