Temperature relaxation in dense plasmas

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.

Electron-ion coupling factor for temperature relaxation in dense plasmas

We compare two formulas obtained from first principles to calculate the electron-ion coupling factor for temperature relaxation in dense plasmas. The quantum average-atom model is used to calculate this electron-ion coupling factor. It is shown that if the two formulas agree at sufficiently high temperature so that the potential energy is of limited importance, i.e., when the plasma is said to be kinetic, and are consistent with the Landau-Spitzer formula, then they strongly differ in the warm-dense-matter regime. Only one of the two is shown to be consistent with quantum molecular dynamics approach. We use this point to determine which formula is valid to describe temperature relaxation between electrons and ions in warm and hot dense plasmas.

Theory of the electron-ion temperature relaxation rate spanning the hot solid metals and plasma phases

We present a theory for the rate of energy exchange between electrons and ions-also known as the electron-ion coupling factor-in physical systems ranging from hot solid metals to plasmas, including liquid metals and warm dense matter. The paper provides the theoretical foundations of a recent work [J. Simoni and J. Daligault, Phys. Rev. Lett. 122, 205001 (2019)PRLTAO0031-900710.1103/PhysRevLett.122.205001], where first-principles quantum molecular dynamics calculations based on this theory were presented for representative materials and conditions. We first derive a general expression for the electron-ion coupling factor that includes self-consistently the quantum mechanical and statistical nature of electrons, the thermal and disorder effects, and the correlations between particles. The electron-ion coupling is related to the friction coefficients felt by individual ions due to their nonadiabatic interactions with the electrons. Each coefficient satisfies a Kubo relation given by the time integral of the autocorrelation function of the interaction force of an ion with the electrons. Exact properties and different representations of the general expressions are discussed. We then show that our theory reduces to well-known models in limiting cases. In particular, we show that it simplifies to the standard electron-phonon coupling formula in the limit of hot solids with lattice and electronic temperatures much greater than the Debye temperature, and that it extends the electron-phonon coupling formula beyond the harmonic phonon approximation. For plasmas, we show that the theory readily reduces to the well-known Spitzer formula in the hot plasma limit, to the Fermi "golden rule" formula in the limit of weak electron-ion interactions, and to other models proposed to go beyond the latter approximation. We explain that the electron-ion coupling is particularly well adapted to average atom models, which offer an effective way to include nonideal interaction effects to the standard models and at a much reduced computational cost in comparison to first-principles quantum molecular dynamics simulations.

Multidimensional Chebyshev interpolation for warm and hot dense matter

We propose a scheme based on a multidimensional Chebyshev interpolation to approximate smooth functions that depend on more than one variable. The present method generalizes the one dimensional Chebyshev approximation. The multidimensional approach can be used for generating databases like equation of state in the warm and hot dense matter. It is well suited to the present advance of massively parallel supercomputers.

Molecular dynamics studies of electron-ion temperature equilibration in hydrogen plasmas within the coupled-mode regime

We use classical molecular dynamics (MD) to study electron-ion temperature equilibration in two-component plasmas in regimes for which the presence of coupled collective modes has been predicted to substantively reduce the equilibration rate. Guided by previous kinetic theory work, we examine hydrogen plasmas at a density of n=10^{26}cm^{-3}, T_{i}=10^{5}K, and 10^{7}K<T_{e}<10^{9}K. The nonequilibrium classical MD simulations are performed with interparticle interactions modeled by quantum statistical potentials (QSPs). Our MD results indicate (i) a large effect from time-varying potential energy, which we quantify by appealing to an adiabatic two-temperature equation of state, and (ii) a notable deviation in the energy equilibration rate when compared to calculations from classical Lenard-Balescu theory including the QSPs. In particular, it is shown that the energy equilibration rates from MD are more similar to those of the theory when coupled modes are neglected. We suggest possible reasons for this surprising result and propose directions of further research along these lines.

Dynamic properties of the energy loss of multi-MeV charged particles traveling in two-component warm dense plasmas

The energy loss of multi-MeV charged particles moving in two-component warm dense plasmas (WDPs) is studied theoretically beyond the random-phase approximation. The short-range correlations between particles are taken into account via dynamic local field corrections (DLFC) in a Mermin dielectric function for two-component plasmas. The mean ionization states are obtained by employing the detailed configuration accounting model. The Yukawa-type effective potential is used to derive the DLFC. Numerically, the DLFC are obtained via self-consistent iterative operations. We find that the DLFC are significant around the maximum of the stopping power. Furthermore, by using the two-component extended Mermin dielectric function model including the DLFC, the energy loss of a proton with an initial energy of ∼15 MeV passing through a WDP of beryllium with an electronic density around the solid value n_{e}≈3×10^{23}cm^{-3} and with temperature around ∼40 eV is estimated numerically. The numerical result is reasonably consistent with the experimental observations [A. B. Zylsta et al., Phys. Rev. Lett. 111, 215002 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.215002]. Our results show that the partial ionization and the dynamic properties should be of importance for the stopping of charged particles moving in the WDP.

Temperature relaxation in dense plasma mixtures

We present a model to calculate temperature-relaxation rates in dense plasma mixtures. The electron-ion relaxation rates are calculated using an average-atom model and the ion-ion relaxation rates by the Landau-Spitzer approach. This method allows the study of the temperature relaxation in many-temperature electron-ion and ion-ion systems such as those encountered in inertial confinement fusion simulations. It is of interest for general nonequilibrium thermodynamics dealing with energy flows between various systems and should find broad use in present high energy density experiments.