Dynamical local field corrections on energy loss in plasmas of all degeneracies

Molecular dynamics investigation of the stopping power of warm dense hydrogen for electrons

A variety of theoretical models have been proposed to calculate the stopping power of charged particles in matter, which is a fundamental issue in many fields. However, the approximation adopted in these theories will be challenged under warm dense matter conditions. Molecular dynamics (MD) simulation is a good way to validate the effectiveness of these models. We investigate the stopping power of warm dense hydrogen for electrons with projectile energies ranging from 400-10000 eV by means of an electron force field (eFF) method, which can effectively avoid the Coulomb catastrophe in conventional MD calculations. It is found that the stopping power of warm dense hydrogen decreases with increasing temperature of the sample at those high projectile velocities. This phenomenon could be explained by the effect of electronic structure dominated by bound electrons, which is further explicated by a modified random phase approximation (RPA) model based on local density approximation proper to inhomogeneous media. Most of the models extensively accepted by the plasma community, e.g., Landau-Spitzer model, Brown-Preston-Singleton model and RPA model, cannot well address the effect caused by bound electrons so that their predictions of stopping power contradict our result. Therefore, the eFF simulations of this paper reveals the important role played by the bound electrons on stopping power in warm dense plasmas.

Stopping power of hot dense deuterium-tritium plasmas mixed with impurities to charged particles

In this work, we studied the stopping power of deuterium-tritium (DT) plasmas mixed with impurities to the injected charged particles. Based on the Brown-Preston-Singleton model, the analytical expression for the change ratio of stopping power (denoted by η) induced by impurities in DT plasmas is developed, in which both classical short-distance collision part and quantum correction contribution are purely linear response to the impurity concentration ξ_{X}, while the classical long-range collision brings about higher-order nonlinear response to ξ_{X}. Furthermore, the expression for change ratio of deposition depth (denoted by χ) of charged particles induced by impurities in DT plasmas is also derived. As applications, we systemically investigated the energy loss of α particles deposited into a hot dense DT plasma mixed with impurity X(X=C, Si, Ge), where the temperature and density of DT are smaller than 10 keV and 500 g/cm^{3} and the concentration of Xξ_{X} is less than 5%. The numerical results suggest that (i) for the case of C mixed into DT, both change ratios of stopping power and deposition depth of α particles (i.e., η and χ) are linear response to the concentration of C ξ_{C}; (ii) for the case of Si mixed into DT, the second-order nonlinear response of η and χ to ξ_{Si} cannot be ignored when the densities of DT are larger than 200 g/cm^{3}; and (iii) for the case of Ge mixed into DT, the second- and third-order nonlinear response of η and χ to ξ_{Ge} are very remarkable because of the higher ionization degree and heavier atomic mass of Ge. The formulas and findings in this work may be helpful to the research of internal confinement fusion (ICF) related implosion physics and may provide useful theoretical guidance and data for the design of ICF target.

First-Principles Estimation of Electronic Temperature from X-Ray Thomson Scattering Spectrum of Isochorically Heated Warm Dense Matter

Through the perturbation formula of time-dependent density functional theory broadly employed in the calculation of solids, we provide a first-principles calculation of x-ray Thomson scattering spectrum of isochorically heated aluminum foil, as considered in the experiments of Sperling et al. [Phys. Rev. Lett. 115, 115001 (2015)PRLTAO0031-900710.1103/PhysRevLett.115.115001], where ions were constrained near their lattice positions. From the calculated spectra, we find that the electronic temperature cannot exceed 2 eV, much smaller than the previous estimation of 6 eV via the detailed balance relation. Our results may well be an indication of unique electronic properties of warm dense matter, which can be further illustrated by future experiments. The lower electronic temperature predicted partially relieves the concern on the heating of x-ray free electron laser to the sample when used in structure measurement.

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.

Nuclear-plus-interference-scattering effect on the energy deposition of multi-MeV protons in a dense Be plasma

The nuclear plus interference scattering (NIS) effect on the stopping power of hot dense beryllium (Be) plasma for multi-MeV protons is theoretically investigated by using the generalized Brown-Preston-Singleton (BPS) model, in which a NIS term is taken into account. The analytical formula of the NIS term is detailedly derived. By using this formula, the density and temperature dependence of the NIS effect is numerically studied, and the results show that the NIS effect becomes more and more important with increasing the plasma temperature or density. Different from the cases of protons traveling through the deuterium-tritium plasmas, for a Be plasma, a prominent oscillation valley structure is observed in the NIS term when the proton's energy is close to E_{p}=7MeV. Furthermore, the penetration distance is remarkably reduced when the NIS term is considered.

Generalized Lenard-Balescu calculations of electron-ion temperature relaxation in beryllium plasma

The problem of electron-ion temperature relaxation in beryllium plasma at various densities (0.185-18.5g/cm^{3}) and temperatures [(1.0-8)×10^{3} eV] is investigated by using the generalized Lenard-Balescu theory. We consider the correlation effects between electrons and ions via classical and quantum static local field corrections. The numerical results show that the electron-ion pair distribution function at the origin approaches the maximum when the electron-electron coupling parameter equals unity. The classical result of the Coulomb logarithm is in agreement with the quantum result in both the weak (Γ_{ee}<10^{-2}) and strong (Γ_{ee}>1) electron-electron coupling ranges, whereas it deviates from the quantum result at intermediate values of the coupling parameter (10^{-2}<Γ_{ee}<1). We find that with increasing density of Be, the Coulomb logarithm will decrease and the corresponding relaxation rate ν_{ie} will increase. In addition, a simple fitting law ν_{ie}/ν_{ie}^{(0)}=a(ρ_{Be}/ρ_{0})^{b} is determined, where ν_{ie}^{(0)} is the relaxation rate corresponding to the normal metal density of Be and ρ_{0}, a, and b are the fitting parameters related to the temperature and the degree of ionization 〈Z〉 of the system. Our results are expected to be useful for future inertial confinement fusion experiments involving Be plasma.

Dielectric function of dense plasmas, their stopping power, and sum rules

Mathematical, particularly, asymptotic properties of the random-phase approximation, Mermin approximation, and extended Mermin-type approximation of the coupled plasma dielectric function are analyzed within the method of moments. These models are generalized for two-component plasmas. Some drawbacks and advantages of the above models are pointed out. The two-component plasma stopping power is shown to be enhanced with respect to that of the electron fluid.

Influence of local-field corrections on Thomson scattering in collision-dominated two-component plasmas

The dynamic structure factor, which determines the Thomson scattering spectrum, is calculated via an extended Mermin approach. It incorporates the dynamical collision frequency as well as the local-field correction factor. This allows to study systematically the impact of electron-ion collisions as well as electron-electron correlations due to degeneracy and short-range interaction on the characteristics of the Thomson scattering signal. As such, the plasmon dispersion and damping width is calculated for a two-component plasma, where the electron subsystem is completely degenerate. Strong deviations of the plasmon resonance position due to the electron-electron correlations are observed at increasing Brueckner parameters r(s). These results are of paramount importance for the interpretation of collective Thomson scattering spectra, as the determination of the free electron density from the plasmon resonance position requires a precise theory of the plasmon dispersion. Implications due to different approximations for the electron-electron correlation, i.e., different forms of the one-component local-field correction, are discussed.