Proton stopping using a full conserving dielectric function in plasmas at any degeneracy

Ion energy-loss characteristics and friction in a free-electron gas at warm dense matter and nonideal dense plasma conditions

We investigate the energy-loss characteristics of an ion in warm dense matter (WDM) and dense plasmas concentrating on the influence of electronic correlations. The basis for our analysis is a recently developed ab initio quantum Monte Carlo- (QMC) based machine learning representation of the static local field correction (LFC) [Dornheim et al., J. Chem. Phys. 151, 194104 (2019)JCPSA60021-960610.1063/1.5123013], which provides an accurate description of the dynamical density response function of the electron gas at the considered parameters. We focus on the polarization-induced stopping power due to free electrons, the friction function, and the straggling rate. In addition, we compute the friction coefficient which constitutes a key quantity for the adequate Langevin dynamics simulation of ions. Considering typical experimental WDM parameters with partially degenerate electrons, we find that the friction coefficient is of the order of γ/ω_{pi}=0.01, where ω_{pi} is the ionic plasma frequency. This analysis is performed by comparing QMC-based data to results from the random-phase approximation (RPA), the Mermin dielectric function, and the Singwi-Tosi-Land-Sjölander (STLS) approximation. It is revealed that the widely used relaxation time approximation (Mermin dielectric function) has severe limitations regarding the description of the energy loss of ions in a correlated partially degenerate electrons gas. Moreover, by comparing QMC-based data with the results obtained using STLS, we find that the ion energy-loss properties are not sensitive to the inaccuracy of the static local field correction (LFC) at large wave numbers, k/k_{F}>2 (with k_{F} being the Fermi wave number), but that a correct description of the static LFC at k/k_{F}≲1.5 is important.

High-frequency response of classical strongly coupled plasmas

The dynamic structure factor (DSF) of the Yukawa system is here obtained with highly converged molecular dynamics (MD) over the entire liquid phase. The data provide a rigorous test of theoretical models of ion-acoustic wave-dispersion relations, the intermediate scattering function, and the high-frequency response. We compare our MD results with seven diverse models, finding good agreement among those that enforce the three basic sum rules for dispersion properties, although one of the models has previously unreported spurious peaks. The MD simulations reveal that at intermediate frequencies ω, the high-frequency response of the DSF follows a power law, going approximately as ω^{-p}, where p>0, and p shows nontrivial dependencies on the wave vector q and the plasma parameters κ and Γ. In contrast, among the seven comparison models, the predicted high-frequency response is found to be independent of {q,κ,Γ}. This high-frequency power suggests a useful fitting form. In addition, these results expose limitations of several models and, moreover, suggest that some approaches are difficult or impossible to extend because of the lack of finite moments. We also find the double-plasmon resonance peak in our MD simulations that none of the theoretical models predicts.

Experimental evidence for the enhanced and reduced stopping regimes for protons propagating through hot plasmas

Our understanding of the dynamics of ion collisional energy loss in a plasma is still not complete, in part due to the difficulty and lack of high-quality experimental measurements. These measurements are crucial to benchmark existing models. Here, we show that such a measurement is possible using high-flux proton beams accelerated by high intensity short pulse lasers, where there is a high number of particles in a picosecond pulse, which is ideal for measurements in quickly expanding plasmas. By reducing the energy bandwidth of the protons using a passive selector, we have made proton stopping measurements in partially ionized Argon and fully ionized Hydrogen plasmas with electron temperatures of hundreds of eV and densities in the range 1020-1021 cm-3. In the first case, we have observed, consistently with previous reports, enhanced stopping of protons when compared to stopping power in non-ionized gas. In the second case, we have observed for the first time the regime of reduced stopping, which is theoretically predicted in such hot and fully ionized plasma. The versatility of these tunable short-pulse laser based ion sources, where the ion type and energy can be changed at will, could open up the possibility for a variety of ion stopping power measurements in plasmas so long as they are well characterized in terms of temperature and density. In turn, these measurements will allow tests of the validity of existing theoretical models.

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.

Calculations on charge state and energy loss of argon ions in partially and fully ionized carbon plasmas

The energy loss of argon ions in a target depends on their velocity and charge density. At the energies studied in this work, it depends mostly on the free and bound electrons in the target. Here the random-phase approximation is used for analyzing free electrons at any degeneracy. For the plasma-bound electrons, an interpolation between approximations for low and high energies is applied. The Brandt-Kitagawa (BK) model is employed to depict the projectile charge space distribution, and the stripping criterion of Kreussler et al. is used to determine its equilibrium charge state Q(eq). This latter criterion implies that the equilibrium charge state depends slightly on the electron density and temperature of the plasma. On the other hand, the effective charge Q(eff) is obtained as the ratio between the energy loss of the argon ion and that of the proton for the same plasma conditions. This effective charge Q(eff) is larger than the equilibrium charge state Q(eq) due to the incorporation of the BK charge distribution. Though our charge-state estimations are not exactly the same as the experimental values, our energy loss agrees quite well with the experiments. It is noticed that the energy loss in plasmas is higher than that in the same cold target of about, ∼42-62.5% and increases with carbon plasma ionization. This confirms the well-known enhanced plasma stopping. It is also observed that only a small part of this energy loss enhancement is due to an increase of the argon charge state, namely only ∼2.2 and 5.1%, for the partially and the fully ionized plasma, respectively. The other contribution is connected with a better energy transfer to the free electrons at plasma state than to the bound electrons at solid state of about, ∼38.8-57.4%, where higher values correspond to a fully ionized carbon 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.

Heavy ion charge-state distribution effects on energy loss in plasmas

According to dielectric formalism, the energy loss of the heavy ion depends on its velocity and its charge density. Also, it depends on the target through its dielectric function; here the random phase approximation is used because it correctly describes fully ionized plasmas at any degeneracy. On the other hand, the Brandt-Kitagawa (BK) model is employed to depict the projectile charge space distribution, and the stripping criterion of Kreussler et al. is used to determine its mean charge state [Q]. This latter criterion implies that the mean charge state depends on the electron density and temperature of the plasma. Also, the initial charge state of the heavy ion is crucial for calculating [Q] inside the plasma. Comparing our models and estimations with experimental data, a very good agreement is found. It is noticed that the energy loss in plasmas is higher than that in the same cold gas cases, confirming the well-known enhanced plasma stopping (EPS). In this case, EPS is only due to the increase in projectile effective charge Q(eff), which is obtained as the ratio between the energy loss of each heavy ion and that of the proton in the same plasma conditions. The ratio between the effective charges in plasmas and in cold gases is higher than 1, but it is not as high as thought in the past. Finally, another significant issue is that the calculated effective charge in plasmas Q(eff) is greater than the mean charge state [Q], which is due to the incorporation of the BK charge distribution. When estimations are performed without this distribution, they do not fit well with experimental data.

Evaluation of slowing down of proton and deuteron beams in CH₂, LiH, and Al partially ionized plasmas

In this work, proton and deuteron stopping due to free and bound electrons in partially ionized plasma targets is evaluated. The stopping of target free electrons is calculated using the dielectric formalism, well described in our previous works. In the case of target bound electrons, a short expression to calculate their contribution to the stopping is used, where mean excitation energies are obtained by means of the Hartree-Fock method. Experiments with different kinds of plasmas are analyzed. For LiH plasma, estimated plasma stopping fits experimental data very well, within the error bars, recognizing the well-known enhanced plasma stopping. In the case of CH_{2} plasma, we obtain, from estimated ionization, that total stopping power increases when target electron density does. Our estimations are very similar to experimental data which show the same behavior with target free and bound electron density. Finally, in Al plasma, we compare directly our calculations with experimental data finding a very close agreement, where both stoppings have the same dependence on target ionicity. All these comparisons verify our theoretical model which estimates the proton or deuteron energy loss in partially ionized plasmas.

Hydrodynamic theory for ion structure and stopping power in quantum plasmas

We present a theory for the dynamical ion structure factor (DISF) and ion stopping power in an unmagnetized collisional quantum plasma with degenerate electron fluids and nondegenerate strongly correlated ion fluids. Our theory is based on the fluctuation dissipation theorem and the quantum plasma dielectric constant that is deduced from a linearized viscoelastic quantum hydrodynamical (LVQHD) model. The latter incorporates the essential physics of quantum forces, which are associated with the quantum statistical pressure, electron-exchange, and electron-correlation effects, the quantum electron recoil effect caused by the dispersion of overlapping electron wave functions that control the dynamics of degenerate electron fluids, and the viscoelastic properties of strongly correlated ion fluids. Both degenerate electrons and nondegenerate strongly correlated ions are coupled with each other via the space charge electric force. Thus, our LVQHD theory is valid for a collisional quantum plasma at atomic scales with a wide range of the ion coupling parameter, the plasma composition, and plasma number densities that are relevant for compressed plasmas in laboratories (inertial confinement fusion schemes) and in astrophysical environments (e.g., warm dense matter and the cores of white dwarf stars). It is found that quantum electron effects and viscoelastic properties of strongly correlated ions significantly affect the features of the DISF and the ion stopping power (ISP). Unlike previous theories, which have studied ion correlations in terms of the ion coupling parameter, by neglecting the essential physics of collective effects that are competing among each other, we have here developed a method to evaluate the dependence of the plasma static and dynamical features in terms of individual parameters, like the Wigner-Seitz radius, the ion atomic number, and the ion temperature. It is found that due to the complex nature of charge screening in quantum plasmas, the ion coupling parameter alone cannot be a good measure for determining ion correlation effects in a collisional quantum plasma, and such a characteristic of a dense quantum plasma should be evaluated against each of the plasma parameters involved. The present investigation thus provides testable predictions for the DISF and ISP and is henceforth applicable to a wide range of compressed plasma categories ranging from laboratory to astrophysical warm dense matter.

Short-time electron dynamics in aluminum excited by femtosecond extreme ultraviolet radiation

The femtosecond dynamics of the electrons in aluminum after an intense extreme ultraviolet pulse is investigated by Monte Carlo simulations. Transient distributions of the conduction band electrons show an almost thermalized, low-energy part and a high-energy tail. Constructing emission spectra from these data, we find excellent agreement with measurements. The radiative decay mainly reflects the colder part of the distribution, whereas the highly excited electrons dominate the bremsstrahlung spectrum. For the latter, we also find good agreement between predicted and measured energy scales.