Influence of damping on proton energy loss in plasmas of all degeneracies

Mixed stochastic-deterministic time-dependent density functional theory: application to stopping power of warm dense carbon

Warm dense matter (WDM) describes an intermediate phase, between condensed matter and classical plasmas, found in natural and man-made systems. In a laboratory setting, WDM is often created dynamically. It is typically laser or pulse-power generated and can be difficult to characterize experimentally. Measuring the energy loss of high energy ions, caused by a WDM target, is both a promising diagnostic and of fundamental importance to inertial confinement fusion research. However, electron coupling, degeneracy, and quantum effects limit the accuracy of easily calculable kinetic models for stopping power, while high temperatures make the traditional tools of condensed matter, e.g. time-dependent density functional theory (TD-DFT), often intractable. We have developed a mixed stochastic-deterministic approach to TD-DFT which provides more efficient computation while maintaining the required precision for model discrimination. Recently, this approach showed significant improvement compared to models when compared to experimental energy loss measurements in WDM carbon. Here, we describe this approach and demonstrate its application to warm dense carbon stopping across a range of projectile velocities. We compare direct stopping-power calculation to approaches based on combining homogeneous electron gas response with bound electrons, with parameters extracted from our TD-DFT calculations.

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.

Optical Response of an Interacting Polaron Gas in Strongly Polar Crystals

Optical conductivity of an interacting polaron gas is calculated within an extended random phase approximation which takes into account mixing of collective excitations of the electron gas with longitudinal optical (LO) phonons. This mixing is important for the optical response of strongly polar crystals where the static dielectric constant is rather high, as in the case of strontium titanate. The present calculation sheds light on unexplained features of experimentally observed optical conductivity spectra in n-doped SrTiO 3 . These features appear to be due to dynamic screening of the electron–electron interaction by polar optical phonons and hence do not require additional mechanisms for their explanation.

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.

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

In this work, we present a dielectric function including the three conservation laws (density, momentum and energy) when we take into account electron-electron collisions in a plasma at any degeneracy. This full conserving dielectric function (FCDF) reproduces the random phase approximation (RPA) and Mermin ones, which confirms this outcome. The FCDF is applied to the determination of the proton stopping power. Differences among diverse dielectric functions in the proton stopping calculation are minimal if the plasma electron collision frequency is not high enough. These discrepancies can rise up to 2% between RPA values and the FCDF ones, and to 8% between the Mermin ones and FCDF ones. The similarity between RPA and FCDF results is not surprising, as all conservation laws are also considered in RPA dielectric function. Even for plasmas with low collision frequencies, those discrepancies follow the same behavior as for plasmas with higher frequencies. Then, discrepancies do not depend on the plasma degeneracy but essentially do on the value of the plasma collision frequency.

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

Random phase approximation (RPA) has become one of the most used methods to describe the energy loss of charged particles in plasmas. The RPA is usually valid for high-velocity projectiles and in the weak coupling limit of the electron gas. However, for partially coupled plasmas RPA is not sufficient and the electronic coupling must be taken into account. This coupling can be considered through local field corrections. In this work, we have constructed a dynamical local field correction (DLFC) function from Mermin dielectric function. This DLFC function has the advantage to describe plasmas at any degeneracy. Mermin DLFC function is compared with other DLFC functions from the literature in the energy loss calculation. We see important differences between them; they are significant at low velocities and very relevant around the maximum, almost 30%.