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

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.

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.

Ab Initio Studies on the Stopping Power of Warm Dense Matter with Time-Dependent Orbital-Free Density Functional Theory

Electronic transport properties of warm dense matter, such as electrical or thermal conductivities and nonadiabatic stopping power, are of particular interest to geophysics, planetary science, astrophysics, and inertial confinement fusion (ICF). One example is the α-particle stopping power of dense deuterium-tritium (DT) plasmas, which must be precisely known for current small-margin ICF target designs to ignite. We have developed a time-dependent orbital-free density functional theory (TD-OF-DFT) method for ab initio investigations of the charged-particle stopping power of warm dense matter. Our current dependent TD-OF-DFT calculations have reproduced the recently well-characterized stopping power experiment in warm dense beryllium. For α-particle stopping in warm and solid-density DT plasmas, the ab initio TD-OF-DFT simulations show a lower stopping power up to ∼25% in comparison with three stopping-power models often used in the high-energy-density physics community.

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.

A viscous quantum hydrodynamics model based on dynamic density functional theory

Dynamic density functional theory (DDFT) is emerging as a useful theoretical technique for modeling the dynamics of correlated systems. We extend DDFT to quantum systems for application to dense plasmas through a quantum hydrodynamics (QHD) approach. The DDFT-based QHD approach includes correlations in the the equation of state self-consistently, satisfies sum rules and includes irreversibility arising from collisions. While QHD can be used generally to model non-equilibrium, heterogeneous plasmas, we employ the DDFT-QHD framework to generate a model for the electronic dynamic structure factor, which offers an avenue for measuring hydrodynamic properties, such as transport coefficients via x-ray Thomson scattering.