Temperature determination using Kalpha spectra from M -shell Ti ions

Thermal excitation signals in the inhomogeneous warm dense electron gas

We investigate the emergence of electronic excitations from the inhomogeneous electronic structure at warm dense matter parameters based on first-principles calculations. The emerging modes are controlled by the imposed perturbation amplitude. They include satellite signals around the standard plasmon feature, transformation of plasmons to optical modes, and double-plasmon modes. These modes exhibit a pronounced dependence on the temperature. This makes them potentially invaluable for the diagnostics of plasma parameters in the warm dense matter regime. We demonstrate that these modes can be probed with present experimental techniques.

Microstructured layered targets for improved laser-induced x-ray backlighters

We present the usage of two-layer targets with laser-illuminated front-side microstructures for x-ray backlighter applications. The targets consisted of a silicon front layer and copper back side layer. The structured layer was irradiated by the 500-fs PHELIX laser with an intensity above 10^{20}Wcm^{-2}. The total emission and one-dimensional extent of the copper Kα x-ray emission as well as a wide spectral range between 7.9 and 9.0 keV were recorded with an array of crystal spectrometers. The measurements show that the front-side modifications of the silicon in the form of conical microstructures maintain the same peak brightness of the Kα emission as flat copper foils while suppressing the thermal emission background significantly. The observed Kα source sizes can be influenced by tilting the conical microstructures with respect to the laser axis. Overall, the recorded copper Kα photon yields were in the range of 10^{11}sr^{-1}, demonstrating the suitability of these targets for probing applications without subjecting the probed material to additional heating from thermal line emission.

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.

The characteristic radiation of copper Kα1,2,3,4

A characterization of the Cu Kα_1,2 spectrum is presented, including the 2p satellite line, Kα_3,4, the details of which are robust enough to be transferable to other experiments. This is a step in the renewed attempts to resolve inconsistencies in characteristic X-ray spectra between theory, experiment and alternative experimental geometries. The spectrum was measured using a rotating anode, monolithic Si channel-cut double-crystal monochromator and backgammon detector. Three alternative approaches fitted five Voigt profiles to the data: a residual analysis approach; a peak-by-peak fit; and a simultaneous constrained method. The robustness of the fit is displayed across three spectra obtained with different instrumental broadening. Spectra were not well fitted by transfer of any of three prior characterizations from the literature. Integrated intensities, line widths and centroids are compared with previous empirical fits. The novel experimental setup provides insight into the portability of spectral characterizations of X-ray spectra. From the parameterization, an estimated 3d shake probability of 18% and a 2p shake probability of 0.5% are reported.

Monochromatic 2D Kα Emission Images Revealing Short-Pulse Laser Isochoric Heating Mechanism

The rapid heating of a thin titanium foil by a high intensity, subpicosecond laser is studied by using a 2D narrow-band x-ray imaging and x-ray spectroscopy. A novel monochromatic imaging diagnostic tuned to 4.51 keV Ti Kα was used to successfully visualize a significantly ionized area (⟨Z⟩>17±1) of the solid density plasma to be within a ∼35  μm diameter spot in the transverse direction and 2  μm in depth. The measurements and a 2D collisional particle-in-cell simulation reveal that, in the fast isochoric heating of solid foil by an intense laser light, such a high ionization state in solid titanium is achieved by thermal diffusion from the hot preplasma in a few picoseconds after the pulse ends. The shift of Kα and formation of a missing Kα cannot be explained with the present atomic physics model. The measured Kα image is reproduced only when a phenomenological model for the Kα shift with a threshold ionization of ⟨Z⟩=17 is included. This work reveals how the ionization state and electron temperature of the isochorically heated nonequilibrium plasma are independently increased.

Continuum Lowering and Fermi-Surface Rising in Strongly Coupled and Degenerate Plasmas

Continuum lowering is a well known and important physics concept that describes the ionization potential depression (IPD) in plasmas caused by thermal- or pressure-induced ionization of outer-shell electrons. The existing IPD models are often used to characterize plasma conditions and to gauge opacity calculations. Recent precision measurements have revealed deficits in our understanding of continuum lowering in dense hot plasmas. However, these investigations have so far been limited to IPD in strongly coupled but nondegenerate plasmas. Here, we report a first-principles study of the K-edge shifting in both strongly coupled and fully degenerate carbon plasmas, with quantum molecular dynamics calculations based on the all-electron density-functional theory. The resulting K-edge shifting versus plasma density, as a probe to the continuum lowering and the Fermi-surface rising, is found to be significantly different from predictions of existing IPD models. In contrast, a simple model of "single-atom-in-box," developed in this work, accurately predicts K-edge locations as ab initio calculations provide.

Imaging at an x-ray absorption edge using free electron laser pulses for interface dynamics in high energy density systems

Tuning the energy of an x-ray probe to an absorption line or edge can provide material-specific measurements that are particularly useful for interfaces. Simulated hard x-ray images above the Fe K-edge are presented to examine ion diffusion across an interface between Fe₂O₃ and SiO₂ aerogel foam materials. The simulations demonstrate the feasibility of such a technique for measurements of density scale lengths near the interface with submicron spatial resolution. A proof-of-principle experiment is designed and performed at the Linac coherent light source facility. Preliminary data show the change of the interface after shock compression and heating with simultaneous fluorescence spectra for temperature determination. The results provide the first demonstration of using x-ray imaging at an absorption edge as a diagnostic to detect ultrafast phenomena for interface physics in high-energy-density systems.

Equation of state, phonons, and lattice stability of ultrafast warm dense matter

Using the two-temperature model for ultrafast matter (UFM), we compare the equation of state, pair-distribution functions g(r), and phonons using the neutral pseudoatom (NPA) model with results from density functional theory (DFT) codes and molecular dynamics (MD) simulations for Al, Li, and Na. The NPA approach uses state-dependent first-principles pseudopotentials from an "all-electron" DFT calculation with finite-T exchange-correlation functional (XCF). It provides pair potentials, structure factors, the "bound" and "free" states, as well as a mean ionization Z[over ¯] unambiguously. These are not easily accessible via DFT+MD calculations which become prohibitive for T/T_{F} exceeding ∼0.6, where T_{F} is the Fermi temperature. Hence, both DFT+MD and NPA methods can be compared up to ∼8eV, while higher T can be addressed via the NPA. The high-T_{e} phonon calculations raise the question of UFM lattice stability and surface ablation in thin UFM samples. The ablation forces in a UFM slab are used to define an "ablation time" competing with phonon formation times in thin UFM samples. Excellent agreement for all properties is found between NPA and standard DFT codes, even for Li where a strongly nonlocal pseudopotential is used in DFT codes. The need to use pseudopotentials appropriate to the ionization state Z[over ¯] is emphasized. The effect of finite-T XCF is illustrated via its effect on the pressure and the electron-density distribution at a nucleus.

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.

Effects of target heating on experiments using Kα and Kβ diagnostics

We describe the impact of heating and ionization on emission from the target of Kα and Kβ radiation induced by the propagation of hot electrons generated by laser-matter interaction. We consider copper as a test case and, starting from basic principles, we calculate the changes in emission wavelength, ionization cross section, and fluorescence yield as Cu is progressively ionized. We have finally considered the more realistic case when hot electrons have a distribution of energies with average energies of 50 and 500 keV (representative respectively of "shock ignition" and of "fast ignition" experiments) and in which the ions are distributed according to ionization equilibrium. In addition, by confronting our theoretical calculations with existing data, we demonstrate that this study offers a generic theoretical background for temperature diagnostics in laser-plasma interactions.

Measurement of charged-particle stopping in warm dense plasma

We measured the stopping of energetic protons in an isochorically heated solid-density Be plasma with an electron temperature of ∼32  eV, corresponding to moderately coupled [(e^{2}/a)/(k_{B}T_{e}+E_{F})∼0.3] and moderately degenerate [k_{B}T_{e}/E_{F}∼2] "warm-dense matter" (WDM) conditions. We present the first high-accuracy measurements of charged-particle energy loss through dense plasma, which shows an increased loss relative to cold matter, consistent with a reduced mean ionization potential. The data agree with stopping models based on an ad hoc treatment of free and bound electrons, as well as the average-atom local-density approximation; this work is the first test of these theories in WDM plasma.

Predictions of x-ray scattering spectra for warm dense matter

We present calculations of x-ray scattering spectra based on ionic and electronic structure factors that are computed from a new model for warm dense matter. In this model, which has no free parameters, the ionic structure is determined consistently with the electronic structure of the bound and free states. The x-ray scattering spectrum is thus fully determined by the plasma temperature, density and nuclear charge, and the experimental parameters. The combined model of warm dense matter and of the x-ray scattering theory is validated against an experiment on room-temperature, solid beryllium. It is then applied to experiments on warm dense beryllium and aluminum. Generally good agreement is found with the experiments. However, some significant discrepancies are revealed and appraised. Based on the strength of our model, we discuss the current state of x-ray scattering experiments on warm dense matter and their potential to determine plasma parameters, to discriminate among models, and to reveal interesting and difficult to model physics in dense plasmas.

Partial ionization in dense plasmas: comparisons among average-atom density functional models

Nuclei interacting with electrons in dense plasmas acquire electronic bound states, modify continuum states, generate resonances and hopping electron states, and generate short-range ionic order. The mean ionization state (MIS), i.e, the mean charge Z of an average ion in such plasmas, is a valuable concept: Pseudopotentials, pair-distribution functions, equations of state, transport properties, energy-relaxation rates, opacity, radiative processes, etc., can all be formulated using the MIS of the plasma more concisely than with an all-electron description. However, the MIS does not have a unique definition and is used and defined differently in different statistical models of plasmas. Here, using the MIS formulations of several average-atom models based on density functional theory, we compare numerical results for Be, Al, and Cu plasmas for conditions inclusive of incomplete atomic ionization and partial electron degeneracy. By contrasting modern orbital-based models with orbital-free Thomas-Fermi models, we quantify the effects of shell structure, continuum resonances, the role of exchange and correlation, and the effects of different choices of the fundamental cell and boundary conditions. Finally, the role of the MIS in plasma applications is illustrated in the context of x-ray Thomson scattering in warm dense matter.

Spatially resolved analysis of Kα x-ray emission from plasmas induced by a femtosecond weakly relativistic laser pulse at various polarizations

Spatially resolved K-shell spectroscopy is used here to investigate the interaction of an ultrashort laser pulse (λ=800 nm, τ=40 fs) with a Ti foil under intense irradiation (Iλ(2)=2×10(18)Wμm(2)cm(-2)) and the following fast electron generation and transport into the target. The effect of laser pulse polarization (p, s, and circular) on the Kα yield and line shape is probed. The radial structure of intensity and width of the lines, obtained by a discretized Abel deconvolution algorithm, suggests an annular distribution of both the hot electron propagation into the target and the target temperature. An accurate modeling of Kα line shapes was performed, revealing temperature gradients, going from a few eV up to 15-20 eV, depending on the pulse polarization. Results are discussed in terms of mechanisms of hot electron generation and of their transport through the preplasma in front of the target.

≃10 eV ionization shift in Ir Kα2 from a near-coincident Lu K-edge

Close to an x-ray filter's K-edge the transmission depends strongly on the photon energy. For a few atom pairs, the K-edge of one is only a few tens of eV higher than a K-line energy of another, so that a small change in the line's energy becomes a measurable change in intensity behind such a matching filter. Lutetium's K-edge is ≃27 eV above iridium's Kα(2) line, ≃63.287 keV for cold Ir. A Lu filter reduces this line's intensity by ≃10 % when it is emitted by a plasma, indicating an ionization shift Δε≃10±1 eV.

Compact, rugged in-chamber transmission spectrometers (7-28 keV) for the Sandia Z facility

We describe a pair of time-integrated transmission spectrometers that are designed to survey 7-28 keV (1.9 to 0.43 Å) x-ray photons produced by experiments on the Sandia Z pulsed power facility. Each spectrometer uses a quartz 10-11 crystal in a Cauchois geometry with a slit to provide spatial resolution along one dimension. The spectrometers are located in the harsh environment of the Z vacuum chamber, which necessitates that their design be compact and rugged. Example data from calibration tests and Z experiments are shown that illustrate the utility of the instruments.

X-ray Thomson scattering in warm dense matter at low frequencies

The low-frequency portion of the x-ray Thomson scattering spectrum is determined by electrons that follow the slow ion motion. This ion motion is characterized by the ion-ion dynamic structure factor, which contains a wealth of information about the ions, including structure and collective modes. The frequency-integrated (diffraction) contribution is considered first. An effective dressed-particle description of warm dense matter is derived from the quantum Ornstein-Zernike equations, and this is used to identify a Yukawa model for warm dense matter. The efficacy of this approach is validated by comparing a predicted structure with data from the extreme case of a liquid metal; good agreement is found. A Thomas-Fermi model is then introduced to allow the separation of bound and free states at finite temperatures, and issues with the definition of the ionization state in warm dense matter are discussed. For applications, analytic structure factors are given on either side of the Kirkwood line. Finally, several models are constructed for describing the slow dynamics of warm dense matter. Two classes of models are introduced that both satisfy the basic sum rules. One class of models is the "plasmon-pole"-like class, which yields the dispersion of ion-acoustic waves. Damping is then included via generalized hydrodynamics models that incorporate viscous contributions.

Temperature and Kalpha-yield radial distributions in laser-produced solid-density plasmas imaged with ultrahigh-resolution x-ray spectroscopy

We study warm dense matter formed by subpicosecond laser irradiation at several 10(19) W/cm(2) of thin Ti foils using x-ray spectroscopy with high spectral (E/DeltaE approximately 15,000) and one-dimensional spatial (Deltax=13.5 microm) resolutions. Ti Kalpha doublets modeled by line-shape calculations are compared with Abel-inverted single-pulse experimental spectra and provide radial distributions of the bulk-electron temperature and the absolute-photon number Kalpha yield in the target interiors. A core with approximately 40 eV extends homogeneously up to ten times the laser-focus size. The spatial distributions of the bulk-electron temperature and Kalpha yield are strongly correlated.

Fast-electron-relaxation measurement for laser-solid interaction at relativistic laser intensities

We present measurements of the fast-electron-relaxation time in short-pulse (0.5 ps) laser-solid interactions for laser intensities of 10(17), 10(18), and 10(19) Wcm2, using a picosecond time-resolved x-ray spectrometer and a time-integrated electron spectrometer. We find that the laser coupling to hot electrons increases as the laser intensity becomes relativistic, and that the thermalization of fast electrons occurs over time scales on the order of 10 ps at all laser intensities. The experimental data are analyzed using a combination of models that include Kalpha generation, collisional coupling, and plasma expansion.

Collisional relaxation of superthermal electrons generated by relativistic laser pulses in dense plasma

Energy relaxation of the hot electron population generated by relativistic laser pulses in overdense plasma is analyzed for densities ranging from below to 1000 times solid density. It is predicted that longitudinal beam-plasma instabilities, which dominate energy transfer between hot electrons and plasma at lower densities, are suppressed by collisions beyond solid density. The respective roles of collisional energy transfer modes, i.e., direct collisions, diffusion, and resistive return current heating, are identified with respect to plasma density. The transition between the kinetic and the collisional regimes and scalings of collisional process are demonstrated by a fully integrated one-dimensional collisional particle simulation.