Analysis of Thomson scattering from nonequilibrium plasmas

Transmissions of an x-ray free electron laser pulse through Al: Influence of nonequilibrium electron kinetics

A theoretical model for investigating the radiative transfer of an x-ray free electron laser (XFEL) pulse is developed based on a one-dimensional radiative transfer equation. The population dynamics of energy levels is obtained by rate equation approximation coupling with the Fokker-Planck equation, in which the electron energy distribution function (EEDF) is self-consistently determined. As an illustrative example, XFEL pulse propagation through a solid-density aluminum (Al) is investigated. The characteristics of the temporal evolution of the x-ray pulse shape, level population, and EEDF are demonstrated. The EEDF usually has two parts in XFEL-Al interactions: the near equilibrium part in the lower energy regions and the nonequilibrium part in the higher energy region. The deep gap between the two parts is quickly filled in the solid-density Al plasma. The pulse shape is distorted and the duration shortens as the x-ray pulse propagates through the Al sample. The x-ray transmission spectra were compared with experimental and other theoretical results, and good agreement was found. There are slight discrepancies between the transmission obtained by solving the Fokker-Planck equation and Maxwellian assumptions because nonequilibrium electrons in the higher energy region account for only a small fraction of the total electrons.

Picosecond to microsecond dynamics of X-ray irradiated materials at MHz pulse repetition rate

Modern X-ray free-electron lasers (XFELs) produce intense femtosecond X-ray pulses able to cause significant damage to irradiated targets. Energetic photoelectrons created upon X-ray absorption, and Auger electrons emitted after relaxation of core-hole states trigger secondary electron cascades, which contribute to the increasing transient free electron density on femtosecond timescales. Further evolution may involve energy and particle diffusion, creation of point defects, and lattice heating. This long-timescale (up to a microsecond) X-ray-induced dynamics is discussed on the example of silicon in two-dimensional geometry. For modeling, we apply an extended Two-Temperature model with electron density dynamics, nTTM, which describes relaxation of an irradiated sample between two successive X-ray pulses, emitted from XFEL at MHz pulse repetition rate. It takes into account ambipolar carrier diffusion, electronic and atomic heat conduction, as well as electron-ion coupling. To solve the nTTM system of equations in two dimensions, we developed a dedicated finite-difference integration algorithm based on Alternating Direction Implicit method with an additional predictor-corrector scheme. We show first results obtained with the model and discuss its possible applications for XFEL optics, detectors, and for diagnostics tools. In particular, the model can estimate the timescale of material relaxation relevant for beam diagnostic applications during MHz operation of contemporary and future XFELs.

Development of a new quantum trajectory molecular dynamics framework

An extension to the wave packet description of quantum plasmas is presented, where the wave packet can be elongated in arbitrary directions. A generalized Ewald summation is constructed for the wave packet models accounting for long-range Coulomb interactions and fermionic effects are approximated by purpose-built Pauli potentials, self-consistent with the wave packets used. We demonstrate its numerical implementation with good parallel support and close to linear scaling in particle number, used for comparisons with the more common wave packet employing isotropic states. Ground state and thermal properties are compared between the models with differences occurring primarily in the electronic subsystem. Especially, the electrical conductivity of dense hydrogen is investigated where a 15% increase in DC conductivity can be seen in our wave packet model compared with other models. This article is part of the theme issue 'Dynamic and transient processes in warm dense matter'.

Nonequilibrium band occupation and optical response of gold after ultrafast XUV excitation

Free electron lasers offer unique properties to study matter in states far from equilibrium as they combine short pulses with a large range of photon energies. In particular, the possibility to excite core states drives new relaxation pathways that, in turn, also change the properties of the optically and chemically active electrons. Here, we present a theoretical model for the dynamics of the nonequilibrium occupation of the different energy bands in solid gold driven by exciting deep core states. The resulting optical response is in excellent agreement with recent measurements and, combined with our model, provides a quantitative benchmark for the description of electron-phonon coupling in strongly driven gold. Focusing on sub-picosecond time scales, we find essential differences between the dynamics induced by XUV and visible light.

Density functional tight binding approach utilized to study X-ray-induced transitions in solid materials

Intense X-ray pulses from free-electron lasers can trigger ultrafast electronic, structural and magnetic transitions in solid materials, within a material volume which can be precisely shaped through adjustment of X-ray beam parameters. This opens unique prospects for material processing with X rays. However, any fundamental and applicational studies are in need of computational tools, able to predict material response to X-ray radiation. Here we present a dedicated computational approach developed to study X-ray induced transitions in a broad range of solid materials, including those of high chemical complexity. The latter becomes possible due to the implementation of the versatile density functional tight binding code DFTB+ to follow band structure evolution in irradiated materials. The outstanding performance of the implementation is demonstrated with a comparative study of XUV induced graphitization in diamond.

An interplay of various damage channels in polyethylene exposed to ultra-short XUV/X-ray pulses

Polyethylene (PE) irradiated with femtosecond extreme ultraviolet or X-ray laser pulses in a single-shot damage regime is studied theoretically. The employed microscopic simulation tool XTANT-3 traces nonequilibrium electron kinetics, energy exchange between electrons and atoms, nonthermal modification of interatomic potential, and the induced atomic response. It is found that the nonthermal detachment of hydrogen atoms in bulk PE starts at the threshold deposited dose of ∼0.05 eV per atom. With an increase in the dose, more hydrogen atoms detach from the carbon backbone. At a dose of ∼0.3 eV per atom, hydrogen behaves like a liquid flowing around carbon chains. It is accompanied by the appearance of defect energy levels within the band gap. At a dose of ∼0.5 eV per atom, carbon chains actively bend and cross-link. In the range of doses from ∼0.5 eV per atom to ∼0.9 eV per atom, the electronic excitation induces formation of new carbon structures embedded in the hydrogen liquid, such as benzene-like rings. The band gap collapses at such doses, merging the valence and the conduction bands. Finally, at doses above ∼0.9 eV per atom, the carbon subsystem also melts into liquid. All of these damage mechanisms are mainly nonthermal, triggered by promotion of electrons from the valence into the conduction band of PE. At high doses, however, thermal electron-ion coupling is extremely fast causing equilibration of the electronic and the ionic temperatures within a hundred femtoseconds.

Nonthermal phase transitions in metals

It is well known that sufficiently thick metals irradiated with ultrafast laser pulses exhibit phonon hardening, in contrast to ultrafast nonthermal melting in covalently bonded materials. It is still an open question how finite size metals react to irradiation. We show theoretically that generally metals, under high electronic excitation, undergo nonthermal phase transitions if material expansion is allowed (e.g. in finite samples). The nonthermal phase transitions are induced via an increase of the electronic pressure which leads to metal expansion. This, in turn, destabilizes the lattice triggering a phase transition without a thermal electron-ion coupling mechanism involved. We find that hexagonal close-packed metals exhibit a diffusionless transition into a cubic phase, whereas metals with a cubic lattice melt. In contrast to covalent solids, nonthermal phase transitions in metals are not ultrafast, predicative on the lattice expansion.

Thomson scattering from dense inhomogeneous plasmas

X-ray Thomson scattering experiments in the soft and hard x-ray regime yield information on fundamental parameters of high-density systems. Pump-probe experiments with variable time delay provide insight into the excitation and relaxation dynamics in dense plasmas. On short time scales, a local thermodynamic equilibrium description might not be sufficient. Besides nonequilibrium effects on the electron distribution function, spatial inhomogeneities influence the scattering signal. Generalizing previous approaches of Belyi [Phys. Rev. E 97, 053204 (2018)2470-004510.1103/PhysRevE.97.053204] and Kozlowski et al. [Sci. Rep. 6, 24283 (2016)2045-232210.1038/srep24283], we discuss implications for Thomson scattering spectra for inhomogeneous plasmas in the warm dense matter regime based on a gradient expansion within real-time Green's-functions theory. Especially in the collective scattering regime, Thomson scattering spectra are modifed substantially by spatial inhomogeneities. Within a first-order gradient expansion, the dispersion relation for plasmons is determined. In particular, the ratio of the heights of the plasmon peaks is changed which prevents a simple estimation of the plasma temperature from the detailed balance relation.

Liquid Structure of Shock-Compressed Hydrocarbons at Megabar Pressures

We present results for the ionic structure in hydrocarbons (polystyrene, polyethylene) that were shock compressed to pressures of up to 190 GPa, inducing rapid melting of the samples. The structure of the resulting liquid is then probed using in situ diffraction by an x-ray free electron laser beam, demonstrating the capability to obtain reliable diffraction data in a single shot, even for low-Z samples without long range order. The data agree well with ab initio simulations, validating the ability of such approaches to model mixed samples in states where complex interparticle bonds remain, and showing that simpler models are not necessarily valid. While the results clearly exclude the possibility of complete carbon-hydrogen demixing at the conditions probed, they also, in contrast to previous predictions, indicate that diffraction is not always a sufficient diagnostic for this phenomenon.

Quantum theory for the dynamic structure factor in correlated two-component systems in nonequilibrium: Application to x-ray scattering

We present a quantum theory for the dynamic structure factors in nonequilibrium, correlated, two-component systems such as plasmas or warm dense matter. The polarization function, which is needed as the input for the calculation of the structure factors, is calculated in nonequilibrium based on a perturbation expansion in the interaction strength. To make our theory applicable for x-ray scattering, a generalized Chihara decomposition for the total electron structure factor in nonequilibrium is derived. Examples are given and the influence of correlations and exchange on the structure and the x-ray-scattering spectrum are discussed for a model nonequilibrium distribution, as often encountered during laser heating of materials, as well as for two-temperature systems.

Pair potentials for warm dense matter and their application to x-ray Thomson scattering in aluminum and beryllium

Ultrafast laser experiments yield increasingly reliable data on warm dense matter, but their interpretation requires theoretical models. We employ an efficient density functional neutral-pseudoatom hypernetted-chain (NPA-HNC) model with accuracy comparable to ab initio simulations and which provides first-principles pseudopotentials and pair potentials for warm-dense matter. It avoids the use of (i) ad hoc core-repulsion models and (ii) "Yukawa screening" and (iii) need not assume ion-electron thermal equilibrium. Computations of the x-ray Thomson scattering (XRTS) spectra of aluminum and beryllium are compared with recent experiments and with density-functional-theory molecular-dynamics (DFT-MD) simulations. The NPA-HNC structure factors, compressibilities, phonons, and conductivities agree closely with DFT-MD results, while Yukawa screening gives misleading results. The analysis of the XRTS data for two of the experiments, using two-temperature quasi-equilibrium models, is supported by calculations of their temperature relaxation times.

Atomic bound state and scattering properties of effective momentum-dependent potentials

Effective classical dynamics provide a potentially powerful avenue for modeling large-scale dynamical quantum systems. We have examined the accuracy of a Hamiltonian-based approach that employs effective momentum-dependent potentials (MDPs) within a molecular-dynamics framework through studies of atomic ground states, excited states, ionization energies, and scattering properties of continuum states. Working exclusively with the Kirschbaum-Wilets (KW) formulation with empirical MDPs [C. L. Kirschbaum and L. Wilets, Phys. Rev. A 21, 834 (1980)0556-279110.1103/PhysRevA.21.834], optimization leads to very accurate ground-state energies for several elements (e.g., N, F, Ne, Al, S, Ar, and Ca) relative to Hartree-Fock values. The KW MDP parameters obtained are found to be correlated, thereby revealing some degree of transferability in the empirically determined parameters. We have studied excited-state orbits of electron-ion pair to analyze the consequences of the MDP on the classical Coulomb catastrophe. From the optimized ground-state energies, we find that the experimental first- and second-ionization energies are fairly well predicted. Finally, electron-ion scattering was examined by comparing the predicted momentum transfer cross section to a semiclassical phase-shift calculation; optimizing the MDP parameters for the scattering process yielded rather poor results, suggesting a limitation of the use of the KW MDPs for plasmas.

Dynamic conductivity and plasmon profile of aluminum in the ultra-fast-matter regime

We use an explicitly isochoric two-temperature theory to analyze recent x-ray laser scattering data for aluminum in the ultra-fast-matter (UFM) regime up to 6 eV. The observed surprisingly low conductivities are explained by including strong electron-ion scattering effects using the phase shifts calculated via the neutral-pseudo-atom model. The difference between the static conductivity for UFM-Al and equilibrium aluminum in the warm-dense matter state is clearly brought out by comparisons with available density-fucntional+molecular-dynamics simulations. Thus the applicability of the Mermin model to UFM is questioned. The static and dynamic conductivity, collision frequency, and the plasmon line shape, evaluated within the simplest Born approximation for UFM aluminum, are in good agreement with experiment.

Theory of Thomson scattering in inhomogeneous media

Thomson scattering of laser light is one of the most fundamental diagnostics of plasma density, temperature and magnetic fields. It relies on the assumption that the properties in the probed volume are homogeneous and constant during the probing time. On the other hand, laboratory plasmas are seldom uniform and homogeneous on the temporal and spatial dimensions over which data is collected. This is particularly true for laser-produced high-energy-density matter, which often exhibits steep gradients in temperature, density and pressure, on a scale determined by the laser focus. Here, we discuss the modification of the cross section for Thomson scattering in fully-ionized media exhibiting steep spatial inhomogeneities and/or fast temporal fluctuations. We show that the predicted Thomson scattering spectra are greatly altered compared to the uniform case, and may lead to violations of detailed balance. Therefore, careful interpretation of the spectra is necessary for spatially or temporally inhomogeneous systems.

Ab initio calculation of the ion feature in x-ray Thomson scattering

The spectrum of x-ray Thomson scattering is proportional to the dynamic structure factor. An important contribution is the ion feature which describes elastic scattering of x rays off electrons. We apply an ab initio method for the calculation of the form factor of bound electrons, the slope of the screening cloud of free electrons, and the ion-ion structure factor in warm dense beryllium. With the presented method we can calculate the ion feature from first principles. These results will facilitate a better understanding of x-ray scattering in warm dense matter and an accurate measurement of ion temperatures which would allow determining nonequilibrium conditions, e.g., along shock propagation.

Evidence for a glassy state in strongly driven carbon

Here, we report results of an experiment creating a transient, highly correlated carbon state using a combination of optical and x-ray lasers. Scattered x-rays reveal a highly ordered state with an electrostatic energy significantly exceeding the thermal energy of the ions. Strong Coulomb forces are predicted to induce nucleation into a crystalline ion structure within a few picoseconds. However, we observe no evidence of such phase transition after several tens of picoseconds but strong indications for an over-correlated fluid state. The experiment suggests a much slower nucleation and points to an intermediate glassy state where the ions are frozen close to their original positions in the fluid.

Reduced coupled-mode approach to electron-ion energy relaxation

We present a reduced model for the energy transfer via coupled collective modes in two-temperature plasmas based on quantum statistical theory. The model is compared with exact numerical evaluations of the coupled-mode (CM) energy transfer rate and with alternative reduced approaches over a range of conditions in the warm dense matter (WDM) and inertial confinement fusion (ICF) regimes. Our approach shows excellent agreement with an exact treatment of the CM rate and supports the importance of the coupled-mode effect for the temperature and energy relaxation in WDM and ICF plasmas. We find that electronic damping of collective ion density fluctuations is crucial for correctly describing the mode spectrum and, thus, the energy exchange. The reduced CM approach is studied over a wide parameter space, enabling us to establish its limits of applicability.

Nonequilibrium electron dynamics in materials driven by high-intensity x-ray pulses

We calculated the evolution of the electron system in solid-density matter irradiated by high-intensity x-ray pulses between 2 and 8 keV using molecular dynamics. For pulses shorter than 40 fs, the kinetic energy distribution of the electrons is highly nonthermal during and right after the pulse, and a large fraction of the absorbed x-ray energy resides with the fast photoelectrons which equilibrate on the timescale of the pulse length. The average ionization and electron temperature of the bulk of the electrons are significantly lower than their equilibrium values.

Stimulated scattering of electromagnetic waves carrying orbital angular momentum in quantum plasmas

We investigate stimulated scattering instabilities of coherent circularly polarized electromagnetic (CPEM) waves carrying orbital angular momentum (OAM) in dense quantum plasmas with degenerate electrons and nondegenerate ions. For this purpose, we employ the coupled equations for the CPEM wave vector potential and the driven (by the ponderomotive force of the CPEM waves) equations for the electron and ion plasma oscillations. The electrons are significantly affected by the quantum forces (viz., the quantum statistical pressure, the quantum Bohm potential, as well as the electron exchange and electron correlations due to electron spin), which are included in the framework of the quantum hydrodynamical description of the electrons. Furthermore, our investigation of the stimulated Brillouin instability of coherent CPEM waves uses the generalized ion momentum equation that includes strong ion coupling effects. The nonlinear equations for the coupled CPEM and quantum plasma waves are then analyzed to obtain nonlinear dispersion relations which exhibit stimulated Raman, stimulated Brillouin, and modulational instabilities of CPEM waves carrying OAM. The present results are useful for understanding the origin of scattered light off low-frequency density fluctuations in high-energy density plasmas where quantum effects are eminent.

Novel attractive force between ions in quantum plasmas

We report a new attractive force between ions that are shielded by degenerate electrons in quantum plasmas. Specifically, we show that the electric potential around an isolated ion has a hard core negative part that resembles the Lennard-Jones-type potential. Physically, the new electric potential is attributed to the consideration of the quantum statistical pressure and the quantum Bohm potential, as well as the electron exchange and electron correlations due to electron-1/2 spin within the framework of the quantum hydrodynamical description of quantum plasmas. The shape of the attractive potential is determined by the ratio between the Bohr radius and the Wigner-Seitz radius of degenerate electrons. The existence of the hard core negative potential will be responsible for the attraction of ions forming lattices and atoms or molecules, as well as for critical points and phase transitions in quantum plasmas at nanoscales.

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.