E. Brambrink’s research while affiliated with European XFEL and other places


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Publications (214)


A two-dimensional schematic of a von Hámos detector with a mosaic crystal, with the paths of two different photon energies, E 1 and E 2 > E 1, to the detector also shown. In full von Hámos geometry, the crystal is cylindrically bent with a radius of curvature r, while X cam is the distance from the source to a point on the detector. Mosaic focusing in this geometry is represented by photons incident on the crystal at different angles reflecting off crystallites at angles to the surface normal, which then focus back to the same point on the detector. In the present two-dimensional geometry, the crystal and detector are lines along the dispersion axis, with the crystal having a finite thickness.
The differential reflectivity from depth broadening in three scenarios involving a 40  μm thick graphite crystal, considering up to p = 4 reflections. Note the marked increase in reflectivity when mosaicity is taken into account. In all cases, the circular markers indicate the energy difference on detector that a photon can be reflected to. (a) Depth broadening for a photon with different energies incident at its Bragg angle on a crystal without mosaicity. Note that the shift on the detector is only for Δ E > 0 and that the maximum Δ E is different for each photon energy. (b) The same as (a), but now the crystal has a mosaicity γ = 0.08 °. (c) Depth broadening for a fixed photon energy on a mosaic crystal at different angles of incidence.
A break down of the effects contributing to mosaic broadening, just for reflections from the surface of an 80 mm long HAPG crystal. Left: A plot of Eq. (10) in von Hámos geometry for different incident photon energies E 0, showing the energy shift on the detector vs the shift in the angle of incidence on the crystal from the photon’s Bragg angle. The mosaic broadening is toward higher energies on the detector than the photon energy, and there is an overlap in the position on the detector that the crystal will reflect to. The vertical dotted lines indicate the edges of the crystal. Right: The mosaic function as it appears on the detector. The drops in the reflectivity are when the edges of the crystal are reached.
A comparison of the HAPG rocking curve using a single crystal thickness (orange dashed), a uniformly averaged curve for different thickness (green dashed-dot), and experimental measurements of the rocking curve from Ref. 24 (red points). The experimental curve has an FWHM of 116  μrad. The theoretical and experimental curves are for an 8.048 keV photon. Note that the theoretical curves have been shifted down in angle by 32.3  μrad to center on zero arising from dynamical diffraction theory.²¹ Also shown are fits to the experimental data using a Voigt profile (blue solid) and Student’s t-distribution (gray dotted). Inset: Focused plot on the wings of the curves. The scale of both axes is shared with the main plot.
A Voigt profile intrinsic rocking curve in terms of the angle of incidence on the crystal (left) and the energy on the detector (right). The vertical dotted lines indicate cutoffs due to the edges of the crystal. The FWHM of the IRC is 55.7  μrad, with a Gaussian FWHM of 50.4  μrad and a Lorentzian FWHM of 9.48  μrad.

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Effects of mosaic crystal instrument functions on x-ray Thomson scattering diagnostics
  • Article
  • Full-text available

September 2024

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35 Reads

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1 Citation

Journal of Applied Physics

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Hannah Bellenbaum

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Mosaic crystals, with their high integrated reflectivities, are widely employed in spectrometers used to diagnose high energy density systems. X-ray Thomson scattering (XRTS) has emerged as a powerful diagnostic tool of these systems, providing in principle direct access to important properties such as the temperature via detailed balance. However, the measured XRTS spectrum is broadened by the spectrometer instrument function (IF), and without careful consideration of the IF one risks misdiagnosing system conditions. Here, we consider in detail the IF of 40 and 100 μm mosaic Highly Annealed Pyrolytic Graphite crystals, and how the broadening varies across the spectrometer in an energy range of 6.7–8.6 keV. Notably, we find a strong asymmetry in the shape of the IF toward higher energies. As an example, we consider the effect of the asymmetry in the IF on the temperature inferred via XRTS for simulated 80 eV CH plasmas and find that the temperature can be overestimated if an approximate symmetric IF is used. We, therefore, expect a detailed consideration of the full IF will have an important impact on system properties inferred via XRTS in both forward modeling and model-free approaches.

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Formation of high-aspect-ratio nanocavity in LiF crystal using a femtosecond of x-ray FEL pulse

September 2024

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25 Reads

Sub-picosecond optical laser processing of metals is actively utilized for modification of a heated surface layer. But for deeper modification of different materials a laser in the hard x-ray range is required. Here, we demonstrate that a single 9-keV x-ray pulse from a free-electron laser can form a um-diameter cylindrical cavity with length of ~1 mm in LiF surrounded by shock-transformed material. The plasma-generated shock wave with TPa-level pressure results in damage, melting and polymorphic transformations of any material, including transparent and non-transparent to conventional optical lasers. Moreover, cylindrical shocks can be utilized to obtain a considerable amount of exotic high-pressure polymorphs. Pressure wave propagation in LiF, radial material flow, formation of cracks and voids are analyzed via continuum and atomistic simulations revealing a sequence of processes leading to the final structure with the long cavity. Similar results can be produced with semiconductors and ceramics, which opens a new pathway for development of laser material processing with hard x-ray pulses.


Visualizing plasmons and ultrafast kinetic instabilities in laser-driven solids using X-ray scattering

September 2024

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111 Reads

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1 Citation

Ultra-intense lasers that ionize atoms and accelerate electrons in solids to near the speed of light can lead to kinetic instabilities that alter the laser absorption and subsequent electron transport, isochoric heating, and ion acceleration. These instabilities can be difficult to characterize, but X-ray scattering at keV photon energies allows for their visualization with femtosecond temporal resolution on the few nanometer mesoscale. Here, we perform such experiment on laser-driven flat silicon membranes that shows the development of structure with a dominant scale of 60 nm in the plane of the laser axis and laser polarization, and 95 nm in the vertical direction with a growth rate faster than 0.1 fs⁻¹. Combining the XFEL experiments with simulations provides a complete picture of the structural evolution of ultra-fast laser-induced plasma density development, indicating the excitation of plasmons and a filamentation instability. Particle-in-cell simulations confirm that these signals are due to an oblique two-stream filamentation instability. These findings provide new insight into ultra-fast instability and heating processes in solids under extreme conditions at the nanometer level with possible implications for laser particle acceleration, inertial confinement fusion, and laboratory astrophysics.


FIG. 1. Schematic illustration of the setup in Interaction Chamber 1 (IC1) modified from Wollenweber et al. [26]. The x-ray beam is seeded at 7703 eV in the SASE2 undulator including a SASE pedestal. The beam is passed through a four-bounce Si (111) monochromator to remove this SASE pedestal before being focused onto an Al foil. The x-rays are scattered, collected, and focused by a spherically bent diced analyzer crystal onto a Jungfrau detector with asymmetric pixels. Both the analyzer and detector are mounted onto curved rails to vary the scattering angle θ. The detector is shown in two configurations: at 13.6 • corresponding to (π/2 − θ B ) the Bragg angle with the detector plane directly above the sample; and the highest angle. The scattering angle can be freely set between 3.6 • and 25.6 • in this study. The combination of the monochromated beam and ultrahigh resolution spectrometer allows for the high-fidelity measurements of electronic structure.
FIG. 2. Measured XRTS intensity for five different wave numbers as a function of the photon energy loss E = E 0 − E s in units of integrated intensity in photons/shot. The curves are offset vertically for clarity and show the variation in position, intensity, and shape of the plasmon in aluminium. Further details on the collection of the spectra are provided in the table in the Supplemental Material [38]. Inset: example spectrum of the narrow quasielastic scattering (red) for the highest wave number, and a Gaussian fit with σ = 0.19 eV (black dashed). The intensity of the quasielastic scattering uses the same scale as the main figure.
FIG. 3. Plasmon dispersion of aluminium. Crosses: experimental peak position and associated uncertainty, with red below the pair continuum, and blue in the pair continuum; red dashed line: the experimental data fitted to the dispersion of Eq. (2); black stars: previous EELS measurements of the Al plasmon by Sprösser-Prou et al. [29]; green circles: TDDFT average plasmon position, with the error bars indicating the standard deviation of the peak position in the q range; gray squares: TDDFT plasmon position only at the central q value. The shaded gray area indicates the pair continuum [40], and the dotted vertical line the Fermi wave number q F in bulk Al with a face-centered cubic (fcc) lattice [41].
FIG. 4. Using high-resolution XRTS measurements (solid red) to benchmark first-principles TDDFT simulations at q 0 = 0.92 Å −1 . The solid green curve is from a single TDDFT simulation at q 0 = 0.932 Å −1 , the closest our simulation box size allows us to get to the central q value. The blue dashed curves have been obtained from single TDDFT simulations at different q values in the experimental range: 0.858, 0.914, 0.972, 1.029 Å −1 . The solid black line has been averaged over the five individual TDDFT results with equal weighting. The red area indicates the experimental uncertainty in the plasmon position.
Ultrahigh resolution x-ray Thomson scattering measurements at the European X-ray Free Electron Laser

June 2024

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63 Reads

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8 Citations

Using an ultrahigh resolution ( Δ E ∼ 0.1 eV ) setup to measure electronic features in x-ray Thomson scattering (XRTS) experiments at the European XFEL in Germany, we have studied the collective plasmon excitation in aluminium at ambient conditions, which we can measure very accurately even at low momentum transfers. As a result, we can resolve previously reported discrepancies between time-dependent density functional theory simulations and experimental observations. The demonstrated capability for high-resolution XRTS measurements will be a game changer for the diagnosis of experiments with matter under extreme densities, temperatures, and pressures, and unlock the full potential of state-of-the-art x-ray free electron laser (XFEL) facilities to study planetary interior conditions, to understand inertial confinement fusion applications, and for material science and discovery. Published by the American Physical Society 2024


Plasma screening in mid-charged ions observed by K-shell line emission

June 2024

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152 Reads

Dense plasma environment affects the electronic structure of ions via variations of the microscopic electrical fields, also known as plasma screening. This effect can be either estimated by simplified analytical models, or by computationally expensive and to date unverified numerical calculations. We have experimentally quantified plasma screening from the energy shifts of the bound-bound transitions in matter driven by the x-ray free electron laser (XFEL). This was enabled by identification of detailed electronic configurations of the observed K{\alpha}, K\b{eta} and K{\gamma} lines. This work paves the way for improving plasma screening models including connected effects like ionization potential depression and continuum lowering, which will advance the understanding of atomic physics in Warm Dense Matter regime.


Effects of Mosaic Crystal Instrument Functions on X-ray Thomson Scattering Diagnostics

June 2024

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61 Reads

Mosaic crystals, with their high integrated reflectivities, are widely-employed in spectrometers used to diagnose high energy density systems. X-ray Thomson scattering (XRTS) has emerged as a powerful diagnostic tool of these systems, providing in principle direct access to important properties such as the temperature via detailed balance. However, the measured XRTS spectrum is broadened by the spectrometer instrument function (IF), and without careful consideration of the IF one risks misdiagnosing system conditions. Here, we consider in detail the IF of mosaic crystals and how the broadening varies across the spectrometer. Notably, we find a strong asymmetry in the shape of the IF towards higher energies. As an example, we consider the effect on the inferred temperature, and find that it can be overestimated if an approximate symmetric IF is used. We therefore expect a detailed consideration of the full IF will have an important impact on system properties inferred via XRTS in both forward modelling and model-free approaches.


Shock compression experiments using the DiPOLE 100-X laser on the high energy density instrument at the European x-ray free electron laser: Quantitative structural analysis of liquid Sn

April 2024

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254 Reads

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1 Citation

X-ray free electron laser (XFEL) sources coupled to high-power laser systems offer an avenue to study the structural dynamics of materials at extreme pressures and temperatures. The recent commissioning of the DiPOLE 100-X laser on the high energy density (HED) instrument at the European XFEL represents the state-of-the-art in combining x-ray diffraction with laser compression, allowing for compressed materials to be probed in unprecedented detail. Here, we report quantitative structural measurements of molten Sn compressed to 85(5) GPa and ∼ 3500 K. The capabilities of the HED instrument enable liquid density measurements with an uncertainty of ∼ 1 % at conditions which are extremely challenging to reach via static compression methods. We discuss best practices for conducting liquid diffraction dynamic compression experiments and the necessary intensity corrections which allow for accurate quantitative analysis. We also provide a polyimide ablation pressure vs input laser energy for the DiPOLE 100-X drive laser which will serve future users of the HED instrument.


Impulse coupling measurement of metallic and carbon targets during laser ablation through ballistic pendulum experiments and simulations

April 2024

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74 Reads

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1 Citation

Laser ablation propulsion and orbit cleaning are developing areas of research. The general aim of laser-based techniques applied to this field is to maximize the momentum transfer produced by a laser shot. This work presents results from ballistic pendulum experiments under vacuum on aluminum, copper, tin, gold, and porous graphite targets. The work has focused on the metrology of the laser experiments to ensure good stability over a wide range of laser parameters (laser intensity ranging from 4 GW/cm 2 to 8.7 TW/cm 2, pulse duration from 80 ps to 15 ns, and wavelengths of 528 or 1057 nm). The results presented compile data from three experimental campaigns spanning from 2018 to 2021 on two different laser platforms and using different pulse durations, energies, and wavelengths. The study is complemented by the simulation of the momentum from the mono-dimensional Lagrangian code ESTHER. The first part of this work gives a detailed description of the experimental setup used, the ESTHER code, and the treatment of the simulations. The second part focuses on the experimental results. The third part describes the simulation results and provides a comparison with the experimental data. The last part presents possible improvements for future work on the subject.



Investigation on laser absorption and x-ray radiation in microstructured titanium targets heated by short-pulse relativistic laser pulses

January 2024

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110 Reads

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1 Citation

Physical Review Research

The enhancement effect of a microstructured surface on laser absorption and characteristic K α emission has been investigated by measuring K-shell emission from titanium (Ti) targets irradiated with high-intensity ( ∼ 10 20 W cm − 2 ), subpicosecond (500 fs) laser pulses. The experimental results indicate a modest enhancement ( 1.6 × ) of K α emission from microstructured targets compared to flat foils, but with a similar intensity and profile of He α and Li-like satellites. Particle-in-cell (PIC) simulations are implemented to further understand the underlying physical processes in the laser interaction with both targets, interpreting the mechanisms responsible for the K α enhancement. The reasons for the lower-than-expected enhancement of K α emission are discussed. The rapid heating of the bulk plasma might result in the premature shutdown of K α emission before the thermalization of hot electrons or even the end of laser pulses, suggesting that the use of K α emission as a diagnostic of the hot-electron yield or relaxation could lead to a misinterpretation. Published by the American Physical Society 2024


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Citations (70)


... In practice, the measured XRTS intensity can be accurately expressed as [19] I(q, E) = S ee (q, E) ⊛ R(E) , ...

Reference:

Model-free Rayleigh weight from x-ray Thomson scattering measurements
Effects of mosaic crystal instrument functions on x-ray Thomson scattering diagnostics

... 3 One of the most important experiments for WDM is X-ray Thomson scattering (XRTS). 11,12 XRTS involves the measurement of scattered coherent hard xrays and directly probes the dynamic structure factor (DSF). Based on detailed balance, the DSF is related to the electron density-density response function. ...

Ultrahigh resolution x-ray Thomson scattering measurements at the European X-ray Free Electron Laser

... With the worldwide proliferation of high-power, long-pulse laser-compression platforms that allow us to shock or ramp compress solid targets rapidly and reproducibly to gigapascal-scale pressure states, coupled to ultrafast x-ray diagnostics that capture transformations of their crystal structure in situ within the nanosecond window before they disintegrate, the experimental observation of polymorphism under extreme loading conditions has become almost routine. The study of pressure-induced polymorphism informs our understanding of condensed matter physics at its most fundamental level, and at a rate that will only increase in the coming decade with the arrival of high-repetition-rate instruments such as the DiPOLE 100-X laser at the European X-ray Free-Electron Laser (EuXFEL) [14]. ...

Shock compression experiments using the DiPOLE 100-X laser on the high energy density instrument at the European x-ray free electron laser: Quantitative structural analysis of liquid Sn

... Figures 8 and 9 show the momentum as a function of the laser pulse energy and the momentum coupling as a function of the Iλ ffiffi ffi τ p parameter, respectively. For both figures, the results are compared with experiments performed on a similar setup in previous campaigns, 45 where no confining layer was used to enhance the momentum imparted to the target material. In the specific case of Fig. 9, the results are also compared with the results from Rudder's work. ...

Impulse coupling measurement of metallic and carbon targets during laser ablation through ballistic pendulum experiments and simulations

... Additionally, they are also the most widely used pump source for Ti:Sa femtosecond [2,3] and OPCPA [4,5] laser amplifiers. Laser sources with energy levels ranging from the joule level up to several kilojoules find application in plasma physics and shock physics experiments, as they allow generation of extreme pressure and temperature conditions during short amount of time [6,7]. Recent advancements have shown that combining hundreds of kilojoule class lasers is one of the most promising ways for achieving controllable nuclear fusion by inertial confinement fusion [8]. ...

Zr-based metallic glasses Hugoniot under laser shock compression and spall strength evolution with the strain rate ( > 10 7 s − 1 )
  • Citing Article
  • August 2023

International Journal of Impact Engineering

... Under these conditions, the absorbed energy density was ξ1 = 297 kJ/cm 3 and ξ2 = 895 kJ/cm 3 , respectively (see Methods for conversion details). It is worth noting that these impact values are 2 orders of magnitude higher than the threshold value for LiF crystal damage (∼ 4 kJ/cm 3 per pulse) determined in our previous work 25 . After each irradiation, the crystal was moved in a direction perpendicular to the beam so that the next irradiation would fall on the fresh surface of the sample. ...

Damage threshold of LiF crystal irradiated by femtosecond hard XFEL pulse sequence

... which relates the dynamic structure factor to the dynamic density response function. For example, Eq. (110) constitutes the basis of LR-TDDFT simulations of XRTS measurements [17,265,618,[697][698][699][700][701][702][703]. In practice, XRTS measurements of hydrogen are generally challenging due to its comparably small scattering cross section [259,260]. ...

Toward using collective x-ray Thomson scattering to study C–H demixing and hydrogen metallization in warm dense matter conditions
  • Citing Article
  • May 2023

... An X-ray beam with a photon energy of 9 keV (λ = 0.138 nm) and a duration of ~20 fs (full width at half maximum -FWHM) was focused through beryllium compound refractive lenses (CRLs) into a spot with a size of dFWHM = 0.41 μm, see Fig. 1A. A more detailed description of the focal spot size measurements for this experiment is given in 14 . The target was a circle LiF crystal with a diameter of 20 mm and a thickness of 2 mm and was put at the point of best focusing of the beam. ...

Direct LiF imaging diagnostics on refractive X-ray focusing at the EuXFEL High Energy Density instrument

... Two examples of facilities meeting the above requirements are the European X-ray Free Electron Laser (EU.XFEL) [82,87] and the SPring-8 Angstrom Compact Free Electron Laser (SACLA) [83,84]. ...

ReLaX: the HiBEF high-intensity short-pulse laser driver for relativistic laser-matter interaction and strong-field science at the HED instrument at EuXFEL

High Power Laser Science and Engineering

... Investigating matter at extremely high temperatures and densities has attracted considerable interest from researchers in recent years. Experimental study of warm dense matter (WDM) at such laser facilities as NIF [1], European XFEL [2], and OMEGA [3] opens a path to reveal the internal structure of planets down to their cores, both in our solar system and beyond [4]. Also, these high-pressure experiments will allow us to test theories of states of matter under extreme conditions of density and temperature [5][6][7][8][9][10]. ...

The High Energy Density Scientific Instrument at the European XFEL