Abstract
The gravitational pressure in many astrophysical objects exceeds one gigabar (one billion atmospheres)1,2,3, creating extreme conditions where the distance between nuclei approaches the size of the K shell. This close proximity modifies these tightly bound states and, above a certain pressure, drives them into a delocalized state4. Both processes substantially affect the equation of state and radiation transport and, therefore, the structure and evolution of these objects. Still, our understanding of this transition is far from satisfactory and experimental data are sparse. Here we report on experiments that create and diagnose matter at pressures exceeding three gigabars at the National Ignition Facility5 where 184 laser beams imploded a beryllium shell. Bright X-ray flashes enable precision radiography and X-ray Thomson scattering that reveal both the macroscopic conditions and the microscopic states. The data show clear signs of quantum-degenerate electrons in states reaching 30 times compression, and a temperature of around two million kelvins. At the most extreme conditions, we observe strongly reduced elastic scattering, which mainly originates from K-shell electrons. We attribute this reduction to the onset of delocalization of the remaining K-shell electron. With this interpretation, the ion charge inferred from the scattering data agrees well with ab initio simulations, but it is significantly higher than widely used analytical models predict6.
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Data availability
The three additional scattering spectra not shown in Fig. 2b are included as Extended Data Figs. 1–3. Additional data are available upon request from the corresponding author. Source data are provided with this paper.
Code availability
The Multi-Component Scattering Spectra (MCSS) code40 for analysing X-ray Thomson scattering spectra is not publicly available. An open-source code is currently under development with support from some members of our team.
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Acknowledgements
We thank the entire NIF operations, diagnostics, target design and assembly teams for support; K. Boehm and P. di Nicola for coordinating the target builds; N. Rice and H. Huang for making and metrologizing the beryllium capsules; D. Kalantar and N. Masters for resolving any alignment and machine safety issues; B. Remington and J. Lütgert for reading the manuscript and providing feedback; and M. Meamber for helping with figure design and formatting. The work of T.D., B.B., L.D., O.L.L., M.J.M, A.M.S. and P.A.S. was performed under the auspices of the US Department of Energy under contract no. DE-AC52-07NA27344, and was supported by Laboratory Directed Research and Development (LDRD) grant no. 18-ERD-033. The DFT-MD calculations were performed at the North-German Supercomputing Alliance (HLRN) facilities and at the IT and Media Center of the University of Rostock. M.B., M.S., B.B.L.W. and R.R. acknowledge support by the Deutsche Forschungsgemeinschaft (DFG) within the FOR 2440. M.B. was also partially supported by the European Horizon 2020 programme within the Marie Skłodowska-Curie actions (xICE grant number 894725). D.K. was supported by the Helmholtz Association under VH-NG-1141. D.K. and R.W.F. acknowledge support by the US Department of Energy, Office of Science, Office of Fusion Energy Sciences, award DE-AC02-05CH11231, and National Nuclear Security Administration, award DE-NA0003842. R.W.F. acknowledges support from the Department of Energy, National Nuclear Security Administration Award DE-NA0003842, and the Department of Energy, Office of Science, Office of Fusion Energy Sciences Awards DE-SC0021184 and DE-SC0018298. The work of L.B.F. and S.H.G. was supported by US Department of Energy, Fusion Energy Sciences under FEP 100182. The work of M.P.B. was partially supported by the Centre for Advanced Systems Understanding (CASUS), which is financed by Germany’s Federal Ministry of Education and Research (BMBF) and by the Saxon state government out of the State budget approved by the Saxon State Parliament. We also acknowledge the NIF Discovery Science programme for providing access to the facility. This document was prepared as an account of work sponsored by an agency of the US government. Neither the US government nor Lawrence Livermore National Security, LLC, nor any of their employees makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favouring by the United States government or Lawrence Livermore National Security, LLC. The views and opinions of authors expressed herein do not necessarily state or reflect those of the US government or Lawrence Livermore National Security, LLC, and shall not be used for advertising or product endorsement purposes.
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P.N., R.W.F. and S.H.G. proposed the experiments and aided in obtaining experimental beam time at NIF. A.Y., L.D., T.D. and O.L.L. developed the Be implosion design. T.D. fielded the experiments together with D.K., B.B., M.J.M. and A.M.S. The XRTS spectra were analysed by T.D., M.P.B., D.K. and L.B.F. Additional data analysis and feedback on analysis methods were provided by P.N., O.L.L., B.B., M.J.M., M.S. and A.M.S. D.O.G., D.A.C., J.V., R.A.B., M.P.B. and P.A.S. provided results for the ionization in dense plasmas and developed the framework for modelling XRTS spectra. M.B., M.S., B.B.L.W. and R.R. performed and analysed the DFT-MD simulations. All co-authors provided input on the interpretation of the data and their impact on astrophysics and ICF. T.D. and D.O.G. wrote the paper.
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Extended data figures and tables
Extended Data Fig. 1 X-ray Thomson scattering spectrum and fit for data set #1.
The data (black) was recorded on experiment N170214-002-999 on the first spectrometer channel (strip 1) at 0.31 ns after peak emission, t0. The best fit (red), consisting of the free-free (blue), bound-free (green) and elastic (purple) scattering contributions, yields a temperature of T = (110 ± 15) eV, a free electron density of ne = (1.34 ± 0.15) × 1024 cm−3 and an ion charge of \(\bar{Z}=3.0\pm 0.1\) resulting in a mass density of ϱ = (6.7 ± 1.0) g/cm3 (see row #1 in Table 1).
Extended Data Fig. 2 X-ray Thomson scattering spectrum and fit for data set #2.
The data (black) was recorded on experiment N180602-001-999 on the first spectrometer channel (strip 1) at 0.48 ns after peak emission, t0. The best fit (red), consisting of the free-free (blue), bound-free (green) and elastic scattering (purple) contributions, yieldsr a temperature of T = (119 ± 15) eV, a free electron density of ne = (1.9 ± 0.2) × 1024 cm−3 and an ion charge of \(\bar{Z}=3.05\pm 0.1\) resulting in a mass density of ϱ = (9.3 ± 1.3) g/cm3 (see row #2 in Table 1).
Extended Data Fig. 3 X-ray Thomson scattering spectrum and fit for data set #4.
The data (black) was recorded on experiment N180602-001-999 on the second spectrometer channel (strip 3) at 0.78 ns after peak emission, t0. The best fit (red), consisting of the free-free (blue), bound-free (green) and elastic scattering (purple) contributions, yields a temperature of T = (160 ± 20) eV, a free electron density of ne = (12 ± 1.5) × 1024 cm−3 and an ion charge of \(\bar{Z}=3.3\pm 0.1\) resulting in a mass density of ϱ = (55 ± 8) g/cm3 (see row #4 in Table 1).
Extended Data Fig. 4 Radiation hydrodynamic simulations.
Results of one-dimensional radiation-hydrodynamic simulations using the HYDRA code illustrating the implosion dynamics of the beryllium shell. These simulations are tuned to reproduce the observed timing of radiography experiment N160801-001-999 (see also Extended Data Fig. 5a). (a) Simulation results for the evolution of the mass density and (b) a zoom-in for the behaviour close to stagnation. Panels (c) and (d) show radial profiles of mass density and temperature for different times near stagnation, respectively. The target geometry and the hohlraum radiation driving the implosion are shown in Fig. 1. The simulation predicts the highest core compression and peak x-ray emission at t0 = 17.9 ns. About 1 ns earlier, the main shock reaches the centre of the shell. As it is reflected and travels outwards, it sweeps up the in-falling shell material resulting in compression to mass densities of several 10s of g/cm3 and a substantial temperature increase. Based on these simulations, and consistent with the observation from the XRTS, the lower density tail of in-falling beryllium shell is minimized between 500 and 800 ps after peak x-ray emission.Note that this Be implosion design is very different from optimized high-performance implosions with deuterium-tritium (DT) fuel layers that aim for creating a burning plasma24. Specifically, the Be shell is at a much higher adiabat (pressure over related Fermi pressure due to an elevated temperature) because (i) shocks are mistimed as shock timing was optimized for a corresponding experiment with a DT ice layer on the inside of the shell and (ii) the shell has no pre-heat shielding layer (usually made of Cu-doped Be near the inside surface). In addition, the implosion velocity is intentionally reduced by almost twofold to 200 km/s in order to reduce x-ray background signals for the XRTS measurements. All these facts contribute to an approximately tenfold reduced compression compared to what can be achieved in optimized layered implosions where the DT fuel reaches densities of 500 g/cm3 and beyond.
Extended Data Fig. 5 Raw data from radiography measurements near stagnation.
Radiography data for two implosion experiments using the 2D-ConA platform34 with (a) an Fe He-α area backlighter (6.7 keV) and (b) a Cu backlighter (8.4 keV). These measurements cover the probe times used for X-ray Thomson scattering measurements (18.2–18.7 ns). Peak x-ray emission (t0) was observed at 17.88 ns and 17.91 ns for N160801 and N170214, respectively12. The measurements use multi-pinhole (dph = 20 μm) imaging at 6 times magnification and capture about 40 images with 100 ps integration time on 4 multi-channel plate strips that are individually timed. Each strip covers a time period of 230 ps as indicated below the strips. The shell is initially held by a gold cone (cf. Fig. 1(g)), that is located on the right-hand side of the images, about 900 μm from the centre of the shell. The field of view of each of the frames is about 800 × 800 μm2. Except for the backlighter material, the targets were identical within assembly tolerances and the experiments used the same laser drive request. The data demonstrate very good shot-to-shot repeatability in terms of implosion timing and shape of the imploded shell material.
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Döppner, T., Bethkenhagen, M., Kraus, D. et al. Observing the onset of pressure-driven K-shell delocalization. Nature 618, 270–275 (2023). https://doi.org/10.1038/s41586-023-05996-8
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DOI: https://doi.org/10.1038/s41586-023-05996-8
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