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

Thomas Gawne1,2,*, Zhandos A. Moldabekov1,2, Oliver S. Humphries3, Karen Appel3, Carsten Baehtz2, Victorien Bouffetier3, Erik Brambrink3, Attila Cangi1,2, Sebastian Göde3 et al.

Zuzana Konôpková3, Mikako Makita3, Mikhail Mishchenko3, Motoaki Nakatsutsumi3, Kushal Ramakrishna1,2, Lisa Randolph3, Sebastian Schwalbe1,2, Jan Vorberger2, Lennart Wollenweber3, Ulf Zastrau3, Tobias Dornheim1,2,†, and Thomas R. Preston3,‡

  • *t.gawne@hzdr.de
  • †t.dornheim@hzdr.de
  • ‡thomas.preston@xfel.eu
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Phys. Rev. B 109, L241112 – Published 12 June, 2024

DOI: https://doi.org/10.1103/PhysRevB.109.L241112

Abstract

Using an ultrahigh resolution (ΔE∼0.1eV) 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 ab initio 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.

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References (63)

  1. J. Sheffield, D. Froula, S. H. Glenzer, and N. C. Luhmann, Plasma Scattering of Electromagnetic Radiation: Theory and Measurement Techniques (Academic Press, 2010).
  2. S. H. Glenzer and R. Redmer, X-ray thomson scattering in high energy density plasmas, Rev. Mod. Phys. 81, 1625 (2009).
  3. G. Gregori, S. H. Glenzer, W. Rozmus, R. W. Lee, and O. L. Landen, Theoretical model of x-ray scattering as a dense matter probe, Phys. Rev. E 67, 026412 (2003).
  4. T. Dornheim, Z. A. Moldabekov, K. Ramakrishna, P. Tolias, A. D. Baczewski, D. Kraus, T. R. Preston, D. A. Chapman, M. P. Böhme, T. Döppner, F. Graziani, M. Bonitz, A. Cangi, and J. Vorberger, Electronic density response of warm dense matter, Phys. Plasmas 30, 032705 (2023).
  5. F. Graziani, M. P. Desjarlais, R. Redmer, and S. B. Trickey (eds.), Frontiers and Challenges in Warm Dense Matter (Springer, International Publishing, 2014).
  6. R. P. Drake, High-Energy-Density Physics: Foundation of Inertial Fusion and Experimental Astrophysics, Graduate Texts in Physics (Springer Science & Business Media, 2006).
  7. A. Benuzzi-Mounaix, S. Mazevet, A. Ravasio, T. Vinci, A. Denoeud, M. Koenig, N. Amadou, E. Brambrink, F. Festa, A. Levy, M. Harmand, S. Brygoo, G. Huser, V. Recoules, J. Bouchet, G. Morard, F. Guyot, T. de Resseguier, K. Myanishi, N. Ozaki et al., Progress in warm dense matter study with applications to planetology, Phys. Scr. T161, 014060 (2014).
  8. A. Becker, W. Lorenzen, J. J. Fortney, N. Nettelmann, M. Schöttler, and R. Redmer, Ab initio equations of state for hydrogen (h-reos.3) and helium (he-reos.3) and their implications for the interior of brown dwarfs, Astrophys. J. Suppl. Series 215, 21 (2014).
  9. A. L. Kritcher, D. C. Swift, T. Döppner, B. Bachmann, L. X. Benedict, G. W. Collins, J. L. DuBois, F. Elsner, G. Fontaine, J. A. Gaffney, S. Hamel, A. Lazicki, W. R. Johnson, N. Kostinski, D. Kraus, M. J. MacDonald, B. Maddox, M. E. Martin, P. Neumayer, A. Nikroo et al., A measurement of the equation of state of carbon envelopes of white dwarfs, Nature (London) 584, 51 (2020).
  10. S. X. Hu, B. Militzer, V. N. Goncharov, and S. Skupsky, First-principles equation-of-state table of deuterium for inertial confinement fusion applications, Phys. Rev. B 84, 224109 (2011).
  11. R. Betti and O. A. Hurricane, Inertial-confinement fusion with lasers, Nat. Phys. 12, 435 (2016).
  12. D. Kraus, A. Ravasio, M. Gauthier, D. O. Gericke, J. Vorberger, S. Frydrych, J. Helfrich, L. B. Fletcher, G. Schaumann, B. Nagler, B. Barbrel, B. Bachmann, E. J. Gamboa, S. Göde, E. Granados, G. Gregori, H. J. Lee, P. Neumayer, W. Schumaker, T. Döppner et al., Nanosecond formation of diamond and lonsdaleite by shock compression of graphite, Nat. Commun. 7, 10970 (2016).
  13. D. Kraus, J. Vorberger, A. Pak, N. J. Hartley, L. B. Fletcher, S. Frydrych, E. Galtier, E. J. Gamboa, D. O. Gericke, S. H. Glenzer, E. Granados, M. J. MacDonald, A. J. MacKinnon, E. E. McBride, I. Nam, P. Neumayer, M. Roth, A. M. Saunders, A. K. Schuster, P. Sun et al., Formation of diamonds in laser-compressed hydrocarbons at planetary interior conditions, Nat. Astron. 1, 606 (2017).
  14. A. Lazicki, D. McGonegle, J. R. Rygg, D. G. Braun, D. C. Swift, M. G. Gorman, R. F. Smith, P. G. Heighway, A. Higginbotham, M. J. Suggit, D. E. Fratanduono, F. Coppari, C. E. Wehrenberg, R. G. Kraus, D. Erskine, J. V. Bernier, J. M. McNaney, R. E. Rudd, G. W. Collins, J. H. Eggert et al., Metastability of diamond ramp-compressed to 2 terapascals, Nature (London) 589, 532 (2021).
  15. J. Vorberger, T. R. Preston, N. Medvedev, M. P. Böhme, Z. A. Moldabekov, D. Kraus, and T. Dornheim, Revealing non-equilibrium and relaxation in laser heated matter, Phys. Lett. A 499, 129362 (2024).
  16. S. H. Glenzer, O. L. Landen, P. Neumayer, R. W. Lee, K. Widmann, S. W. Pollaine, R. J. Wallace, G. Gregori, A. Höll, T. Bornath, R. Thiele, V. Schwarz, W.-D. Kraeft, and R. Redmer, Observations of plasmons in warm dense matter, Phys. Rev. Lett. 98, 065002 (2007).
  17. L. B. Fletcher, H. J. Lee, T. Döppner, E. Galtier, B. Nagler, P. Heimann, C. Fortmann, S. LePape, T. Ma, M. Millot, A. Pak, D. Turnbull, D. A. Chapman, D. O. Gericke, J. Vorberger, T. White, G. Gregori, M. Wei, B. Barbrel, R. W. Falcone et al., Ultrabright x-ray laser scattering for dynamic warm dense matter physics, Nat. Photonics 9, 274 (2015).
  18. S. Frydrych, J. Vorberger, N. J. Hartley, A. K. Schuster, K. Ramakrishna, A. M. Saunders, T. van Driel, R. W. Falcone, L. B. Fletcher, E. Galtier, E. J. Gamboa, S. H. Glenzer, E. Granados, M. J. MacDonald, A. J. MacKinnon, E. E. McBride, I. Nam, P. Neumayer, A. Pak, K. Voigt et al., Demonstration of x-ray thomson scattering as diagnostics for miscibility in warm dense matter, Nat. Commun. 11, 2620 (2020).
  19. A. Descamps, B. K. Ofori-Okai, K. Appel, V. Cerantola, A. Comley, J. H. Eggert, L. B. Fletcher, D. O. Gericke, S. Göde, O. Humphries, O. Karnbach, A. Lazicki, R. Loetzsch, D. McGonegle, C. A. J. Palmer, C. Plueckthun, T. R. Preston, R. Redmer, D. G. Senesky, C. Strohm et al., An approach for the measurement of the bulk temperature of single crystal diamond using an x-ray free electron laser, Sci. Rep. 10, 14564 (2020).
  20. T. Dornheim, M. P. Böhme, D. A. Chapman, D. Kraus, T. R. Preston, Z. A. Moldabekov, N. Schlünzen, A. Cangi, T. Döppner, and J. Vorberger, Imaginary-time correlation function thermometry: A new, high-accuracy and model-free temperature analysis technique for x-ray Thomson scattering data, Phys. Plasmas 30, 042707 (2023).
  21. T. Dornheim, M. Böhme, D. Kraus, T. Döppner, T. R. Preston, Z. A. Moldabekov, and J. Vorberger, Accurate temperature diagnostics for matter under extreme conditions, Nat. Commun. 13, 7911 (2022).
  22. K. Falk, E. J. Gamboa, G. Kagan, D. S. Montgomery, B. Srinivasan, P. Tzeferacos, and J. F. Benage, Equation of state measurements of warm dense carbon using laser-driven shock and release technique, Phys. Rev. Lett. 112, 155003 (2014).
  23. T. Döppner, M. Bethkenhagen, D. Kraus, P. Neumayer, D. A. Chapman, B. Bachmann, R. A. Baggott, M. P. Böhme, L. Divol, R. W. Falcone, L. B. Fletcher, O. L. Landen, M. J. MacDonald, A. M. Saunders, M. Schörner, P. A. Sterne, J. Vorberger, B. B. L. Witte, A. Yi, R. Redmer et al., Observing the onset of pressure-driven k-shell delocalization, Nature (London) (2023).
  24. M. Cazzaniga, Hans-Christian Weissker, S. Huotari, T. Pylkkänen, P. Salvestrini, G. Monaco, G. Onida, and L. Reining, Dynamical response function in sodium and aluminum from time-dependent density-functional theory, Phys. Rev. B 84, 075109 (2011).
  25. K. Ramakrishna, A. Cangi, T. Dornheim, A. Baczewski, and J. Vorberger, First-principles modeling of plasmons in aluminum under ambient and extreme conditions, Phys. Rev. B 103, 125118 (2021).
  26. L. Wollenweber, T. R. Preston, A. Descamps, V. Cerantola, A. Comley, J. H. Eggert, L. B. Fletcher, G. Geloni, D. O. Gericke, S. H. Glenzer, S. Göde, J. Hastings, O. S. Humphries, A. Jenei, O. Karnbach, Z. Konopkova, R. Loetzsch, B. Marx-Glowna, E. E. McBride, D. McGonegle et al., High-resolution inelastic x-ray scattering at the high energy density scientific instrument at the european x-ray free-electron laser, Rev. Sci. Instrum. 92, 013101 (2021).
  27. T. Tschentscher, C. Bressler, J. Grünert, A. Madsen, A. P. Mancuso, M. Meyer, A. Scherz, H. Sinn, and U. Zastrau, Photon beam transport and scientific instruments at the european XFEL, Appl. Sci. 7, 592 (2017).
  28. K. J. Krane, Dispersion and damping of volume plasmons in polycrystalline aluminium and indium, J. Phys. F 8, 2133 (1978).
  29. J Sprösser-Prou, A vom Felde, and J Fink, Aluminum bulk-plasmon dispersion and its anisotropy, Phys. Rev. B 40, 5799 (1989).
  30. E. Runge and E. K. U. Gross, Density-functional theory for time-dependent systems, Phys. Rev. Lett. 52, 997 (1984).
  31. R. Brydson, Electron Energy Loss Spectroscopy (Garland Science, 2020).
  32. B. B. L. Witte, L. B. Fletcher, E. Galtier, E. Gamboa, H. J. Lee, U. Zastrau, R. Redmer, S. H. Glenzer, and P. Sperling, Warm dense matter demonstrating non-drude conductivity from observations of nonlinear plasmon damping, Phys. Rev. Lett. 118, 225001 (2017).
  33. M. Bonitz, T. Dornheim, Zh. A. Moldabekov, S. Zhang, P. Hamann, H. Kählert, A. Filinov, K. Ramakrishna, and J. Vorberger, Ab initio simulation of warm dense matter, Phys. Plasmas 27, 042710 (2020).
  34. U. Zastrau, K. Appel, C. Baehtz, O. Baehr, L. Batchelor, A. Berghäuser, M. Banjafar, E. Brambrink, V. Cerantola, Thomas E Cowan, H. Damker, S. Dietrich, S. Di Dio Cafiso, Jörn Dreyer, Hans-Olaf Engel, T. Feldmann, S. Findeisen, M. Foese, D. Fulla-Marsa, S. Göde et al., The high energy density scientific instrument at the European XFEL, J. Synchrotron Radiat. 28, 1393 (2021).
  35. A. Mozzanica, M. Andrä, R. Barten, A. Bergamaschi, S. Chiriotti, M. Brückner, R. Dinapoli, E. Fröjdh, D. Greiffenberg, F. Leonarski, C. Lopez-Cuenca, D. Mezza, S. Redford, C. Ruder, B. Schmitt, X. Shi, D. Thattil, G. Tinti, S. Vetter, and J. Zhang, The JUNGFRAU detector for applications at synchrotron light sources and XFELs, Synchrotron Radiation News 31, 16 (2018).
  36. A. Mozzanica, A. Bergamaschi, M. Brueckner, S. Cartier, R. Dinapoli, D. Greiffenberg, J. Jungmann-Smith, D. Maliakal, D. Mezza, M. Ramilli, C. Ruder, L. Schaedler, B. Schmitt, X. Shi, and G. Tinti, Characterization results of the JUNGFRAU full scale readout ASIC, J. Instrum. 11, C02047 (2016).
  37. T. R. Preston, S. Göde, J.-P. Schwinkendorf, K. Appel, E. Brambrink, V. Cerantola, H. Höppner, M. Makita, A. Pelka, C. Prescher, K. Sukharnikov, A. Schmidt, I. Thorpe, T. Toncian, A. Amouretti, D. Chekrygina, R. W. Falcone, K. Falk, L. B. Fletcher, E. Galtier et al., Design and performance characterisation of the HAPG von Hámos Spectrometer at the High Energy Density Instrument of the European XFEL, J. Instrum. 15, P11033 (2020).
  38. See Supplemental Material http://link.aps.org/supplemental/10.1103/PhysRevB.109.L241112 for additional details on the experimental details, simulations, and wave number averaging.
  39. P. Sperling, E. J. Gamboa, H. J. Lee, H. K. Chung, E. Galtier, Y. Omarbakiyeva, H. Reinholz, G. Röpke, U. Zastrau, J. Hastings, L. B. Fletcher, and S. H. Glenzer, Free-electron x-ray laser measurements of collisional-damped plasmons in isochorically heated warm dense matter, Phys. Rev. Lett. 115, 115001 (2015).
  40. G. Giuliani and G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, 2008).
  41. Z. A. Moldabekov, T. D. Gawne, S. Schwalbe, T. R. Preston, J. Vorberger, and T. Dornheim, Excitation signatures of isochorically heated electrons in solids at finite wavenumber explored from first principles, Phys. Rev. Res. 6, 023219 (2024).
  42. D. Bohm and E. P. Gross, Theory of plasma oscillations. a. origin of medium-like behavior, Phys. Rev. 75, 1851 (1949).
  43. C. Ullrich, Time-Dependent Density-Functional Theory: Concepts and Applications, Oxford Graduate Texts (Oxford University Press, Oxford, 2012).
  44. A. Savitzky and M. J. E. Golay, Smoothing and differentiation of data by simplified least squares procedures. Anal. Chem. 36, 1627 (1964).
  45. P. Virtanen, R. Gommers, T. E. Oliphant, M. Haberland, T. Reddy, D. Cournapeau, E. Burovski, P. Peterson, W. Weckesser, J. Bright, S. J. van der Walt, M. Brett, J. Wilson, K. J. Millman, N. Mayorov, A. R. J. Nelson, E. Jones, R. Kern, E. Larson, C. J. Carey et al., SciPy 1.0: Fundamental algorithms for scientific computing in python, Nature Methods 17, 261 (2020).
  46. J. J. Mortensen, L. B. Hansen, and K. W. Jacobsen, Real-space grid implementation of the projector augmented wave method, Phys. Rev. B 71, 035109 (2005).
  47. J. Enkovaara, C. Rostgaard, J. J. Mortensen, J. Chen, M. Dułak, L. Ferrighi, J. Gavnholt, C. Glinsvad, V. Haikola, H. A. Hansen, H. H. Kristoffersen, M. Kuisma, A. H. Larsen, L. Lehtovaara, M. Ljungberg, O. Lopez-Acevedo, P. G. Moses, J. Ojanen, T. Olsen, V. Petzold et al., Electronic structure calculations with GPAW: A real-space implementation of the projector augmented-wave method, J. Phys.: Condens. Matter 22, 253202 (2010).
  48. M. Walter, H. Häkkinen, L. Lehtovaara, M. Puska, J. Enkovaara, C. Rostgaard, and J. J. Mortensen, Time-dependent density-functional theory in the projector augmented-wave method, J. Chem. Phys. 128, 244101 (2008).
  49. J. Yan, J. J. Mortensen, K. W. Jacobsen, and K. S. Thygesen, Linear density response function in the projector augmented wave method: Applications to solids, surfaces, and interfaces, Phys. Rev. B 83, 245122 (2011).
  50. A. H. Larsen, J. J. Mortensen, J. Blomqvist, I. E. Castelli, R. Christensen, M. Dułak, J. Friis, M. N. Groves, B. Hammer, C. Hargus, E. D. Hermes, P. C. Jennings, P. B. Jensen, J. Kermode, J. R. Kitchin, E. L. Kolsbjerg, J. Kubal, K. Kaasbjerg, S. Lysgaard, J. B. Maronsson et al., The atomic simulation environment–a Python library for working with atoms, J. Phys.: Condens. Matter 29, 273002 (2017).
  51. S. R. Bahn and K. W. Jacobsen, An object-oriented scripting interface to a legacy electronic structure code, Comput. Sci. Eng. 4, 56 (2002).
  52. R. W. G Wyckoff, Crystal Structures (Interscience Publishers, New York, 1948).
  53. J. P. Perdew and Y. Wang, Accurate and simple analytic representation of the electron-gas correlation energy, Phys. Rev. B 45, 13244 (1992).
  54. P. Hamann, L. Kordts, A. Filinov, M. Bonitz, T. Dornheim, and J. Vorberger, Prediction of a roton-type feature in warm dense hydrogen, Phys. Rev. Res. 5, 033039 (2023).
  55. T. Dornheim, Z. Moldabekov, J. Vorberger, H. Kählert, and M. Bonitz, Electronic pair alignment and roton feature in the warm dense electron gas, Commun. Phys. 5, 304 (2022).
  56. Z. Moldabekov, T. D. Gawne, S. Schwalbe, T. R. Preston, J. Vorberger, and T. Dornheim, Ultrafast heating induced suppression of d-band dominance in the electronic excitation spectrum of cuprum, ACS Omega (2024), doi:10.1021/acsomega.4c02920.
  57. S. Liu, C. Grech, M. Guetg, S. Karabekyan, V. Kocharyan, N. Kujala, C. Lechner, T. Long, N. Mirian, W. Qin, S. Serkez, S. Tomin, J. Yan, S. Abeghyan, J. Anton, V. Blank, U. Boesenberg, F. Brinker, Y. Chen, W. Decking et al., Cascaded hard X-ray self-seeded free-electron laser at megahertz repetition rate, Nat. Photonics 17, 984 (2023).
  58. C. Mo, Z.-G. Fu, P. Zhang, W. Kang, W. Zhang, and X. T. He, First-principles method for x-ray thomson scattering including both elastic and inelastic features in warm dense matter, Phys. Rev. B 102, 195127 (2020).
  59. Y. Zhang, C. Mo, P. Zhang, and W. Kang, A composite ansatz for calculation of dynamical structure factor, Chin. Phys. Lett. 41, 017801 (2024).
  60. A. D. Baczewski, L. Shulenburger, M. P. Desjarlais, S. B. Hansen, and R. J. Magyar, X-ray thomson scattering in warm dense matter without the chihara decomposition, Phys. Rev. Lett. 116, 115004 (2016).
  61. Z. Moldabekov, M. Böhme, J. Vorberger, D. Blaschke, and T. Dornheim, Ab Initio static exchange–correlation kernel across Jacob's Ladder without functional derivatives, J. Chem. Theory Comput. 19, 1286 (2023).
  62. M. Schörner, M. Bethkenhagen, T. Döppner, D. Kraus, L. B. Fletcher, S. H. Glenzer, and R. Redmer, X-ray thomson scattering spectra from density functional theory molecular dynamics simulations based on a modified chihara formula, Phys. Rev. E 107, 065207 (2023).
  63. C. Bostedt, S. Boutet, D. M. Fritz, Z. Huang, H. Ja Lee, H. T. Lemke, A. Robert, W. F. Schlotter, J. J. Turner, and G. J. Williams, Linac coherent light source: The first five years, Rev. Mod. Phys. 88, 015007 (2016).

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Phys. Rev. B 109, L241112– Published 12 June, 2024
  • Received 4 March 2024
  • Revised 15 May 2024
  • Accepted 20 May 2024
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