Ultrahigh Resolution X-ray Thomson Scattering Measurements at the European XFEL
Abstract: Using a novel ultrahigh resolution ($\Delta E \sim 0.1\,$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 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.
- S. H. Glenzer and R. Redmer, “X-ray thomson scattering in high energy density plasmas,” Rev. Mod. Phys 81, 1625 (2009).
- 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).
- Tobias Dornheim, Zhandos A. Moldabekov, Kushal Ramakrishna, Panagiotis Tolias, Andrew D. Baczewski, Dominik Kraus, Thomas R. Preston, David A. Chapman, Maximilian P. Böhme, Tilo Döppner, Frank Graziani, Michael Bonitz, Attila Cangi, and Jan Vorberger, “Electronic density response of warm dense matter,” Physics of Plasmas 30, 032705 (2023a).
- R.P. Drake, High-Energy-Density Physics: Foundation of Inertial Fusion and Experimental Astrophysics, Graduate Texts in Physics (Springer International Publishing, 2018).
- Alessandra Benuzzi-Mounaix, Stéphane Mazevet, Alessandra Ravasio, Tommaso Vinci, Adrien Denoeud, Michel Koenig, Nourou Amadou, Erik Brambrink, Floriane Festa, Anna Levy, Marion Harmand, Stéphanie Brygoo, Gael Huser, Vanina Recoules, Johan Bouchet, Guillaume Morard, François Guyot, Thibaut de Resseguier, Kohei Myanishi, Norimasa Ozaki, Fabien Dorchies, Jerôme Gaudin, Pierre Marie Leguay, Olivier Peyrusse, Olivier Henry, Didier Raffestin, Sebastien Le Pape, Ray Smith, and Riccardo Musella, “Progress in warm dense matter study with applications to planetology,” Phys. Scripta T161, 014060 (2014).
- 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. Ser 215, 21 (2014).
- Andrea L. Kritcher, Damian C. Swift, Tilo Döppner, Benjamin Bachmann, Lorin X. Benedict, Gilbert W. Collins, Jonathan L. DuBois, Fred Elsner, Gilles Fontaine, Jim A. Gaffney, Sebastien Hamel, Amy Lazicki, Walter R. Johnson, Natalie Kostinski, Dominik Kraus, Michael J. MacDonald, Brian Maddox, Madison E. Martin, Paul Neumayer, Abbas Nikroo, Joseph Nilsen, Bruce A. Remington, Didier Saumon, Phillip A. Sterne, Wendi Sweet, Alfredo A. Correa, Heather D. Whitley, Roger W. Falcone, and Siegfried H. Glenzer, “A measurement of the equation of state of carbon envelopes of white dwarfs,” Nature 584, 51–54 (2020).
- 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).
- R. Betti and O. A. Hurricane, “Inertial-confinement fusion with lasers,” Nature Physics 12, 435–448 (2016).
- 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, R. W. Falcone, S. H. Glenzer, and M. Roth, “Nanosecond formation of diamond and lonsdaleite by shock compression of graphite,” Nature Communications 7, 10970 (2016).
- 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, T. van Driel, T. Döppner, and R. W. Falcone, “Formation of diamonds in laser-compressed hydrocarbons at planetary interior conditions,” Nature Astronomy 1, 606–611 (2017).
- 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, and J. S. Wark, “Metastability of diamond ramp-compressed to 2 terapascals,” Nature 589, 532–535 (2021).
- Jan Vorberger, Thomas R. Preston, Nikita Medvedev, Maximilian P. Böhme, Zhandos A. Moldabekov, Dominik Kraus, and Tobias Dornheim, “Revealing non-equilibrium and relaxation in laser heated matter,” Physics Letters A 499, 129362 (2024).
- 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).
- 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, C.-C. Kao, H. Nuhn, J. Welch, U. Zastrau, P. Neumayer, J. B. Hastings, and S. H. Glenzer, “Ultrabright x-ray laser scattering for dynamic warm dense matter physics,” Nature Photonics 9, 274–279 (2015).
- 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, M. Roth, P. Sun, D. O. Gericke, T. Döppner, and D. Kraus, “Demonstration of x-ray thomson scattering as diagnostics for miscibility in warm dense matter,” Nature Communications 11, 2620 (2020).
- 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, I. Uschmann, T. G. White, L. Wollenweber, G. Monaco, J. S. Wark, J. B. Hastings, U. Zastrau, G. Gregori, S. H. Glenzer, and E. E. McBride, “An approach for the measurement of the bulk temperature of single crystal diamond using an x-ray free electron laser,” Scientific Reports 10, 14564 (2020).
- Tobias Dornheim, Maximilian P. Böhme, David A. Chapman, Dominik Kraus, Thomas R. Preston, Zhandos A. Moldabekov, Niclas Schlünzen, Attila Cangi, Tilo Döppner, and Jan Vorberger, “Imaginary-time correlation function thermometry: A new, high-accuracy and model-free temperature analysis technique for x-ray Thomson scattering data,” Physics of Plasmas 30, 042707 (2023b).
- Tobias Dornheim, Maximilian Böhme, Dominik Kraus, Tilo Döppner, Thomas R. Preston, Zhandos A. Moldabekov, and Jan Vorberger, “Accurate temperature diagnostics for matter under extreme conditions,” Nature Communications 13, 7911 (2022a).
- 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).
- 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, S. H. Glenzer, and D. O. Gericke, “Observing the onset of pressure-driven k-shell delocalization,” Nature (2023), 10.1038/s41586-023-05996-8.
- Marco Cazzaniga, Hans-Christian Weissker, Simo Huotari, Tuomas Pylkkänen, Paolo Salvestrini, Giulio Monaco, Giovanni Onida, and Lucia Reining, “Dynamical response function in sodium and aluminum from time-dependent density-functional theory,” Phys. Rev. B 84, 075109 (2011).
- Kushal Ramakrishna, Attila Cangi, Tobias Dornheim, Andrew Baczewski, and Jan Vorberger, “First-principles modeling of plasmons in aluminum under ambient and extreme conditions,” Phys. Rev. B 103, 125118 (2021).
- 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, G. Monaco, B. K. Ofori-Okai, C. A. J. Palmer, C. Plückthun, R. Redmer, C. Strohm, I. Thorpe, T. Tschentscher, I. Uschmann, J. S. Wark, T. G. White, K. Appel, G. Gregori, and U. Zastrau, “High-resolution inelastic x-ray scattering at the high energy density scientific instrument at the European X-Ray Free-Electron Laser,” Review of Scientific Instruments 92, 013101 (2021).
- Thomas Tschentscher, Christian Bressler, Jan Grünert, Anders Madsen, Adrian P. Mancuso, Michael Meyer, Andreas Scherz, Harald Sinn, and Ulf Zastrau, “Photon beam transport and scientific instruments at the european xfel,” Applied Sciences 7 (2017), 10.3390/app7060592.
- KJ Krane, “Dispersion and damping of volume plasmons in polycrystalline aluminium and indium,” Journal of Physics F: Metal Physics 8, 2133 (1978).
- J Sprösser-Prou, A Vom Felde, and J Fink, “Aluminum bulk-plasmon dispersion and its anisotropy,” Physical Review B 40, 5799 (1989).
- Erich Runge and E. K. U. Gross, “Density-functional theory for time-dependent systems,” Phys. Rev. Lett. 52, 997–1000 (1984).
- R. Brydson, Electron Energy Loss Spectroscopy (CRC Press, 2020).
- 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).
- 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,” Physics of Plasmas 27, 042710 (2020).
- Ulf Zastrau, Karen Appel, Carsten Baehtz, Oliver Baehr, Lewis Batchelor, Andreas Berghäuser, Mohammadreza Banjafar, Erik Brambrink, Valerio Cerantola, Thomas E Cowan, Horst Damker, Steffen Dietrich, Samuele Di Dio Cafiso, Jörn Dreyer, Hans-Olaf Engel, Thomas Feldmann, Stefan Findeisen, Manon Foese, Daniel Fulla-Marsa, Sebastian Göde, Mohammed Hassan, Jens Hauser, Thomas Herrmannsdörfer, Hauke Höppner, Johannes Kaa, Peter Kaever, Klaus Knöfel, Zuzana Konôpková, Alejandro Laso García, Hanns-Peter Liermann, Jona Mainberger, Mikako Makita, Eike-Christian Martens, Emma E. McBride, Dominik Möller, Motoaki Nakatsutsumi, Alexander Pelka, Christian Plueckthun, Clemens Prescher, Thomas R Preston, Michael Röper, Andreas Schmidt, Wolfgang Seidel, Jan-Patrick Schwinkendorf, Markus O. Schoelmerich, Ulrich Schramm, Andreas Schropp, Cornelius Strohm, Konstantin Sukharnikov, Peter Talkovski, Ian Thorpe, Monika Toncian, Toma Toncian, Lennart Wollenweber, Shingo Yamamoto, and Thomas Tschentscher, “The High Energy Density Scientific Instrument at the European XFEL,” Journal of Synchrotron Radiation 28, 1393–1416 (2021).
- 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, 16–20 (2018).
- 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,” Journal of Instrumentation 11 (2016), 10.1088/1748-0221/11/02/C02047.
- 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, M. Harmand, N.J. Hartley, S.P. Hau-Riege, P. Heimann, L.G. Huang, O.S. Humphries, O. Karnbach, D. Kraus, H.J. Lee, B. Nagler, S. Ren, A.K. Schuster, M. Smid, K. Voigt, M. Zhang, and U. Zastrau, “Design and performance characterisation of the HAPG von Hámos Spectrometer at the High Energy Density Instrument of the European XFEL,” Journal of Instrumentation 15, P11033–P11033 (2020).
- 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).
- G. Giuliani and G. Vignale, Quantum Theory of the Electron Liquid (Cambridge University Press, Cambridge, 2008).
- Zhandos A. Moldabekov, Thomas D. Gawne, Sebastian Schwalbe, Thomas R. Preston, Jan Vorberger, and Tobias Dornheim, “Excitation signatures of isochorically heated electrons in solids at finite wavenumber explored from first principles,” (2024a), arXiv:2402.09005 [physics.comp-ph] .
- D. Bohm and E. P. Gross, “Theory of plasma oscillations. a. origin of medium-like behavior,” Phys. Rev. 75, 1851–1864 (1949).
- C. Ullrich, Time-Dependent Density-Functional Theory: Concepts and Applications, Oxford Graduate Texts (OUP Oxford, 2012).
- See Supplemental Material for additional details.
- Paul Hamann, Linda Kordts, Alexey Filinov, Michael Bonitz, Tobias Dornheim, and Jan Vorberger, “Prediction of a roton-type feature in warm dense hydrogen,” Phys. Rev. Res. 5, 033039 (2023).
- Tobias Dornheim, Zhandos Moldabekov, Jan Vorberger, Hanno Kählert, and Michael Bonitz, “Electronic pair alignment and roton feature in the warm dense electron gas,” Communications Physics 5, 304 (2022b).
- Zhandos Moldabekov, Thomas D. Gawne, Sebastian Schwalbe, Thomas R. Preston, Jan Vorberger, and Tobias Dornheim, “Ultrafast heating induced suppression of d𝑑ditalic_d-band dominance in the electronic excitation spectrum of cuprum,” (2024b), arXiv:2403.17815 [physics.chem-ph] .
- Shan Liu, Christian Grech, Marc Guetg, Suren Karabekyan, Vitali Kocharyan, Naresh Kujala, Christoph Lechner, Tianyun Long, Najmeh Mirian, Weilun Qin, Svitozar Serkez, Sergey Tomin, Jiawei Yan, Suren Abeghyan, Jayson Anton, Vladimir Blank, Ulrike Boesenberg, Frank Brinker, Ye Chen, Winfried Decking, Xiaohao Dong, Steve Kearney, Daniele La Civita, Anders Madsen, Theophilos Maltezopoulos, Angel Rodriguez-Fernandez, Evgeni Saldin, Liubov Samoylova, Matthias Scholz, Harald Sinn, Vivien Sleziona, Deming Shu, Takanori Tanikawa, Sergey Terentiev, Andrei Trebushinin, Thomas Tschentscher, Maurizio Vannoni, Torsten Wohlenberg, Mikhail Yakopov, and Gianluca Geloni, “Cascaded hard X-ray self-seeded free-electron laser at megahertz repetition rate,” Nature Photonics 17, 984–991 (2023).
- Chongjie Mo, Zhen-Guo Fu, Ping Zhang, Wei Kang, Weiyan 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).
- Yupei Zhang, Chongjie Mo, Ping Zhang, and Wei Kang, “A composite ansatz for calculation of dynamical structure factor,” Chinese Physics Letters 41, 017801 (2024).
- 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).
- Zhandos Moldabekov, Maximilian Böhme, Jan Vorberger, David Blaschke, and Tobias Dornheim, “Ab Initio Static Exchange–Correlation Kernel across Jacob’s Ladder without Functional Derivatives,” Journal of Chemical Theory and Computation 19, 1286–1299 (2023).
- Maximilian Schörner, Mandy Bethkenhagen, Tilo Döppner, Dominik Kraus, Luke B. Fletcher, Siegfried H. Glenzer, and Ronald 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).
- Christoph Bostedt, Sébastien Boutet, David M. Fritz, Zhirong Huang, Hae Ja Lee, Henrik T. Lemke, Aymeric Robert, William F. Schlotter, Joshua J. Turner, and Garth J. Williams, “Linac coherent light source: The first five years,” Rev. Mod. Phys. 88, 015007 (2016).
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