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Measurement of turbulent velocity and bounds for thermal diffusivity in laser shock compressed foams by x-ray photon correlation spectroscopy

Charles Heaton1,*, Hao Yin2,3, Dimitri Khaghani4, Hae Ja Lee4, Hannah Poole1,5, Eric Blackman3,5,6, Nina Boiadjieva4, Xiaoqian M. Chen7, Celine Crépisson1 et al.

Gilbert W. Collins2,5,3,6, Adrien Descamps8, Arianna E. Gleason4, Christian Gutt9, Alexander N. Petsch4,10, Lisa Randolph11, Silke Nelson4, Peregrine McGehee4, Rajan Plumley4,10,12, Christopher Spindloe13, Thomas Stevens1, Charlotte Stuart1, Joshua J. Turner4,10, Hussein Aluie2,3,6, Jessica K. Shang2,3,6, and Gianluca Gregori1

  • *Contact author: charles.heaton@physics.ox.ac.uk
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Phys. Rev. E 112, 045218 – Published 29 October, 2025

DOI: https://doi.org/10.1103/lff9-f3c1

Abstract

Experimental benchmarking of transport coefficients under extreme conditions is required for validation of differing theoretical models. To date, measurement of transport properties of dynamically compressed samples remains a challenge with only a limited number of studies able to quantify transport in high pressure and temperature matter. x-ray photon correlation spectroscopy utilizes coherent x-ray sources to measure time correlations of density fluctuations, thus providing measurements of length and timescale-dependent transport properties. Here, we present a first-of-a-kind experiment to conduct x-ray photon correlation spectroscopy in laser shock compression experiments. We report measurement of the turbulent velocity in the wake of a laser driven supersonic shock and place an upper bound on thermal diffusivity in a solid density plasma on nanosecond timescales.

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References (55)

  1. C. R. Weber, D. S. Clark, A. W. Cook, L. E. Busby, and H. F. Robey, Inhibition of turbulence in inertial-confinement-fusion hot spots by viscous dissipation, Phys. Rev. E 89, 053106 (2014).
  2. T. Guillot, Interiors of giant planets inside and outside the solar system, Science 286, 72 (1999).
  3. T. Guillot, Y. Miguel, B. Militzer, W. Hubbard, Y. Kaspi, E. Galanti, H. Cao, R. Helled, S. Wahl, L. Iess et al., A suppression of differential rotation in Jupiter's deep interior, Nature (London) 555, 227 (2018).
  4. P. E. Grabowski, S. B. Hansen, M. S. Murillo, L. G. Stanton, F. R. Graziani, A. B. Zylstra, S. D. Baalrud, P. Arnault, A. D. Baczewski, L. X. Benedict, C. Blancard, O. Čertík, J. Clérouin, L. A. Collins, S. Copeland, A. A. Correa, J. Dai, J. Daligault, M. P. Desjarlais, M. W. Dharma-wardana et al., Review of the first charged-particle transport coefficient comparison workshop, in High Energy Density Physics (Elsevier B.V., Amsterdam, 2020), Vol. 37.
  5. L. J. Stanek, A. Kononov, S. B. Hansen, B. M. Haines, S. X. Hu, P. F. Knapp, M. S. Murillo, L. G. Stanton, H. D. Whitley, S. D. Baalrud, L. J. Babati, A. D. Baczewski, M. Bethkenhagen, A. Blanchet, R. C. Clay, K. R. Cochrane, L. A. Collins, A. Dumi, G. Faussurier, M. French et al., Review of the second charged-particle transport coefficient code comparison workshop, Phys. Plasmas 31, 052104 (2024).
  6. E. Abramson, J. Brown, L. Slutsky, and S. Wiryana, Measuring speed of sound and thermal diffusivity in the diamond-Anvil cell, Int. J. Thermophys. 22, 405 (2001).
  7. A. F. Goncharov, P. Beck, V. V. Struzhkin, B. D. Haugen, and S. D. Jacobsen, Thermal conductivity of lower-mantle minerals, Phys. Earth Planet. Inter. 174, 24 (2009).
  8. Y. Zhou, Z. Y. Dong, W. P. Hsieh, A. F. Goncharov, and X. J. Chen, Thermal conductivity of materials under pressure, Nature Rev. Phys. 4, 319 (2022).
  9. C. H. Allen, M. Oliver, D. O. Gericke, N. Brouwer, L. Divol, G. E. Kemp, O. L. Landen, L. Morrison, Y. Ping, M. O. Schölmerich et al., Measurement of interfacial thermal resistance in high-energy-density matter, Nat. Commun. 16, 1983 (2025).
  10. S. Jiang, O. L. Landen, H. D. Whitley, S. Hamel, R. London, D. S. Clark, P. Sterne, S. B. Hansen, S. X. Hu, G. W. Collins, and Y. Ping, Thermal transport in warm dense matter revealed by refraction-enhanced x-ray radiography with a deep-neural-network analysis, Commun. Phys. 6, 98 (2023).
  11. V. Favre-Nicolin, Y. Chushkin, P. Cloetens, J. da Silva, S. Leake, B. Ruta, and F. Zontone, Dynamics and imaging using coherent x-rays at the european synchrotron, Synchrotron Radiat. News 30, 13 (2017).
  12. O. G. Shpyrko, X-ray photon correlation spectroscopy, J. Synchrotron Radiat. 21, 1057 (2014).
  13. A. R. Sandy, Q. Zhang, and L. B. Lurio, Hard x-ray photon correlation spectroscopy methods for materials studies, Annu. Rev. Mater. Res. 48, 167 (2018).
  14. G. Grübel, G. B. Stephenson, C. Gutt, H. Sinn, and T. Tschentscher, Xpcs at the european x-ray free electron laser facility, Nucl. Instrum. Methods Phys. Res., Sect. B 262, 357 (2007).
  15. F. Lehmkühler, P. Kwasniewski, W. Roseker, B. Fischer, M. A. Schroer, K. Tono, T. Katayama, M. Sprung, M. Sikorski, S. Song, J. Glownia, M. Chollet, S. Nelson, A. Robert, C. Gutt, M. Yabashi, T. Ishikawa, and G. Grübel, Sequential single shot x-ray photon correlation spectroscopy at the sacla free electron laser, Sci. Rep. 5, 17193 (2015).
  16. W. Roseker, S. O. Hruszkewycz, F. Lehmkühler, M. Walther, H. Schulte-Schrepping, S. Lee, T. Osaka, L. Strüder, R. Hartmann, M. Sikorski, S. Song, A. Robert, P. H. Fuoss, M. Sutton, G. B. Stephenson, and G. Grübel, Towards ultrafast dynamics with split-pulse x-ray photon correlation spectroscopy at free electron laser sources, Nat. Commun. 9, 1704 (2018).
  17. B. J. Berne and R. Pecora, Dynamic Light Scattering: With Applications to Chemistry, Biology, and Physics (Courier Corporation, North Chelmsford, MA, 2000).
  18. A. Cornet, A. Ronca, J. Shen, F. Zontone, Y. Chushkin, M. Cammarata, G. Garbarino, M. Sprung, F. Westermeier, T. Deschamps et al., High-pressure x-ray photon correlation spectroscopy at fourth-generation synchrotron sources, J. Synchrotron Radiat. 31, 527 (2024).
  19. P. Muhunthan, H. Li, G. Vignat, E. R. Toro, K. Younes, Y. Sun, D. Sokaras, T. Weiss, I. Rajkovic, T. Osaka et al., A versatile pressure-cell design for studying ultrafast molecular-dynamics in supercritical fluids using coherent multi-pulse x-ray scattering, Rev. Sci. Instrum. 95, 013901 (2024).
  20. A. Karina, H. Li, T. Eklund, M. Ladd-Parada, B. Massani, M. Filianina, N. Kondedan, A. Rydh, K. Holl, R. Trevorah et al., Multicomponent dynamics in amorphous ice studied using x-ray photon correlation spectroscopy at elevated pressure and cryogenic temperatures, Commun. Chem. 8, 82 (2025).
  21. D. Ferreira, R. Bachelard, W. Guerin, R. Kaiser, and M. Fouché, Connecting field and intensity correlations: The siegert relation and how to test it, Am. J. Phys. 88, 831 (2020).
  22. J.-P. Hansen and I. R. McDonald, Theory of Simple Liquids: With Applications to Soft Matter (Academic Press, San Diego, CA, 2013).
  23. M. H. Seaberg, B. Holladay, J. C. T. Lee, M. Sikorski, A. H. Reid, S. A. Montoya, G. L. Dakovski, J. D. Koralek, G. Coslovich, S. Moeller, W.F. Schlotter, R. Streubel, S.D. Kevan, P. Fischer, E. E. Fullerton, J. L. Turner, F. J. Decker, S. K. Sinha, S. Roy, and J. J. Turner, Nanosecond x-ray photon correlation spectroscopy on magnetic skyrmions, Phys. Rev. Lett. 119, 067403 (2017).
  24. A. Majumdar, H. Li, P. Muhunthan, A. Späh, S. Song, Y. Sun, M. Chollet, D. Sokaras, D. Zhu, and M. Ihme, Direct observation of ultrafast cluster dynamics in supercritical carbon dioxide using x-ray photon correlation spectroscopy, Nat. Commun. 15, 10540 (2024).
  25. Y. Sun, G. Carini, M. Chollet, F.-J. Decker, M. Dunne, P. Fuoss, S. O. Hruszkewycz, T. J. Lane, K. Nakahara, S. Nelson, A. Robert, T. Sato, S. Song, G. B. Stephenson, M. Sutton, T. B. Van Driel, C. Weninger, and D. Zhu, Nonuniform flow dynamics probed by nanosecond x-ray speckle visibility spectroscopy, Phys. Rev. Lett. 127, 058001 (2021).
  26. C. Gutt, L.-M. Stadler, A. Duri, T. Autenrieth, O. Leupold, Y. Chushkin, and G. Grübel, Measuring temporal speckle correlations at ultrafast x-ray sources, Opt. Express 17, 55 (2009).
  27. B. Nagler, B. Arnold, G. Bouchard, R. F. Boyce, R. M. Boyce, A. Callen, M. Campell, R. Curiel, E. Galtier, J. Garofoli et al., The matter in extreme conditions instrument at the linac coherent light source, J. Synchrotron Radiat. 22, 520 (2015).
  28. Y. Sun, F.-J. Decker, J. Turner, S. Song, A. Robert, and D. Zhu, Pulse intensity characterization of the LCLS nanosecond double-bunch mode of operation, J. Synchrotron Radiat. 25, 642 (2018).
  29. J. Amann, W. Berg, V. Blank, F.-J. Decker, Y. Ding, P. Emma, Y. Feng, J. Frisch, D. Fritz, J. Hastings et al., Demonstration of self-seeding in a hard-x-ray free-electron laser, Nat. Photon. 6, 693 (2012).
  30. A. S. Moore, N. B. Meezan, J. Milovich, S. Johnson, R. Heredia, T. F. Baumann, M. Biener, S. D. Bhandarkar, H. Chen, L. Divol, N. Izumi, A. Nikroo, K. Baker, O. Jones, O. L. Landen, W. W. Hsing, J. D. Moody, C. A. Thomas, B. Lahmann, J. Williams et al., Foam-lined Hohlraum, inertial confinement fusion experiments on the national ignition facility, Phys. Rev. E 102, 051201(R) (2020).
  31. P. M. Celliers and M. Millot, Imaging velocity interferometer system for any reflector (visar) diagnostics for high energy density sciences, Rev. Sci. Instrum. 94, 011101 (2023).
  32. H. Radousky, M. Armstrong, and N. Goldman, Time resolved x-ray diffraction in shock compressed systems, J. Appl. Phys. 129, 040901 (2021).
  33. S. H. Glenzer and R. Redmer, X-ray thomson scattering in high energy density plasmas, Rev. Mod. Phys. 81, 1625 (2009).
  34. F.-J. Decker, K. L. Bane, W. Colocho, S. Gilevich, A. Marinelli, J. C. Sheppard, J. L. Turner, J. J. Turner, S. L. Vetter, A. Halavanau et al., Tunable x-ray free electron laser multi-pulses with nanosecond separation, Sci. Rep. 12, 3253 (2022).
  35. B. L. Henke, E. M. Gullikson, and J. C. Davis, X-ray interactions: Photoabsorption, scattering, transmission, and reflection at E = 50-30,000 ev, Z = 1-92, At. Data Nucl. Data Tables 54, 181 (1993).
  36. R. W. Paddock, M. W. von der Leyen, R. Aboushelbaya, P. A. Norreys, D. J. Chapman, D. E. Eakins, M. Oliver, R. J. Clarke, M. Notley, C. D. Baird, N. Booth, C. Spindloe, D. Haddock, S. Irving, R. H. H. Scott, J. Pasley, M. Cipriani, F. Consoli, B. Albertazzi, M. Koenig, A. S. Martynenko, L. Wegert, P. Neumayer, P. Tchorz, P. Raczka, P. Mabey, W. Garbett, R. M. N. Goshadze, V. V. Karasiev, and S. X. Hu, Measuring the principal hugoniot of inertial-confinement-fusion-relevant TMPTA plastic foams, Phys. Rev. E 107, 025206 (2023).
  37. J. T. Larsen and S. M. Lane, Hyades—A plasma hydrodynamics code for dense plasma studies, J. Quant. Spectrosc. Radiat. Transfer 51, 179 (1994), special issue radiative properties of hot dense matter.
  38. J. Sheffield, D. Froula, S. H. Glenzer, and N. C. Luhmann, Jr., Plasma Scattering of Electromagnetic Radiation: Theory and Measurement Techniques (Academic Press, San Diego, CA, 2010).
  39. 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).
  40. 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).
  41. A. Pelka, G. Gregori, D. O. Gericke, J. Vorberger, S. H. Glenzer, M. M. Günther, K. Harres, R. Heathcote, A. L. Kritcher, N. L. Kugland, B. Li, M. Makita, J. Mithen, D. Neely, C. Niemann, A. Otten, D. Riley, G. Schaumann, M. Schollmeier, A. Tauschwitz, and M. Roth, Ultrafast melting of carbon induced by intense proton beams, Phys. Rev. Lett. 105, 265701 (2010).
  42. J. Lütgert, P. Hesselbach, M. Schörner, V. Bagnoud, R. Belikov, P. Drechsel, B. Heuser, O. Humphries, P. Katrik, B. Lindqvist et al., Temperature and structure measurements of heavy-ion-heated diamond using in situ x-ray diagnostics, Matter Radiat. Extremes 9, 047802 (2024).
  43. K. Wünsch, J. Vorberger, G. Gregori, and D. O. Gericke, X-ray scattering as a probe for warm dense mixtures and high-pressure miscibility, Europhys. Lett. 94, 25001 (2011).
  44. See Supplemental Material at http://link.aps.org/supplemental/10.1103/lff9-f3c1 for information on the source monitor to verify self-seeding spectrum, derivation of the model for Fplasma(q,τ), fitting for the spatial overlap, derivation of the speckle intensity distribution, moments of the speckle intensity distribution function and powder x-ray diffraction of ambient TMTPA.
  45. J. W. Goodman, Statistical properties of laser speckle patterns, in Laser Speckle and Related Phenomena (Springer, Berlin, 1975), pp. 9–75.
  46. S. Chakraborty and D. Chakravarty, Discrete gamma distributions: Properties and parameter estimations, Commun. Stat. Theory Methods 41, 3301 (2012).
  47. Y. Sun, J. Montana-Lopez, P. Fuoss, M. Sutton, and D. Zhu, Accurate contrast determination for x-ray speckle visibility spectroscopy, J. Synchrotron Radiat. 27, 999 (2020).
  48. S. O. Hruszkewycz, M. Sutton, P. H. Fuoss, B. Adams, S. Rosenkranz, K. F. Ludwig Jr, W. Roseker, D. Fritz, M. Cammarata, D. Zhu, S. Lee, H. Lemke, C. Gutt, A. Robert, G. Grubel, and G. B. Stephenson, High contrast x-ray speckle from atomic-scale order in liquids and glasses, Phys. Rev. Lett. 109, 185502 (2012).
  49. S. Busch, T. H. Jensen, Y. Chushkin, and A. Fluerasu, Dynamics in shear flow studied by x-ray photon correlation spectroscopy, Eur. Phys. J. E 26, 55 (2008).
  50. H.-C. Li and R. W. Houim, Pore-scale resolved simulation of quenching, acceleration, and transition to detonation of hydrogen explosions by metal foams, Combust. Flame 259, 113118 (2024).
  51. S. Davidovits, C. Federrath, R. Teyssier, K. S. Raman, D. C. Collins, and S. R. Nagel, Turbulence generation by shock interaction with a highly nonuniform medium, Phys. Rev. E 105, 065206 (2022).
  52. H. Yin, C. Heaton, E. G. Blackman, A. E. Gleason, J. J. Turner, G. W. Collins, G. Gregori, J. K. Shang, and H. Aluie, Theory of x-ray photon correlation spectroscopy for multiscale flows, Phys. Rev. Res. 7, 023202 (2025).
  53. J. P. Mithen, J. Daligault, and G. Gregori, Extent of validity of the hydrodynamic description of ions in dense plasmas, Phys. Rev. E 83, 015401(R) (2011).
  54. D. Zhu, M. Cammarata, J. M. Feldkamp, D. M. Fritz, J. B. Hastings, S. Lee, H. T. Lemke, A. Robert, J. L. Turner, and Y. Feng, A single-shot transmissive spectrometer for hard x-ray free electron lasers, Appl. Phys. Lett. 101, 034103 (2012).
  55. C. Heaton and G. Gregori, Dataset for Measurement of turbulent velocity and bounds for thermal diffusivity in laser shock compressed foams by X-ray photon correlation spectroscopy (University of Oxford, 2025), https://dx.doi.org/10.5287/ora-brnr9da2n.

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Phys. Rev. E 112, 045218– Published 29 October, 2025
  • Received 15 July 2025
  • Accepted 2 October 2025
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