- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Ionization and temperature measurements in warm dense copper using x-ray absorption spectroscopy

T. Cordova1,2,*, E. V. Marley1, D. A. Chin3, R. A. London1, H. A. Scott1, M. K. G. Kruse1, T. Döppner1, F. N. Beg2, F. Coppari1 et al.

M. Millot1, J. Emig1, S. B. Hansen4, P. M. Nilson3, P. Sterne1, and M. J. MacDonald1

  • *Contact author: tcordova@ucsd.edu
PDF

Phys. Rev. Research 8, 013223 – Published 27 February, 2026

DOI: https://doi.org/10.1103/7vf4-flqv

Abstract

We detail experimental results inferring ionization and temperature for warm dense copper plasmas at several times solid density (15–25 g/cm3) and temperatures of 10–21 eV. Experiments performed at the OMEGA Laser Facility generate uniform warm dense matter conditions via symmetric shock compression of a buried copper layer. The plasma is probed with a laser-generated x-ray source to collect the K-shell x-ray absorption spectrum. Fitting bound-bound absorption contributions from constituent charge states of copper provides an estimated Z¯ of approximately 4–7 for these warm dense copper plasmas. We find that these partially ionized plasmas have K-edge shifts of 12–30 eV and bound-bound resonance 1s→3p absorption shifts of 4–26 eV with respect to the cold K edge. This study provides necessary experimental data to improve ionization and opacity models in the warm dense matter regime.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (40)

  1. 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).
  2. A. B. Zylstra, O. A. Hurricane, D. A. Callahan, A. L. Kritcher, J. E. Ralph, H. F. Robey, J. S. Ross, C. V. Young, K. L. Baker, D. T. Casey, et al., Burning plasma achieved in inertial fusion, Nature (London) 601, 542 (2022).
  3. D. E. Osterbrock, The internal structure of red dwarf stars, Astrophys. J. 118, 529 (1953).
  4. T. Guillot, Interiors of giant planets inside and outside the solar system, Science 286, 72 (1999).
  5. J. Lütgert, M. Bethkenhagen, B. Bachmann, L. Divol, D. O. Gericke, S. H. Glenzer, G. N. Hall, N. Izumi, S. F. Khan, O. L. Landen, et al., Platform for probing radiation transport properties of hydrogen at conditions found in the deep interiors of red dwarfs, Phys. Plasmas 29, 083301 (2022).
  6. S. X. Hu, L. A. Collins, T. R. Boehly, J. D. Kress, V. N. Goncharov, and S. Skupsky, First-principles thermal conductivity of warm-dense deuterium plasmas for inertial confinement fusion applications, Phys. Rev. E 89, 043105 (2014).
  7. M. J. MacDonald, D. A. Liedahl, G. V. Brown, D. Åberg, D. T. Cliche, M. E. Foord, P. E. Grabowski, R. F. Heeter, D. J. Hoarty, R. A. London, M. E. Martin, J. Nilsen, M. V. Patel, H. A. Scott, R. Shepherd, H. D. Whitley, and K. Widmann, Quantifying electron temperature distributions from time-integrated x-ray emission spectra, Rev. Sci. Instrum. 93, 093517 (2022).
  8. D. A. Liedahl and M. J. MacDonald, X-ray spectroscopy of multi-temperature plasmas using the differential emission measure formalism, Phys. Plasmas 32, 090902 (2025).
  9. B. I. Cho, K. Engelhorn, A. A. Correa, T. Ogitsu, C. P. Weber, H. J. Lee, J. Feng, P. A. Ni, Y. Ping, A. J. Nelson, D. Prendergast, R. W. Lee, R. W. Falcone, and P. A. Heimann, Electronic structure of warm dense copper studied by ultrafast x-ray absorption spectroscopy, Phys. Rev. Lett. 106, 167601 (2011).
  10. S. B. Hansen, E. C. Harding, P. F. Knapp, M. R. Gomez, T. Nagayama, and J. E. Bailey, Fluorescence and absorption spectroscopy for warm dense matter studies and ICF plasma diagnostics, Phys. Plasmas 25, 056301 (2018).
  11. M. J. MacDonald, C. A. Di Stefano, T. Döppner, L. B. Fletcher, K. A. Flippo, D. Kalantar, E. C. Merritt, S. J. Ali, P. M. Celliers, R. Heredia, et al., The colliding planar shocks platform to study warm dense matter at the national ignition facility, Phys. Plasmas 30, 062701 (2023).
  12. D. T. Bishel, E. V. Marley, M. B. Schneider, D. A. Liedahl, R. F. Heeter, M. E. Foord, G. E. Kemp, Y. Frank, J. A. Emig, G. Pérez-Callejo, P. M. Nilson, D. A. Chin, J. R. Rygg, and G. W. Collins, Ionization disequilibrium in K- and L-shell ions, Phys. Plasmas 30, 073303 (2023).
  13. T. Boehly, D. Brown, R. Craxton, R. Keck, J. Knauer, J. Kelly, T. Kessler, S. Kumpan, S. Loucks, S. Letzring, F. Marshall, R. McCrory, S. Morse, W. Seka, J. Soures, and C. Verdon, Initial performance results of the OMEGA laser system, Opt. Commun. 133, 495 (1997).
  14. C. Fortmann, H. J. Lee, T. Döppner, R. W. Falcone, A. L. Kritcher, O. L. Landen, and S. H. Glenzer, Measurement of the adiabatic index in Be compressed by counterpropagating shocks, Phys. Rev. Lett. 108, 175006 (2012).
  15. L. B. Fletcher, H. J. Lee, T. Döppner, E. Galtier, B. Nagler, P. Heimann, C. Fortmann, S. LePape, T. Ma, M. Millot, et al., Ultrabright x-ray laser scattering for dynamic warm dense matter physics, Nat. Photon. 9, 274 (2015).
  16. D. Bailie, S. White, R. Irwin, C. Hyland, R. Warwick, B. Kettle, N. Breslin, S. N. Bland, D. J. Chapman, S. P. D. Mangles, R. A. Baggot, E. R. Tubman, and D. Riley, K-edge structure in shock-compressed chlorinated parylene, Atoms 11, 135 (2023).
  17. M. F. Gu, The flexible atomic code, Can. J. Phys. 86, 675 (2008).
  18. H. Nguyen, M. Koenig, D. Benredjem, M. Caby, and G. Coulaud, Atomic structure and polarization line shift in dense and hot plasmas, Phys. Rev. A 33, 1279 (1986).
  19. F. Dorchies, F. Festa, V. Recoules, O. Peyrusse, A. Benuzzi-Mounaix, E. Brambrink, A. Levy, A. Ravasio, M. Koenig, T. Hall, and S. Mazevet, X-ray absorption K edge as a diagnostic of the electronic temperature in warm dense aluminum, Phys. Rev. B 92, 085117 (2015).
  20. J. C. Stewart and K. D. Pyatt, Jr., Lowering of ionization potentials in plasmas, Astrophys. J. 144, 1203 (1966).
  21. G. Ecker and W. Kröll, Lowering of the ionization energy for a plasma in thermodynamic equilibrium, Phys. Fluids 6, 62 (1963).
  22. O. Ciricosta, S. M. Vinko, H.-K. Chung, B.-I. Cho, C. R. D. Brown, T. Burian, J. Chalupský, K. Engelhorn, R. W. Falcone, C. Graves, et al., Direct measurements of the ionization potential depression in a dense plasma, Phys. Rev. Lett. 109, 065002 (2012).
  23. O. Ciricosta, S. M. Vinko, B. Barbrel, D. S. Rackstraw, T. R. Preston, T. Burian, J. Chalupský, B. I. Cho, H. K. Chung, G. L. Dakovski, et al., Measurements of continuum lowering in solid-density plasmas created from elements and compounds, Nat. Commun. 7, 11713 (2016).
  24. D. J. Hoarty, P. Allan, S. F. James, C. R. D. Brown, L. M. R. Hobbs, M. P. Hill, J. W. O. Harris, J. Morton, M. G. Brookes, R. Shepherd, J. Dunn, H. Chen, E. Von Marley, P. Beiersdorfer, H. K. Chung, R. W. Lee, G. Brown, and J. Emig, Observations of the effect of ionization-potential depression in hot dense plasma, Phys. Rev. Lett. 110, 265003 (2013).
  25. M. R. Gomez, S. A. Slutz, A. B. Sefkow, D. B. Sinars, K. D. Hahn, S. B. Hansen, E. C. Harding, P. F. Knapp, P. F. Schmit, C. A. Jennings, et al., Experimental demonstration of fusion-relevant conditions in magnetized liner inertial fusion, Phys. Rev. Lett. 113, 155003 (2014).
  26. A. Benuzzi-Mounaix, F. Dorchies, V. Recoules, F. Festa, O. Peyrusse, A. Levy, A. Ravasio, T. Hall, M. Koenig, N. Amadou, E. Brambrink, and S. Mazevet, Electronic structure investigation of highly compressed aluminum with K edge absorption spectroscopy, Phys. Rev. Lett. 107, 165006 (2011).
  27. T. Döppner, M. Bethkenhagen, D. Kraus, P. Neumayer, D. A. Chapman, B. Bachmann, R. A. Baggott, M. P. Böhme, L. Divol, R. W. Falcone, et al., Observing the onset of pressure-driven K-shell delocalization, Nature (London) 618, 270 (2023).
  28. M. L. Spaeth, K. R. Manes, D. H. Kalantar, P. E. Miller, J. E. Heebner, E. S. Bliss, D. R. Spec, T. G. Parham, P. K. Whitman, P. J. Wegner, et al., Description of the NIF laser, Fusion Sci. Technol. 69, 25 (2016).
  29. 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).
  30. M. M. Marinak, S. W. Haan, T. R. Dittrich, R. E. Tipton, and G. B. Zimmerman, A comparison of three-dimensional multimode hydrodynamic instability growth on various national ignition facility capsule designs with hydra simulations, Phys. Plasmas 5, 1125 (1998).
  31. D. A. Chin, P. M. Nilson, D. Mastrosimone, D. Guy, J. J. Ruby, D. T. Bishel, J. F. Seely, F. Coppari, Y. Ping, J. R. Rygg, and G. W. Collins, High-resolution x-ray spectrometer for x-ray absorption fine structure spectroscopy, Rev. Sci. Instrum. 94, 013101 (2023).
  32. N. A. Pablant, M. Bitter, P. C. Efthimion, L. Gao, K. W. Hill, B. F. Kraus, J. Kring, M. J. MacDonald, N. Ose, Y. Ping, M. B. Schneider, S. Stoupin, and Y. Yakusevitch, Design and expected performance of a variable-radii sinusoidal spiral x-ray spectrometer for the national ignition facility, Rev. Sci. Instrum. 92, 093904 (2021).
  33. L. M. Barker and R. E. Hollenbach, Laser interferometer for measuring high velocities of any reflecting surface, J. Appl. Phys. 43, 4669 (1972).
  34. T. Schoonjans, A. Brunetti, B. Golosio, M. Sanchez Del Rio, V. A. Solé, C. Ferrero, and L. Vincze, The xraylib library for x-ray-matter interactions. Recent developments, Spectrochim. Acta Part B 66, 776 (2011).
  35. D. Foreman-Mackey, D. W. Hogg, D. Lang, and J. Goodman, emcee: The MCMC hammer, Publ. Astron. Soc. Pac. 125, 306 (2013).
  36. H. R. Griem, Plasma Spectroscopy (McGraw-Hill, New York, 1964).
  37. H. A. Scott, Cretin—A radiative transfer capability for laboratory plasmas, J. Quant. Spectrosc. Radiat. Transfer 71, 689 (2001).
  38. J. D. McHardy, An introduction to the theory and use of SESAME equations of state Tech. Rep., Los Alamos National Lab. (LANL), Los Alamos, NM, USA, 2018, https://doi.org/10.2172/1487368.
  39. T. Akkuş, Y. Şahin, D. Yilmaz, and F. N. Tuzluca, The K-beta/K-alpha intensity ratios of some elements at different azimuthal scattering angles at 59.54 keV, Can. J. Phys. 95, 220 (2017).
  40. 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).

Outline

Information

Phys. Rev. Research 8, 013223– Published 27 February, 2026
  • Received 16 September 2025
  • Accepted 30 January 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation