- Physical Review Journals
All JournalsPhysics Magazine

Physical Review E

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

Impact of ion-electron collisions on nonlocal ion heat conduction, viscous stress, and diffusion

Nicholas Mitchell1,2,*, David Chapman2, and Grigory Kagan1

  • *Contact author: nic.mitchell@firstlightfusion.com
PDF

Phys. Rev. E 114, 035215 – Published 25 September, 2026

DOI: https://doi.org/10.1103/yzxz-6j66

Abstract

This work demonstrates the impact of ion-electron collisions on ion transport for strongly inhomogeneous plasmas in the nonlocal regime, where collisionality is insufficient to enforce local thermal equilibrium due to sharp gradients. Ion heat conduction and viscous stress in both unmagnetized and magnetized plasmas are considered, as well as interspecies diffusion in multispecies plasmas. Most notably, even for equal ion and electron temperatures, ion-electron collisions are found to substantially modify the peak nonlocal heat flow, whereas nonlocal preheats are strongly suppressed since streaming suprathermal particles are further out in the tail of the cold ion distribution where ion-electron collisions become dominant.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (35)

  1. H. Rinderknecht, P. Amendt, S. Wilks, and G. Collins, Kinetic physics in ICF: Present understanding and future directions, Plasma Phys. Controlled Fusion 60, 064001 (2018).
  2. M. J. Rosenberg, F. H. Séguin, P. A. Amendt, S. Atzeni, H. G. Rinderknecht, N. M. Hoffman, A. B. Zylstra, C. K. Li, H. Sio, M. Gatu Johnson, J. A. Frenje, R. D. Petrasso, V. Y. Glebov, C. Stoeckl, W. Seka, F. J. Marshall, J. A. Delettrez, T. C. Sangster, R. Betti, S. C. Wilks, et al., Assessment of ion kinetic effects in shock-driven inertial confinement fusion implosions using fusion burn imaging, Phys. Plasmas 22, 062702 (2015).
  3. E. L. Vold, K. Molvig, A. S. Joglekar, M. I. Ortega, R. Moll, and D. Fenn, Plasma viscosity with mass transport in spherical inertial confinement fusion implosion simulations, Phys. Plasmas 22, 112708 (2015).
  4. S. I. Braginskii, in Transport Processes in a Plasma, edited by M. A. Leontovich, Reviews of Plasma Physics, Vol. 1 (Consultants Bureau, New York, 1965), p. 205, Authorized translation from the Russian by Herbert Lashinsky, University of Maryland, USA.
  5. J.-Y. Ji and E. D. Held, Closure and transport theory for high-collisionality electron-ion plasmas, Phys. Plasmas 20, 042114 (2013).
  6. J.-Y. Ji and E. D. Held, Ion closure theory for high collisionality revisited, Phys. Plasmas 22, 062114 (2015).
  7. A. R. Bell, R. G. Evans, and D. J. Nicholas, Electron energy transport in steep temperature gradients in laser-produced plasmas, Phys. Rev. Lett. 46, 243 (1981).
  8. J. Brodrick, R. Kingham, M. Marinak, M. Patel, A. Chankin, J. Omotani, M. Umansky, D. Del Sorbo, B. Dudson, J. Parker, G. Kerbel, M. Sherlock, and C. Ridgers, Testing nonlocal models of electron thermal conduction for magnetic and inertial confinement fusion applications, Phys. Plasmas 24, 092309 (2017).
  9. H. Zhao, Z. Sheng, and S. Weng, Nonlocal thermal transport in magnetized plasma along different directions, Matter Radiat. Extremes 7, 045901 (2022).
  10. E. M. Epperlein and R. W. Short, A practical nonlocal model for electron heat transport in laser plasmas, Phys. Fluids B 3, 3092 (1991).
  11. G. P. Schurtz, P. D. Nicolaï, and M. Busquet, A nonlocal electron conduction model for multidimensional radiation hydrodynamics codes, Phys. Plasmas 7, 4238 (2000).
  12. M. Holec, J. Nikl, and S. Weber, Nonlocal transport hydrodynamic model for laser heated plasmas, Phys. Plasmas 25, 032704 (2018).
  13. J.-Y. Ji, H. Q. Lee, and E. D. Held, Ion parallel closures, Phys. Plasmas 24, 022127 (2017).
  14. N. T. Mitchell, D. A. Chapman, C. J. McDevitt, M. P. Read, and G. Kagan, A reduced kinetic method for investigating non-local ion heat transport in ideal multi-species plasmas, Plasma Phys. Controlled Fusion 66, 075005 (2024).
  15. N. Mitchell, D. Chapman, and G. Kagan, Nonlocal current-driven heat flow in ideal plasmas, Phys. Rev. E 112, L053202 (2025).
  16. N. Mitchell, D. Chapman, and G. Kagan, A first-principles closure for nonlocal magnetized transport, Plasma Phys. Controlled Fusion 68, 055007 (2026).
  17. P. Amendt, O. L. Landen, H. F. Robey, C. K. Li, and R. D. Petrasso, Plasma barodiffusion in inertial-confinement-fusion implosions: Application to observed yield anomalies in thermonuclear fuel mixtures, Phys. Rev. Lett. 105, 115005 (2010).
  18. G. Kagan and X.-Z. Tang, Thermo-diffusion in inertially confined plasmas, Phys. Lett. A 378, 1531 (2014).
  19. G. Kagan and X.-Z. Tang, Electro-diffusion in a plasma with two ion species, Phys. Plasmas 19, 082709 (2012).
  20. J. H. Ferziger and H. G. Kaper, Mathematical Theory of Transport Processes in Gases (North-Holland, Amsterdam, 1972).
  21. V. M. Zhdanov, Transport Processes in Multicomponent Plasma (CRC, Boca Raton, FL, 2014).
  22. G. Kagan and S. D. Baalrud, Transport formulas for multi-component plasmas within the effective potential theory framework, arXiv:1611.09872.
  23. A. B. Mikhailovskii and V. S. Tsypin, Transport equations and gradient instabilities in a high pressure collisional plasma, Plasma Phys. 13, 785 (1971).
  24. D. Del Sorbo, J.-L. Feugeas, P. Nicolaï, M. Olazabal-Loumé, B. Dubroca, S. Guisset, M. Touati, and V. Tikhonchuk, Reduced entropic model for studies of multidimensional nonlocal transport in high-energy-density plasmas, Phys. Plasmas 22, 082706 (2015).
  25. D. A. Chapman, J. D. Pecover, N. Chaturvedi, N. Niasse, M. P. Read, D. H. Vassilev, J. P. Chittenden, N. Hawker, and N. Joiner, A preliminary assessment of the sensitivity of uniaxially driven fusion targets to flux-limited thermal conduction modeling, Phys. Plasmas 28, 072702 (2021).
  26. A. L. Velikovich, K. G. Whitney, and J. W. Thornhill, A role for electron viscosity in plasma shock heating, Phys. Plasmas 8, 4524 (2001).
  27. Y. B. Zel'dovich and Y. P. Raizer, Physics of Shock Waves and High-Temperature Hydrodynamic Phenomena (Academic, New York, 1967).
  28. R. Koch, Plasma heating by neutral beam injection, Fusion Sci. Technol. 45, 183 (2004).
  29. D. Q. Hwang, J. Hosea, H. Thompson, J. R. Wilson, S. Davis, D. Herndon, R. Kaita, D. Mueller, S. Suckewer, C. Daughney, and P. Colestock, Heating of plasma ions in a tokamak by the second-harmonic ion-cyclotron resonance interaction with radio-frequency waves, Phys. Rev. Lett. 51, 1865 (1983).
  30. S. Chandrasekhar, Dynamical friction. I. General considerations: The coefficient of dynamical friction, Astrophys. J. 97, 255 (1943).
  31. Helander and Sigmar, Collisional Transport in Magnetized Plasmas (Cambridge University, Cambridge, England, 2002).
  32. A. Beresnyak, 2023 NRL plasma formulary, Technical Report, Naval Research Laboratory, Plasma Physics Division, Washington, DC, 2023, https://www.nrl.navy.mil/News-Media/Publications/NRL-Plasma-Formulary/.
  33. G. Kagan, S. Baalrud, and J. Daligault, Influence of coupling on thermal forces and dynamic friction in plasmas with multiple ion species, Phys. Plasmas 24, 072705 (2017).
  34. L. D. Landau and E. M. Lifshitz, Fluid Mechanics, 2nd ed., Course of Theoretical Physics, Vol. 6 (Butterworth-Heinemann, Oxford, 1987).
  35. G. Kagan, D. Svyatskiy, H. G. Rinderknecht, M. J. Rosenberg, A. B. Zylstra, C.-K. Huang, and C. J. McDevitt, Self-similar structure and experimental signatures of suprathermal ion distribution in inertial confinement fusion implosions, Phys. Rev. Lett. 115, 105002 (2015).

Outline

Information

Phys. Rev. E 114, 035215– Published 25 September, 2026
  • Received 29 July 2026
  • Accepted 9 September 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