Skip to main content
SpringerLink
Log in

Transport Processes in a Relativistic Plasma

  • Chapter
  • First Online:
Particle Interactions in High-Temperature Plasmas

Part of the book series: Springer Theses ((Springer Theses))

  • 469 Accesses

Abstract

Thermonuclear burn in inertial confinement fusion is predicted to involve the most extreme temperatures, densities and pressures ever produced in the laboratory (Lindl et al. in Phys Plasmas 11:339, 2004, [1]).

This chapter is an enhanced version of a chapter from an original PhD thesis which is available Open Access from the repository https://spiral.imperial.ac.uk/ of Imperial College London. The original chapter was distributed under the terms of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License (http://creativecommons.org/licenses/by-nc-nd/4.0/), which permits any non-commercial use, duplication, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author and the source, provide a link to the Creative Commons license and indicate if you modified the licensed material. You do not have permission under this license to share adapted material derived from this book or parts of it. The Creative Commons license does not apply to this enhanced chapter, but only to the original chapter of the thesis.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    In fact, this scheme is unconditionally stable for the diffusion equation [30].

  2. 2.

    Our scalings here and in the preceding discussion all apply in the ultra-relativistic limit. In the mildly-relativistic case, no simple scaling is possible, as the correction is a product of both the simple physical arguments here, as well as changes to the shape of the distribution function.

References

  1. Lindl, J.D., et al.: The physics basis for ignition using indirect-drive targets on the National Ignition Facility. Phys. Plasmas 11, 339 (2004)

    Article  ADS  Google Scholar 

  2. Edwards, M.J., et al.: Progress towards ignition on the National Ignition Facility. Phys. Plasmas 20, 070501 (2013)

    Article  ADS  Google Scholar 

  3. Lindl, J., Landen, O., Edwards, J., Moses, E., NIC Team.: Review of the national ignition campaign 2009–2012. Phys. Plasmas 21, 020501 (2014)

    Google Scholar 

  4. Tabak, M., et al.: Ignition and high gain with ultrapowerful lasers. Phys. Plasmas 1, 1626–1634 (1994)

    Article  ADS  Google Scholar 

  5. Betti, R., et al.: Shock ignition of thermonuclear fuel with high areal density. Phys. Rev. Lett. 98, 155001 (2007)

    Article  ADS  Google Scholar 

  6. Tabak, M.: What is the role of tritium-poor fuels in ICF? Nucl. Fusion 36, 147–157 (1996)

    Article  ADS  Google Scholar 

  7. Atzeni, S., Meyer-Ter-Vehn, J.: The Physics of Inertial Fusion: Beam Plasma Interaction, Hydrodynamics, Hot Dense Matter. Oxford University Press, Oxford (2004)

    Book  Google Scholar 

  8. Perkins, L.J., Logan, B.G., Zimmerman, G., Werner, C.J.: Two-dimensional simulations of thermonuclear burn in ignition-scale inertial confinement fusion targets under compressed axial magnetic fields. Phys. Plasmas 20, 072708 (2013)

    Article  ADS  Google Scholar 

  9. Manuel, M.J.E., et al.: First measurements of Rayleigh-Taylor-induced magnetic fields in laser-produced plasmas. Phys. Rev. Lett. 108, 255006 (2012)

    Article  ADS  Google Scholar 

  10. McBride, J.B., Pytte, A.: Relativistic corrections to the conductivity of a collisional plasma in a magnetic field. Phys. Rev. 179, 145–148 (1969)

    Article  ADS  Google Scholar 

  11. Beliaev, S.T., Budker, G.I.: The relativistic kinetic equation. Sov. Phys. Dokl. 1, 218 (1956)

    ADS  Google Scholar 

  12. Dzhavakhishvili, D.I., Tsintsadze, N.L.: Transport phenomena in a completely ionized ultrarelativistic plasma. Sov. Phys. JETP 37, 666 (1973)

    ADS  Google Scholar 

  13. Braginskii, S.I.: In: Leontovich, M.A. (ed.) Reviews of Plasma Physics, vol. 1, p. 205. Consultants Bureau, New York (1965)

    Google Scholar 

  14. Balescu, R., Paiva-Veretennicoff, I., Brenig, L.: Kinetic theory of the plasma-dynamical modes and the transport coefficients of a relativistic plasma. Phys. A 81, 17–46 (1975)

    Article  Google Scholar 

  15. van Erkelens, H., van Leeuwen, W.A.: Relativistic Boltzmann theory for a plasma: X. Electrical conduction of the cosmological fluid. Phys. A 123, 72–98 (1984)

    Article  Google Scholar 

  16. Kremer, G.M., Patsko, C.H.: Relativistic ionized gases: Ohm and Fourier laws from Anderson and Witting model equation. Phys. A 322, 329–344 (2003)

    Article  MATH  Google Scholar 

  17. Braams, B.J., Karney, C.F.F.: Differential form of the collision integral for a relativistic plasma. Phys. Rev. Lett. 59, 1817–1820 (1987)

    Article  ADS  MathSciNet  Google Scholar 

  18. Braams, B.J., Karney, C.F.F.: Conductivity of a relativistic plasma. Phys. Fluids B 1, 1355 (1989)

    Article  ADS  Google Scholar 

  19. Mohanty, J.N., Baral, K.C.: Theory of weakly coupled relativistic plasma-diffusion and transport across a magnetic-field. J. Phys. A 28, 5709–5720 (1995)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  20. Mohanty, J.N., Baral, K.C.: Relativistic theory of cross-field transport and diffusion in a plasma. Phys. Plasmas 3, 804 (1996)

    Article  ADS  Google Scholar 

  21. Honda, M., Mima, K.: Relativistic effects on transport coefficients in collision dominant magnetoactive plasmas. J. Phys. Soc. Jpn. 67, 3420–3428 (1998)

    Article  ADS  Google Scholar 

  22. Metens, T., Balescu, R.: Relativistic transport theory for a two-temperature magnetized plasma. Phys. Fluids B 2, 2076 (1990)

    Article  ADS  Google Scholar 

  23. Spitzer, L., Härm, R.: Transport Phenomena in a Completely Ionized Gas. Phys. Rev. 89, 977–981 (1953)

    Article  ADS  MATH  Google Scholar 

  24. Synge, J.L.: The Relativistic Gas. North-Holland, Amsterdam (1957)

    MATH  Google Scholar 

  25. Shkarofsky, I.P., Johnston, T.W., Bachynski, M.P.: The Particle Kinetics of Plasmas. Addison-Wesley, Boston (1966)

    Google Scholar 

  26. Epperlein, E.M.: The accuracy of Braginskii’s transport coefficients for a Lorentz plasma. J. Phys. D 17, 1823 (1984)

    Article  ADS  Google Scholar 

  27. Bell, A.R., Robinson, A.P.L., Sherlock, M., Kingham, R.J., Rozmus, W.: Fast electron transport in laser-produced plasmas and the KALOS code for solution of the Vlasov–Fokker–Planck equation. Plasma Phys. Controll. F. 48, R37–R57 (2006)

    Article  ADS  Google Scholar 

  28. Shkarofsky, I.P.: Expansion of the relativistic Fokker-Planck equation including non-linear terms and a non-Maxwellian background. Phys. Plasmas 4, 2464 (1997)

    Article  ADS  Google Scholar 

  29. Karney, C.: Fokker-Planck and quasilinear codes. Comput. Phys. Rep. 4, 183–244 (1986)

    Article  ADS  Google Scholar 

  30. Press, W.H., Teukolsky, S.A., Vetterling, W.T., Flannery, B.P.: Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, Cambridge (2007)

    MATH  Google Scholar 

  31. Epperlein, E.M., Haines, M.G.: Plasma transport coefficients in a magnetic field by direct numerical solution of the Fokker-Planck equation. Phys. Fluids 29, 1029 (1986)

    Article  ADS  MATH  Google Scholar 

  32. Spitzer Jr., L.: Physics of Fully Ionized Gases, 2 edn. John Wiley & Sons, New York (1962)

    Google Scholar 

  33. Trubnikov, B.A.: In: Leontovich, M.A. (ed.) Reviews of Plasma Physics, vol. 1, p. 105. Consultants Bureau, New York (1965)

    Google Scholar 

  34. Gray, D.R., Kilkenny, J.D.: The measurement of ion acoustic turbulence and reduced thermal conductivity caused by a large temperature gradient in a laser heated plasma. Plasma Phys. 22, 81–111 (1980)

    Article  ADS  Google Scholar 

  35. Bell, A.R., Evans, R.G., Nicholas, D.J.: Elecron energy transport in steep temperature gradients in laser-produced plasmas. Phys. Rev. Lett. 46, 243–246 (1981)

    Article  ADS  Google Scholar 

  36. Matte, J.P., Virmont, J.: Electron heat transport down steep temperature gradients. Phys. Rev. Lett. 49, 1936–1939 (1982)

    Article  ADS  Google Scholar 

  37. Hochstim, A.R., Massel, G.A.: In: Hochstim, A.R. (ed.) Kinetic Processes in Gases and Plasmas, p. 142. Academic Press, New York (1969)

    Google Scholar 

  38. Rose, S.J.: Electron-positron pair creation in burning thermonuclear plasmas. High Energ. Density Phys. 9, 480–483 (2013)

    Article  ADS  Google Scholar 

  39. Rybicki, G.B., Lightman, A.P.: Radiative Processes in Astrophysics. John Wiley & Sons (2008)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Blackett Laboratory, Department of Physics, Imperial College London, London, UK

    Oliver James Pike

Authors
  1. Oliver James Pike
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Oliver James Pike .

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this chapter

Cite this chapter

Pike, O.J. (2017). Transport Processes in a Relativistic Plasma. In: Particle Interactions in High-Temperature Plasmas. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-63447-0_4

Download citation

Publish with us

Policies and ethics

Search

Navigation