Skip to main content

Theoretical Background

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

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

  • 457 Accesses

Abstract

Chapter 1 discussed how high temperature plasmas may be formed in the laboratory in ICF and high intensity laser-plasma experiments. The purpose of this chapter is to introduce the various theoretical descriptions of these systems.

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

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.

    For example, in a NIF hohlraum, ionised gas densities (\(10^{27}\) m\(^{-3}\)) are produced over of order \(10^{-7}\) m\(^3\) [1].

  2. 2.

    This interpretation relies on the fact that an individual charge is screened at distances of order \(\lambda _D\) due to Debye shielding, which takes of order \(1/\omega _p\) to be established [7]; we assume this to be the case.

  3. 3.

    Collisionless processes are ignored throughout this work.

  4. 4.

    Akama separately obtained this expression using a quantum electrodynamical treatment [12].

  5. 5.

    In fact, as we will see in Chap. 6, it is bremsstrahlung that is the dominant energy loss mechanism for an electron at very high energies.

  6. 6.

    The multi-photon Breit-Wheeler process has been referred to simply as the Breit-Wheeler process by various authors [51,52,53,54]. In this work, the Breit-Wheeler process or Breit-Wheeler pair production always refer to the two-photon process.

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. Klimontovich, Y.L.: The Statistical Theory of Non-Equilibrium Processes in a Plasma. Pergamon, Oxford (1967)

    Google Scholar 

  3. Dawson, J.M.: Particle simulation of plasmas. Rev. Mod. Phys. 55, 403–447 (1983)

    Article  ADS  Google Scholar 

  4. Perez, F., Kemp, A.J., Divol, L., Chen, C.D., Patel, P.K.: Deflection of MeV electrons by self-generated magnetic fields in intense laser-solid interactions. Phys. Rev. Lett. 111, 245001 (2013)

    Article  ADS  Google Scholar 

  5. Dunkel, J., Hänggi, P.: Relativistic brownian motion. Phys. Rep. 471, 1–73 (2009)

    Article  ADS  MathSciNet  Google Scholar 

  6. van Kampen, N.G.: Lorentz-invariance of the distribution in phase space. Physica 43, 244–262 (1969)

    Article  ADS  Google Scholar 

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

    Google Scholar 

  8. Vlasov, A.A.: The vibrational properties of an electron gas. Sov. Phys. Usp. 10, 721–733 (1968)

    Article  ADS  Google Scholar 

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

    Google Scholar 

  10. Chandrasekhar, S.: Brownian motion, dynamical friction, and stellar dynamics. Rev. Mod. Phys. 21, 383–388 (1949)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  11. Lifshitz, E.M., Pitaevskii, L.P.: Physical Kinetics, Volume 10: Course of Theoretical Physics. Butterworth Heinemann, Oxford (1981)

    Google Scholar 

  12. Akama, H.: Relativistic Boltzmann equation for plasmas. J. Phys. Soc. Jpn. 28, 478 (1970)

    Article  ADS  Google Scholar 

  13. Sivukhin, D.V.: In: Leontovich, M.A. (ed.) Reviews of Plasma Physics, vol. 4, p. 93. Consultants Bureau, New York (1966)

    Google Scholar 

  14. Gould, R.J.: Kinetic theory of relativistic plasmas. Phys. Fluids 24, 102 (1981)

    Article  ADS  MATH  Google Scholar 

  15. Stepney, S.: Two-body relaxation in relativistic thermal plasmas. Mon. Not. R. Astron. Soc. 202, 467–481 (1983)

    Article  ADS  MATH  Google Scholar 

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

    ADS  Google Scholar 

  17. Berestetskii, V.B., Lifshitz, E.M., Pitaevskii, L.P.: Quantum Electrodynamics, Volume 4: Course of Theoretical Physics. Butterworth-Heinemann, Oxford (1982)

    Google Scholar 

  18. Fokker, A.D.: Die mittlere Energie rotierender elektrischer Dipole im Strahlungsfeld. Ann. Phys. 348, 810–820

    Google Scholar 

  19. Planck, M.: Ãœber einen Satz der statistischen Dynamik und seine Erweiterung in der Quantentheorie. Sitzungsber. Preuss. Akad. Wiss. 24 (1917)

    Google Scholar 

  20. Jüttner, F.: Das Maxwellsche Gesetz der Geschwindigkeitsverteilung in der Relativtheorie. Ann. Phys. (Leipzig) 339, 856–882 (1911)

    Article  ADS  MATH  Google Scholar 

  21. Cubero, D., Casado-Pascual, J., Dunkel, J., Talkner, P., Hänggi, P.: Thermal equilibrium and statistical thermometers in special relativity. Phys. Rev. Lett. 99 (2007)

    Google Scholar 

  22. Montakhab, A., Ghodrat, M., Barati, M.: Statistical thermodynamics of a two-dimensional relativistic gas. Phys. Rev. E 79, 031124 (2009)

    Article  ADS  Google Scholar 

  23. Dunkel, J., Hänggi, P., Hilbert, S.: Non-local observables and lightcone-averaging in relativistic thermodynamics. Nat. Phys. 5, 741–747 (2009)

    Article  Google Scholar 

  24. Chacón-Acosta, G., Dagdug, L., Morales-Técotl, H.: Manifestly covariant Jüttner distribution and equipartition theorem. Phys. Rev. E 81, 021126 (2010)

    Article  ADS  Google Scholar 

  25. 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 

  26. Karney, C.: Fokker-Planck and Quasilinear Codes. Comp. Phys. Rep. 4, 183–244 (1986)

    Article  ADS  Google Scholar 

  27. Johnston, T.W.: Cartesian tensor scalar product and spherical harmonic expansions in Boltzmann’s equation. Phys. Rev. 120, 1103 (1960)

    Article  ADS  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  29. Haines, M.G.: Magnetic-field generation in laser fusion and hot-electron transport. Can. J. Phys. 64, 912–919

    Google Scholar 

  30. Spitzer, L., Härm, R.: Transport phenomena in a completely ionized gas. Phys. Rev. 89, 977–981 (1953)

    Article  ADS  MATH  Google Scholar 

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

    ADS  Google Scholar 

  32. Haug, E.: Bremsstrahlung and pair production in the field of free electrons. Z. Naturforsch. 30, 1099–1113 (1975)

    ADS  Google Scholar 

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

    Google Scholar 

  34. Dermer, C.D.: Binary collision rates of relativistic thermal plasmas II-Spectra. Astrophys. J. 307, 47–59 (1986)

    Article  ADS  Google Scholar 

  35. Aksenov, A., Ruffini, R., Vereshchagin, G.: Thermalization of nonequilibrium electron-positron-photon plasmas. Phys. Rev. Lett. 99, 125003 (2007)

    Article  ADS  Google Scholar 

  36. Hu, H., Müller, C.: Relativistic three-body recombination with the QED vacuum. Phys. Rev. Lett. 107, 090402 (2011)

    Article  ADS  Google Scholar 

  37. Müller, C., et al.: Electron recombination in dense photonic, electronic and atomic environments. J. Phys. Conf. Ser. 388, 012003 (2012)

    Article  Google Scholar 

  38. Aksenov, A., Ruffini, R., Vereshchagin, G.: Thermalization of the mildly relativistic plasma. Phys. Rev. D 79, 043008 (2009)

    Article  ADS  Google Scholar 

  39. Landau, L.D., Lifshitz, E.M.: Statistical Physics, Part 1, Volume 5: Course of Theoretical Physics, 3 edn. Butterworth-Heinemann, Oxford (1980)

    Google Scholar 

  40. Svensson, R.: Electron-positron pair equilibria in relativistic plasmas. Astrophys. J. 258, 335 (1982)

    Article  ADS  Google Scholar 

  41. Svensson, R.: Steady mildly relativistic thermal plasmas-Processes and properties. Mon. Not. R. Astron. Soc. 209, 175–208 (1984)

    Article  ADS  Google Scholar 

  42. Baring, M.: Reaction rates and spectra in relativistic plasmas. Mon. Not. R. Astron. Soc. 228, 681–693 (1987)

    Article  ADS  MATH  Google Scholar 

  43. Coppi, P.S., Blandford, R.D.: Reaction rates and energy distributions for elementary processes in relativistic pair plasmas. Mon. Not. R. Astron. Soc. 245, 453–507 (1990)

    ADS  Google Scholar 

  44. Landau, L.D., Lifshitz, E.M.: The Classical Theory of Fields, Volume 2: Course of Theoretical Physics, 4 edn. Butterworth-Heinemann, Oxford (1975)

    Google Scholar 

  45. Weaver, T.A.: Reaction rates in a relativistic plasma. Phys. Rev. A 13, 1563–1569 (1976)

    Article  ADS  Google Scholar 

  46. Baring, M.G., Harding, A.K.: Radio-quiet pulsars with ultrastrong magnetic fields. Astrophys. J. Lett. 507, L55–L58 (1998)

    Article  ADS  Google Scholar 

  47. Daugherty, J.K., Harding, A.K.: Pair production in superstrong magnetic fields. Astrophys. J. 273, 761–773 (1983)

    Article  ADS  Google Scholar 

  48. Ritus, V.I.: Quantum effects in the interaction of elementary particles with an intense electromagnetic field. J. Sov. Laser Res. 6, 497–617 (1979)

    Article  Google Scholar 

  49. Schwinger, J.: On gauge invariance and vacuum polarization. Phys. Rev. 82, 664 (1951)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  50. Reiss, H.R.: Absorption of light by light. J. Math. Phys. 3, 59 (1962)

    Article  ADS  MathSciNet  MATH  Google Scholar 

  51. Bamber, C., et al.: Studies of nonlinear QED in collisions of 46.6 GeV electrons with intense laser pulses. Phys. Rev. D 60, 092004 (1999)

    Article  ADS  Google Scholar 

  52. Bulanov, S.S., Esirkepov, T.Z., Thomas, A.G., Koga, J.K., Bulanov, S.V.: Schwinger limit attainability with extreme power lasers. Phys. Rev. Lett. 105, 220407 (2010)

    Article  ADS  Google Scholar 

  53. Ridgers, C.P., et al.: Dense electron-positron plasmas and ultraintense \(\gamma \) rays from laser-irradiated solids. Phys. Rev. Lett. 108, 165006 (2012)

    Article  ADS  Google Scholar 

  54. Titov, A.I., Kämpfer, B., Takabe, H., Hosaka, A.: Breit-Wheeler process in very short electromagnetic pulses. Phys. Rev. A 87, 042106 (2013)

    Article  ADS  Google Scholar 

  55. Keldysh, L.V.: Ionization in the field of a strong electromagnetic wave. Sov. Phys. JETP 20, 1307–1314 (1965)

    MathSciNet  Google Scholar 

  56. Di Piazza, A., Müller, C., Hatsagortsyan, K.Z., Keitel, C.H.: Extremely high-intensity laser interactions with fundamental quantum systems. Rev. Mod. Phys. 84, 1177–1228 (2012)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

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). Theoretical Background. In: Particle Interactions in High-Temperature Plasmas. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-63447-0_2

Download citation

Publish with us

Policies and ethics