Advertisement

Electromagnetic Quantum Plasmas

Chapter
Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP, volume 65)

Abstract

The Wigner formalism is extended to systems with magnetic fields. Fluid variables are defined in terms of the electromagnetic Wigner function. The associated evolution equations are shown to include a pressure dyad composed of three parts, corresponding to kinetic velocities dispersion, osmotic velocities dispersion, and a Bohm contribution. With a closure assumption, the quantum counterpart of magnetohydrodynamics is constructed. Exact equilibrium solutions are discussed, showing an oscillatory pattern not present in classical plasma physics.

Keywords

Wigner Function Coulomb Gauge Quantum Plasma Equilibrium Number Density Quantum Hydrodynamic Model 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Arnold, A. and Steinrück, H: The ‘electromagnetic’ Wigner equation for an electron with spin. J. Appl. Math. Phys. 40, 793–815 (1989)MATHCrossRefGoogle Scholar
  2. 2.
    Attico, N. and Pegoraro, F.: Periodic equilibria of the VlasovMaxwell system. Phys. Plasmas 6, 767–771 (1999)MathSciNetADSCrossRefGoogle Scholar
  3. 3.
    Bittencourt, J. A.: Fundamentals of Plasma Physics. National Institute for Space Research, São José dos Campos (1995)Google Scholar
  4. 4.
    Bohm, D. and Hiley, B. J.: The Undivided Universe: an Ontological Interpretation of Quantum Theory. Routledge, London (1993)Google Scholar
  5. 5.
    Brodin, G. and Marklund, M.: Spin magnetohydrodynamics. New J. Phys. 9, 277–289 (2007)Google Scholar
  6. 6.
    Carruthers, P., Zachariasen, F.: Quantum collision theory with phase-space distributions. Rev. Mod. Phys. 55, 245–285 (1983)MathSciNetADSCrossRefGoogle Scholar
  7. 7.
    Chabrier, G., Douchin, F. and Potekhin, A. F.: Dense astrophysical plasmas. J. Phys.: Cond. Matter 14, 9133–9139 (2002)Google Scholar
  8. 8.
    de Groot, S. R. and Suttorp, L. G.: Foundations of Electrodynamics. North-Holland, Amsterdam (1972)Google Scholar
  9. 9.
    Gasser, I., Lin, C. and Markowich, P. A.: A review of dispersive limits of (non)linear Schrödinger-type equations. Taiwan. J. Math. 4, 501–529 (2000)MathSciNetMATHGoogle Scholar
  10. 10.
    Haas, F.: A magnetohydrodynamic model for quantum plasmas. Phys. Plasmas 12, 062117–062126 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    Haas, F.: Harris sheet solution for magnetized quantum plasmas. Europhys. Lett. 77, 45004–45009 (2007)ADSCrossRefGoogle Scholar
  12. 12.
    Harris, E. G.: On a plasma sheath separating regions of oppositely directed magnetic field. Nuovo Cimento 23 115–121 (1962)MATHCrossRefGoogle Scholar
  13. 13.
    Masmoudi, N. and Mauser, N. J.: The selfconsistent Pauli equation. Monatshefte für Mathematik, 132, 19–24 (2001)MathSciNetMATHCrossRefGoogle Scholar
  14. 14.
    Materdey, T. B. and Seyler, C. E.: The quantum Wigner function in a magnetic field. Int. J. Mod. Phys. B 17, 4555–4592 (2003)ADSCrossRefGoogle Scholar
  15. 15.
    Nicholson, D. R.: Introduction to Plasma Theory. John Wiley, New York (1983)Google Scholar
  16. 16.
    Saikin, S.: A drift-diffusion model for spin-polarized transport in a two-dimensional non-degenerate electron gas controlled by spinorbit interaction. J. Phys.: Condens. Matter 16, 5071–5081 (2004)Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Universidade Federal do ParanáCuritibaBrazil

Personalised recommendations