Hostname: page-component-76fb5796d-x4r87 Total loading time: 0 Render date: 2024-04-27T02:59:36.828Z Has data issue: false hasContentIssue false
  • English
  • Français

Wave dispersion derived from the square-root Klein–Gordon–Poisson system

Published online by Cambridge University Press:  07 February 2013

F. HAAS
F. HAAS*
Affiliation:
Departamento de Física, Universidade Federal do Paraná, 81531-980 Curitiba, PR, Brazil (ferhaas@hotmail.com)
Get access Rights & Permissions [Opens in a new window]

Abstract

Recently, there has been great interest around quantum relativistic models for plasmas. In particular, striking advances have been obtained by means of the Klein–Gordon–Maxwell system, which provides a first-order approach to the relativistic regimes of quantum plasmas. The Klein–Gordon–Maxwell system provides a reliable model as long as the plasma spin dynamics is not a fundamental aspect, to be addressed using more refined (and heavier) models involving the Pauli–Schrödinger or Dirac equations. In this work, a further simplification is considered, tracing back to the early days of relativistic quantum theory. Namely, we revisit the square-root Klein–Gordon–Poisson system, where the positive branch of the relativistic energy–momentum relation is mapped to a quantum wave equation. The associated linear wave propagation is analyzed and compared with the results in the literature. We determine physical parameters where the simultaneous quantum and relativistic effects can be noticeable in weakly coupled electrostatic plasmas.

Type
Papers
Information
Journal of Plasma Physics , Volume 79 , Special Issue 4: Advanced Plasma Concepts , August 2013 , pp. 371 - 376
Copyright
Copyright © Cambridge University Press 2013 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Aki, G. L., Markowich, P. A. and Sparber, C. 2008 Classical limit for semirelativistic Hartree systems. J. Math. Phys. 49, 102110–102120.CrossRefGoogle Scholar
Anchishkin, D. 1997 Nonrelativistic approximations of the relativistic equations and subbarrier relativistic effects. J. Phys. A: Math. Gen. 30, 1303–1321.CrossRefGoogle Scholar
Asenjo, F. A., Zamanian, J., Marklund, M., Brodin, G. and Johansson, P. 2012 Semi-relativistic effects in spin-1/2 quantum plasmas. New J. Phys. 14, 073042–073058.CrossRefGoogle Scholar
Bjorken, J. D. and Drell, S. D. 1964 Relativistic Quantum Mechanics. New York: McGraw-Hill.Google Scholar
Bludman, S. A., Watson, K. M. and Rosenbluth, M. N. 1960 Statistical mechanics of relativistic streams. II. Phys. Fluids 3, 747–757.CrossRefGoogle Scholar
Eliasson, B. and Shukla, P. K. 2012 Relativistic X-ray free-electron lasers in the quantum regime. Phys. Rev. E 85, 065401–065406(R).CrossRefGoogle ScholarPubMed
Fröhlich, J. and Lenzmann, E. 2007 Dynamical collapse of white dwarfs in Hartree- and Hartree–Fock theory. Commun. Math. Phys. 274, 737–750.CrossRefGoogle Scholar
Gill, T. L. and Zachary, W. W. 2005 Analytic representation of the square-root operator. J. Phys. A: Math. Gen. 38, 2479–2495.CrossRefGoogle Scholar
Haas, F. 2011 Quantum Plasmas: An Hydrodynamic Approach. New York: Springer.CrossRefGoogle Scholar
Haas, F., Eliasson, B. and Shukla, P. K. 2012 a Negative energy waves and quantum relativistic Buneman instabilities. Phys. Rev. E 86, 036406–036413.CrossRefGoogle ScholarPubMed
Haas, F., Eliasson, B. and Shukla, P. K. 2012 b Relativistic Klein–Gordon–Maxwell multistream model for quantum plasmas. Phys. Rev. E 85, 056411–056425.CrossRefGoogle ScholarPubMed
Kowalenko, V., Frankel, N. E. and Hines, K. C. 1985 Response theory for particle–anti-particle plasmas. Phys. Rep. 126, 109–187.CrossRefGoogle Scholar
Lieb, E. H. and Thirring, W. E. 1984 Gravitational collapse in quantum mechanics with relativistic kinetic energy. Ann. Phys. 155, 494–512.CrossRefGoogle Scholar
Melrose, D. B. 2008 Quantum Plasmadynamics: Unmagnetized Plasmas. New York: Springer.CrossRefGoogle Scholar
Mendonça, J. T. 2011 Wave kinetics of relativistic quantum plasmas. Phys. Plasmas 18, 062101–062106.CrossRefGoogle Scholar
Michelangeli, A. and Schlein, B. 2012 Dynamical collapse of boson stars. Commun. Math. Phys. 311, 645–687.CrossRefGoogle Scholar
Wigner, E. P. 1932 On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749–759.CrossRefGoogle Scholar
Zawadzki, W. 2005 On the v/c expansion of the Dirac equation with external potentials. Am. J. Phys. 73, 756–758.CrossRefGoogle Scholar
Zhu, J. and Ji, P. 2010 Relativistic quantum corrections to laser wakefield acceleration. Phys. Rev. E 81, 036406–036412.CrossRefGoogle ScholarPubMed
Zhu, J. and Ji, P. 2012 Dispersion relation and Landau damping of waves in high-energy density plasmas. Plasma Phys. Control. Fusion 54, 065004–065009.CrossRefGoogle Scholar