Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-27T14:23:40.609Z Has data issue: false hasContentIssue false
  • English
  • Français

Three-wave interaction and Manley–Rowe relations in quantum hydrodynamics

Published online by Cambridge University Press:  25 March 2014

Erik Wallin ,
Jens Zamanian  and
Gert Brodin
Erik Wallin*
Affiliation:
Department of Physics, Umeå University, SE–901 87 Umeå, Sweden
Jens Zamanian
Affiliation:
Department of Physics, Umeå University, SE–901 87 Umeå, Sweden
Gert Brodin
Affiliation:
Department of Physics, Umeå University, SE–901 87 Umeå, Sweden
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The theory for nonlinear three-wave interaction in magnetized plasmas is reconsidered using quantum hydrodynamics. The general coupling coefficients are calculated for the generalized Bohm de Broglie term. It is found that the Manley–Rowe relations are fulfilled only if the form of the particle dispersive term coincides with the standard expression. The implications of our results are discussed.

Type
Papers
Information
Journal of Plasma Physics , Volume 80 , Issue 4 , August 2014 , pp. 643 - 652
Copyright
Copyright © Cambridge University Press 2014 

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

REFERENCES

Aliev, Yu. M. and Brodin, G. 1990 Instability of a strongly inhomogeneous plasma. Phys. Rev. A 42, 2374–2378.CrossRefGoogle ScholarPubMed
Atwater, H. A. 2007 The promise of plasmonics. Sci. Am. 296, 56–62.CrossRefGoogle ScholarPubMed
Brodin, G. and Stenflo, L. 1988a Parametric instabilities of finite amplitude Alfvén waves. Phys. Scr. 37 (1), 89.CrossRefGoogle Scholar
Brodin, G. and Stenflo, L. 1988b Three-wave coupling coefficients for MHD plasmas. J. Plasma Phys. 39 (2), 277–284.CrossRefGoogle Scholar
Brodin, G. and Stenflo, L. 1989 Three-wave coupling coefficients for magnetized plasmas with pressure anisotropy. J. Plasma Phys. 41, 199–208.CrossRefGoogle Scholar
Dodin, I. Y. 2013 Geometric view on non-Eikonal waves. arXiv preprint arXiv:1310.5050.Google Scholar
Dodin, I. Y., Zhmoginov, A. I. and Fisch, N. J. 2008 Manley–Rowe relations for an arbitrary discrete system. Phys. Lett. A 372 (39), 6094–6096.Google Scholar
Dysthe, K. B., Leer, E., Trulsen, J. and Stenflo, L. 1977 Stimulated Brillouin scattering in the ionosphere. J. Geophys. Res. 82 (4), 717–718.Google Scholar
Gardner, C. L. 1994 The quantum hydrodynamic model for semiconductor devices. SIAM J. Appl. Math. 54 (2), 409–427.Google Scholar
Glenzer, S. H. and Redmer, R. 2009 X-ray Thomson scattering in high energy density plasmas. Rev. Mod. Phys. 81, 1625–1663.Google Scholar
Haas, F. 2011 Quantum Plasmas. New York, NY: Springer.Google Scholar
Haas, F., Marklund, M., Brodin, G. and Zamanian, J. 2010a Fluid moment hierarchy equations derived from quantum kinetic theory. Phys. Lett. A 374 (3), 481–484.CrossRefGoogle Scholar
Haas, F., Zamanian, J., Marklund, M. and Brodin, G. 2010b Fluid moment hierarchy equations derived from gauge invariant quantum kinetic theory. New J. Phys. 12 (7), 073027.CrossRefGoogle Scholar
Harding, A. K. and Lai, D. 2006 Physics of strongly magnetized neutron stars. Rep. Prog. Phys. 69 (9), 2631.Google Scholar
Kadomtsev, B. B. 1965 Plasma Turbulence. London: Academic Press.Google Scholar
Kaufman, A. N. and Stenflo, L. 1975 Action conservation in the presence of a high-frequency field. Plasma Phys. 17 (5), 403.Google Scholar
Kaufman, A. N. and Stenflo, L. 1979 Wave coupling in cold non-uniform magnetoplasma. Phys. Scr. 19, 523.Google Scholar
Kouveliotou, C., Dieters, S., Strohmayer, T., Van Paradijs, J., Fishman, G. J., Meegan, C. A., Hurley, K., Kommers, J., Smith, I., Frail, D., et al. 1998 An X-ray pulsar with a super strong magnetic field in the soft γ-ray repeater SGR1806- 20. Nature 393 (6682), 235–237.Google Scholar
Kruer, W. L. 1988 The Physics of Laser Plasma Interactions. Boston, MA: Addison-Wesley.Google Scholar
Larsson, J. 1996 A new Hamiltonian formulation for fluids and plasmas. Part 3. Multifluid electrodynamics. J. Plasma Phys. 55, 279–300.Google Scholar
Larsson, J. and Stenflo, L. 1973 Three-wave interactions in magnetized plasmas. Beiträge aus der Plasmaphysik 13 (3), 169–181.CrossRefGoogle Scholar
Lashmore-Davies, C. N. 1981 Nonlinear laser plasma interaction theory. In Plasma Physics and Nuclear Fusion Research (ed. Gill, R. D.). London: Academic Press, pp. 319–354, Chap. 14.Google Scholar
Lindgren, T., Larsson, J. and Stenflo, L. 1981 Three-wave coupling coefficients for non-uniform plasmas. J. Plasma Phys. 26, 407–418.CrossRefGoogle Scholar
Lundin, J., Zamanian, J., Marklund, M. and Brodin, G. 2007 Short wavelength electromagnetic propagation in magnetized quantum plasmas. Phys. Plasmas 14, 062112.Google Scholar
Manfredi, G. 2005 How to model quantum plasmas. In Topics in Kinetic Theory (eds. Passot, T., Sulem, C. and Sulem, P.-L.). Toronto, Canada: Fields Institute Communications, pp. 263–287.Google Scholar
Manfredi, G. and Haas, F. 2001 Self-consistent fluid model for a quantum electron gas. Phys. Rev. B 64 (7), 075316.CrossRefGoogle Scholar
Manfredi, G. and Hervieux, P. A. 2007 Autoresonant control of the many-electron dynamics in non-parabolic quantum wells. Appl. Phys. Lett. 91 (6), 061108-061108-3.Google Scholar
Manley, J. M. and Rowe, H. E. 1956 Some general properties of nonlinear elements-part i. general energy relations. Proc. IRE 44 (7), 904–913.Google Scholar
Mironov, V. A., Sergeev, A. M., Vanin, E. V and Brodin, G. 1990 Localized nonlinear wave structures in the nonlinear photon accelerator. Phys. Rev. A 42, 4862–4866.CrossRefGoogle ScholarPubMed
Palmer, D. M., Barthelmy, S., Gehrels, N., Kippen, R. M., Cayton, T., Kouveliotou, C., Eichler, D., Wijers, R. A. M. J., Woods, P. M., Granot, J., et al. 2005 A giant big gamma-ray flare from the magnetar SGR 1806-20. Nature 434, 1107–1109.Google Scholar
Sagdeev, R. Z. and Galeev, A. 1969 Nonlinear Plasma Theory. New York, NY: W. A. Benjamin.Google Scholar
Shahid, M., Hussain, A. and Murtaza, G. 2013 A comparison of parametric decay of oblique Langmuir wave in high and low density magneto-plasmas. Phys. Plasmas 20, 092121.Google Scholar
Shukla, P. K. and Eliasson, B. 2010 Nonlinear aspects of quantum plasma physics. Phys.-Usp. 53 (1), 51.Google Scholar
Shukla, P. K. and Eliasson, B. 2011 Colloquium: nonlinear collective interactions in quantum plasmas with degenerate electron fluids. Rev. Mod. Phys. 83, 885–906.Google Scholar
Sjölund, A. and Stenflo, L. 1967 Nonlinear coupling in a magnetized plasma. Z. Phys. 204 (3), 211–214.Google Scholar
Stenflo, L. 1994 Resonant three-wave interactions in plasmas. Phys. Scr. T50, 15.Google Scholar
Stenflo, L. 2004 Comments on stimulated electromagnetic emissions in the ionospheric plasma. Phys. Scr. T107, 262.CrossRefGoogle Scholar
Stenflo, L. and Larsson, J. 1977 Three-wave coupling coefficients for magnetized plasmas. In Plasma Physics: Nonlinear Theory and Experiments, Proceedings of Nobel Symposium, Vol. 36 (ed. Wilhelmsson, H.). New York, NY: Plenum Press, pp. 152–158.Google Scholar
Tsytovich, V. N. 1970 Nonlinear Effects in Plasmas. New York, NY: Plenum Press.CrossRefGoogle Scholar
Vladimirov, S. V. and Stenflo, L. 1997 Three-wave processes in a turbulent nonstationary plasma. Phys. Plasmas 4, 1249.CrossRefGoogle Scholar
Weiland, J. and Wilhelmsson, H. 1977 Coherent Non-Linear Interaction of Waves in Plasmas. New York, NY: Pergamon Press.Google Scholar
Wolf, S. A., Awschalom, D. D., Buhrman, R. A, Daughton, J. M., von Moln, S., Roukes, M. L., Chtchelkanova, A. Y. and Treger, D. M. 2001 Spintronics: a spin-based electronics vision for the future. Science 294 (5546), 1488–1495.Google Scholar