Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-23T10:55:41.280Z Has data issue: false hasContentIssue false
  • English
  • Français

Parametric decay of wide band Langmuir wave spectra

Published online by Cambridge University Press:  28 November 2016

Mitsuo Kono  and
Hans L. Pécseli Open the ORCID record for Hans L. Pécseli [Opens in a new window]
Mitsuo Kono
Affiliation:
Chuo University, Faculty of Policy Studies, Hachioji, Tokyo 192-0393, Japan
Hans L. Pécseli*
Affiliation:
University of Oslo, Department of Physics, Box 1048 Blindern, N-0316 Oslo, Norway
*
†Email address for correspondence: hans.pecseli@fys.uio.no
Get access Rights & Permissions [Opens in a new window]

Abstract

Previous results obtained for modulational instability of a Langmuir wave spectrum are extended to account also for the Langmuir wave decay. The general model is tested by considering first the parametric decay of single-mode Langmuir waves, and also two-wave models, where several combinations are considered: one wave is modulationally unstable, another decay unstable and one where both waves are unstable with respect to decay. For the general case with continuous wave spectra it is found that distribution of the Langmuir wave energy over a wide wavenumber band reduces the decay rate when the correlation length for the spectrum becomes comparable to the wavelength of the most unstable sound wave among the possible decay products.

Keywords

plasma instabilitiesplasma nonlinear phenomenaplasma waves
Type
Research Article
Information
Journal of Plasma Physics , Volume 82 , Issue 6 , December 2016 , 905820606
Copyright
© Cambridge University Press 2016 

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

Alber, I. E. 1978 Effects of randomness on stability of two-dimensional surface wavetrains. Proc. R. Soc. Lond. 363, 525–546.Google Scholar
Bhakta, J. C. & Majumder, D. 1983 Effect of finite spectral width on the modulational instability of Langmuir-waves. J. Plasma Phys. 30, 203–209.CrossRefGoogle Scholar
Breizman, B. N. & Malkin, V. M. 1980 Dynamics of the modulational instability of a broad spectrum of Langmuir waves. Sov. Phys. JETP 52, 435–441; Russian original Zh. Eks. Teor. Fiz., 79, 857–869 (1980).Google Scholar
Briand, C. 2015 Langmuir waves across the heliosphere. J. Plasma Phys. 81, 325810204.CrossRefGoogle Scholar
Camac, M., Kantrowitz, A. R., Litvak, M. M., Patrick, R. M. & Petschek, H. E. 1962 Shock waves in collision-free plasmas. Nuclear Fusion, Suppl. 2, 423–445.Google Scholar
Chen, H. H. & Liu, C. S. 1978 Nonlinear wave and soliton propagation in media with arbitrary inhomogeneities. Phys. Fluids 21, 377–380.Google Scholar
Daldorff, L. K. S., Pécseli, H. L., Trulsen, J. K., Ulriksen, M. I., Eliasson, B. & Stenflo, L. 2011 Nonlinear beam generated plasma waves as a source for enhanced plasma and ion acoustic lines. Phys. Plasmas 18, 052107.Google Scholar
Dysthe, K. B. & Pécseli, H. L. 1977 Non-linear Langmuir wave modulation in collisionless plasmas. Plasma Phys. 19, 931–943.Google Scholar
Dysthe, K. B., Pécseli, H. L. & Trulsen, J. 1983 Stochastic generation of continuous wave spectra. Phys. Rev. Lett. 50, 353–356.CrossRefGoogle Scholar
Edney, S. D. & Robinson, P. A. 2001 Analytic treatment of weak-turbulence Langmuir wave electrostatic decay. Phys. Plasmas 8, 428–440.CrossRefGoogle Scholar
Fejer, J. A. 1979 Ionospheric modification and parametric instabilities. Rev. Geophys. 17, 135–153.CrossRefGoogle Scholar
Forme, F. 1999 Parametric decay of beam-driven Langmuir wave and enhanced ion-acoustic fluctuations in the ionosphere: a weak turbulence approach. Ann. Geophys. 17, 1172–1181.Google Scholar
Gary, S. P. & Tokar, R. L. 1985 The electron-acoustic mode. Phys. Fluids 28, 2439–2441.Google Scholar
Guio, P. & Forme, F. 2006 Zakharov simulations of Langmuir turbulence: effects on the ion-acoustic waves in incoherent scattering. Phys. Plasmas 13, 122902.Google Scholar
Hanssen, A., Mjølhus, E., Dubois, D. F. & Rose, H. A. 1992 Numerical test of the weak turbulence approximation to ionospheric Langmuir turbulence. J. Geophys. Res. 97, 12073–12091.CrossRefGoogle Scholar
Hanssen, A., Pécseli, H. L., Stenflo, L. & Trulsen, J. 1994 Nonlinear wave interactions in two-electron-temperature plasmas. J. Plasma Phys. 51, 423–432.Google Scholar
Hasegawa, A. 1975 Dynamics of an ensemble of plane waves in nonlinear dispersive media. Phys. Fluids 18, 77–79.CrossRefGoogle Scholar
Ichikawa, Y. H., Imamura, T. & Taniuti, T. 1972 Nonlinear wave modulation in collisionless plasmas. J. Phys. Soc. Japan. 33, 189–197.CrossRefGoogle Scholar
Isham, B., Rietveld, M. T., Guio, P., Forme, F. R. E., Grydeland, T. & Mjølhus, E. 2012 Cavitating Langmuir turbulence in the terrestrial aurora. Phys. Rev. Lett. 108, 105003.Google Scholar
Kadomtsev, B. B. 1965 Plasma Turbulence. Academic.Google Scholar
Khirseli, E. M. & Tsintsadze, N. L. 1980 Nonlinear waves in a two-temperature electron plasma. Fizika Plazmy 6, 1081–1084.Google Scholar
Kono, M. & Škorić, M. M. 2010 Nonlinear Physics of Plasmas, Springer Series on Atomic, Optical, and Plasma Physics, vol. 62. Springer.Google Scholar
Kontar, E. P., Lapshin, V. I. & Mel’nik, V. N. 1998 Numerical and analytical study of the propagation of a monoenergetic electron beam in a plasma. Plasma Phys. Rep. 24, 772–776.Google Scholar
Kontar, E. P. & Pécseli, H. L. 2002 Nonlinear development of electron-beam-driven weak turbulence in an inhomogeneous plasma. Phys. Rev. E 65, 066408.Google Scholar
Kontar, E. P., Ratcliffe, H. & Bian, N. H. 2012 Wave-particle interactions in non-uniform plasma and the interpretation of hard X-ray spectra in solar flares. Astron. Astrophys. 539, A43.Google Scholar
Krafft, C., Volokitin, A. S. & Krasnoselskikh, V. V. 2015 Langmuir wave decay in inhomogeneous solar wind plasmas: simulation results. Astrophys. J. 809, 176.CrossRefGoogle Scholar
Kuznetsov, E. A. 1974 The collapse of electromagnetic waves in a plasma. Zh. Eks. Teor. Fiz. 66, 2037–2047; English translation Sov. Phys. JETP 39, 1003–1007 (1974).Google Scholar
LaBelle, J., Cairns, I. H. & Kletzing, C. A. 2010 Electric field statistics and modulation characteristics of bursty Langmuir waves observed in the cusp. J. Geophys. Res. 115, A10317.Google Scholar
Leaf, B. 1968 Weyl transformation and the classical limit of quantum mechanics. J. Math. Phys. 9, 65–72.CrossRefGoogle Scholar
Malkin, V. 1982 Nonlinear stage of modulational instability. Soviet J. Plasma Phys. 8, 202–206.Google Scholar
Mima, K. & Nishikawa, K. 1984 Parametric Instabilities and wave dissipation on plasma. In Basic Plasma Physics II (ed. Galeev, A. A. & Sudan, R. N.), chap. 6.5, pp. 451–517. North-Holland.Google Scholar
Nishikawa, K. 1968 Parametric excitation of coupled waves. II. Parametric plasmon-photon interaction. J. Phys. Soc. Japan 24, 1152–1158.Google Scholar
Pécseli, H. L. 2014 Modulational stability of electron plasma wave spectra. J. Plasma Phys. 80, 745–769.Google Scholar
Pécseli, H. L. & Trulsen, J. 1990 Wave-number-in-cell simulation of weak Langmuir turbulence. Phys. Rev. Lett. 64, 285–288.Google Scholar
Pécseli, H. L. & Trulsen, J. 1992 A wavenumber-in-cell simulation of weak Langmuir turbulence. Phys. Scr. 46.Google Scholar
Pereira, N. R. & Stenflo, L. 1977 Nonlinear Schrödinger equation including growth and damping. Phys. Fluids 20, 1733–1734.Google Scholar
Perkins, F. W., Oberman, C. & Valeo, E. J. 1974 Parametric instabilities and ionospheric modification. J. Geophys. Res. 79, 1478–1496.Google Scholar
Rasmussen, J. J. & Rypdal, K. 1986 Blow-up in nonlinear Schroedinger equations-I, A general review. Phys. Scr. 33, 481–497.Google Scholar
Sagdeev, R. Z. & Galeev, A. A. 1969 Nonlinear Plasma Theory. W. A. Benjamin Inc.Google Scholar
Shatashvili, N. L. & Tsintsadze, N. L. 1982 Nonlinear Landau damping phenomenon in a strongly turbulent plasma. Phys. Scr. T2B, 511–516.Google Scholar
Shukla, P. K., Stenflo, L. & Faria, R. T. 1998 Modulational instability of random phase plasmons in collisional plasmas. Phys. Plasmas 5, 2846–2848.Google Scholar
Skjæraasen, O., Krane, B., Pécseli, H. L., Stenflo, L. & Trulsen, J. 1996 Nonlinear wave interactions in two-electron-temperature plasmas. Phys. Scr. T63, 34–40.Google Scholar
Tanaka, T. 1977a Three-dimensional parametric decay of a Langmuir wave into another Langmuir and a longitudinal low frequency waves. J. Phys. Soc. Japan. 42, 644–651.CrossRefGoogle Scholar
Tanaka, T. 1977b Three-dimensional parametric decay of a Langmuir wave into another Langmuir and a longitudinal low frequency waves. II. J. Phys. Soc. Japan. 42, 1355–1361.CrossRefGoogle Scholar
Tappert, F. D. & Cole, W. J. 1971 Numerical particle-in-cell simulation of self-consistent wave kinetic equation. SIAM Rev. 13, 282–283.Google Scholar
Thornhill, S. G. & ter Haar, D. 1978 Langmuir turbulence and modulational instability. Phys. Rep. 43, 43–99.Google Scholar
Vedenov, A. A., Gordeev, A. V. & Rudakov, L. I. 1967 Oscillations and instability of a weakly turbulent plasma. Plasma Phys. 9, 719–735.Google Scholar
Vedenov, A. A. & Rudakov, L. I. 1965 Interaction of waves in continuous media. Sov. Phys. Dokl. 9, 1073–1075; Russian original Doklady Akademii Nauk SSSR, 159, 767–770 (1964).Google Scholar
Watanabe, K. & Taniuti, T. 1977 Electron-acoustic mode in a plasma of two-temperature electrons. J. Phys. Soc. Japan 43, 1819–1820.Google Scholar
Weiland, J. & Wilhelmsson, H. 1977 Coherent Non-linear Interaction of Waves in Plasmas, International Series in Natural Philosophy, vol. 88. Pergamon.Google Scholar
Wigner, E. 1932 On the quantum correction for thermodynamic equilibrium. Phys. Rev. 40, 749–759.CrossRefGoogle Scholar
Zakharov, V. E. 1965a A solvable model of weak turbulence. J. Appl. Mech. Tech. Phys. 6, 10–16; Russian original Zh. Prikl. Mek. Tekn. Fiz. 1, 14–20 (1965).Google Scholar
Zakharov, V. E. 1965b Weak turbulence in media with a decay spectrum. Zh. Prikl. Mekh. Tekh. Fiz. 4, 35–39.Google Scholar
Zakharov, V. E. 1972 Collapse of Langmuir waves. Zh. Eks. Teor. Fiz. 62, 1745–1759; see also (1972) Sov. Phys. JETP 35, 908–914.Google Scholar