Hostname: page-component-78c5997874-mlc7c Total loading time: 0 Render date: 2024-11-13T05:29:33.547Z Has data issue: false hasContentIssue false

Stability of electron wave spectra in weakly magnetized plasmas

Published online by Cambridge University Press:  04 December 2017

M. Kono
Affiliation:
Chuo University, Faculty of Policy Studies, Hachioji, Tokyo 192-0393, Japan
H. 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

Abstract

Analytical models for nonlinear electron plasma waves in weakly magnetized plasmas are developed for single as well as multi-mode conditions, with continuous wave spectra being a limiting case. The conditions for wave decay as well as modulational instabilities are analysed. Our results demonstrate that slow or nearly stationary plasma density variations can be found for weakly magnetized plasmas even for weakly nonlinear electron plasma waves without involving cavitation of large amplitude plasma waves. A reduction of the growth rates for decay as well as modulational instabilities are found when the spectral width of the wave spectrum is increased. Some of our results are relevant for the interpretation of the nonlinearly enhanced ion acoustic lines often observed in non-equilibrium ionospheres.

Type
Research Article
Copyright
© Cambridge University Press 2017 

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

Bonnell, J., Kintner, P., Wahlund, J.-E. & Holtet, J. A. 1997 Modulated Langmuir waves: observations from Freja and SCIFER. J. Geophys. Res. 102, 1723317240.Google Scholar
Briand, C. 2015 Langmuir waves across the heliosphere. J. Plasma Phys. 81, 325810204.CrossRefGoogle Scholar
Brodin, G. & Stenflo, L. 2016 A new decay channel for upper-hybrid waves. Phys. Scr. 91, 104005.Google Scholar
Buchert, S. C., van Eyken, A. P., Ogawa, T. & Watanabe, S. 1999 Naturally enhanced ion-acoustic lines seen with the EISCAT Svalbard radar. Adv. Space Res. 23, 16991704.CrossRefGoogle Scholar
Burinskaya, T. M., Rauch, J. L. & Mogilevskii, M. M. 2004 Spectra of Langmuir waves in a magnetized plasma with low-frequency turbulence. Plasma Phys. Rep. 30, 756760.Google Scholar
Camac, M., Kantrowitz, A. R., Litvak, M. M., Patrick, R. M. & Petschek, H. E. 1962 Shock waves in collision-free plasmas. Nucl. Fusion Suppl. 2, 423445.Google Scholar
Dysthe, K. B., Mjølhus, E., Pécseli, H. L. & Stenflo, L. 1978 Langmuir solitons in magnetized plasmas. Plasma Phys. 20, 10871099.Google Scholar
Dysthe, K. B., Mjølhus, E., Pécseli, H. L. & Stenflo, L. 1984 Nonlinear electrostatic wave equations for magnetized plasmas. Plasma Phys. Control. Fusion 26, 443447.Google Scholar
Dysthe, K. B., Mjølhus, E., Pécseli, H. L. & Stenflo, L. 1985 Nonlinear electrostatic wave equations for magnetized plasmas – II. Plasma Phys. Control. Fusion 27, 501508.Google Scholar
Dysthe, K. B. & Pécseli, H. L. 1977 Non-linear Langmuir wave modulation in collisionless plasmas. Plasma Phys. 19, 931943.Google Scholar
Dysthe, K. B. & Pécseli, H. L. 1978 Non-linear Langmuir wave modulation in weakly magnetized plasmas. Plasma Phys. 20, 971989.Google Scholar
Dysthe, K. B., Pécseli, H. L. & Trulsen, J. 1983 Stochastic generation of continuous wave spectra. Phys. Rev. Lett. 50, 353356.CrossRefGoogle Scholar
Faria, R. T. & Shukla, P. K. 1999 Generalized Kaufman–Stenflo equations for collisional magnetoplasmas. Phys. Scr. T82, 79.Google Scholar
Freund, H. P. & Papadopoulos, K. 1980 Oscillating two-stream and parametric decay instabilities in a weakly magnetized plasma. Phys. Fluids 23, 139146.CrossRefGoogle Scholar
Guio, P. & Forme, F. 2006 Zakharov simulations of Langmuir turbulence: effects on the ion-acoustic waves in incoherent scattering. Phys. Plasmas 13, 122902.CrossRefGoogle Scholar
Hsu, P. & Kuehl, H. 1982 Focusing of lower hybrid waves by electromagnetic effects. Nucl. Fusion 22, 16791683.Google 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 Press.Google Scholar
Kadomtsev, B. B. & Karpman, V. I. 1971 Nonlinear waves. Sov. Phys. Uspekhi. 14, 4060.Google Scholar
Kasymov, Z. Z., Näslund, E., Starodub, A. N. & Stenflo, L. 1985 Upper hybrid turbulence in a plasma with magnetized electrons. Phys. Scr. 31, 201204.Google Scholar
Kaufman, A. N. & Stenflo, L. 1975 Upper-hybrid solitons. Phys. Scr. 11, 269270.Google Scholar
Kono, M. & Pécseli, H. L. 2016 Parametric decay of wide band Langmuir wave-spectra. J. Plasma Phys. 82, 905820606.Google Scholar
Kono, M. & Pécseli, H. L.2017 Stability of electron wave spectra in weakly magnetized plasmas: local spectra and correlations. 1–12, Supplementary material. Unpublished. doi:10.5281/zenodo.1035851.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
Kono, M., Škorić, M. M. & ter Haar, D. 1980 Ponderomotive force in a dispersive medium in a variable electromagnetic field. Phys. Rev. Lett. 45, 16291632.Google Scholar
Kontar, E. P. 2001 Propagation of a fast electron cloud in a solar-like plasma of decreasing density. Plasma Phys. Control. Fusion 43, 589601.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
Krafft, C., Volokitin, A. S., Krasnoselskikh, V. V. & de Wit, T. D. 2014 Waveforms of Langmuir turbulence in inhomogeneous solar wind plasmas. J. Geophys. Res. 119, 93699382.Google Scholar
Krasnosel’skikh, V. V. & Sotnikov, V. I. 1977 Plasma-wave collapse in a magnetized plasma. Sov. J. Plasma Phys. 3, 491495; Russian original Fiz. Plazmy 3, 872–879, 1977.Google Scholar
Kuo, S. P. 2015a Ionospheric modifications in high frequency heating experiments. Phys. Plasmas 22, 012901.Google Scholar
Kuo, S. P. 2015b Nonlinear upper hybrid waves and the induced density irregularities. Phys. Plasmas 22, 082904.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
Leung, P., Tran, M. Q. & Wong, A. Y. 1982 Plasma wave collapse generated by the interaction of two oppositely propagating electron beams with a plasma. Plasma Phys. 24, 567575.Google Scholar
Liu, C. & Tripathi, V. 1986 Parametric instabilities in a magnetized plasma. Phys. Rep. 130 (3), 143216.Google Scholar
Marcuvitz, N. 1980 Quasiparticle view of wave-propagation. Proc. IEEE 68, 13801395.Google Scholar
McFarland, M. D. & Wong, A. Y. 1997 Spectral content of strong Langmuir turbulence in the beam plasma interaction. Phys. Plasmas 4, 945955.Google Scholar
Melrose, D. B. 1987 The Zakharov equations: a derivation using kinetic theory. J. Plasma Phys. 37, 241246.Google Scholar
Michelsen, P., Pécseli, H. L., Rasmussen, J. J. & Sato, N. 1977 Stationary density variation produced by a standing plasma wave. Phys. Fluids 20, 10941096.Google Scholar
Nicholson, D. R. 1983 Introduction to Plasma Theory. Wiley.Google Scholar
Ovenden, C. R., Statham, G. & Haar, D. T. 1983 Strong turbulence of a magnetized plasma. I. The generalized Zakharov equations. Plasma Phys. 25, 665679.Google Scholar
Pavlenko, V. I. & Petviashvili, V. I. 1977 Stability and kinetic effects of a standing Langmuir wave. J. Expl Theor. Phys. Lett. 26, 200202; Russian original, Pis’ma Zh. Eksp. Teor. Fiz. 26, 313–315, 1977.Google Scholar
Pécseli, H., Rasmussen, J. J. & Thomsen, K. 1983 Upper hybrid wave collapse in weakly magnetized plasmas. Phys. Lett. A 99, 175179.Google Scholar
Pécseli, H. L. 1985 Solitons and weakly nonlinear waves in plasmas. IEEE Trans. Plasma Sci. PS‐13, 5386.Google Scholar
Pécseli, H. L. 2014 Modulational stability of electron plasma wave spectra. J. Plasma Phys. 80, 745769.Google Scholar
Pécseli, H. L. 2016 Low Frequency Waves and Turbulence in Magnetized Laboratory Plasmas and in the Ionosphere. IOP Publishing.Google Scholar
Pécseli, H. L., Iranpour, K., Holter, Ø., Lybekk, B., Holtet, J., Trulsen, J., Eriksson, A. & Holback, B. 1996 Lower hybrid wave cavities detected by the FREJA satellite. J. Geophys. Res. 101, 52995316.Google Scholar
Pécseli, H. L. & Rasmussen, J. J. 1980 Nonlinear electron plasma waves in strongly magnetized plasmas. Plasma Phys. 22, 421438.Google Scholar
Pécseli, H. L., Rasmussen, J. J., Tagare, S. G. & Thomsen, K. 1986 Weakly nonlinear electron-plasma waves in collisional plasmas. Plasma Phys. Control. Fusion 28, 485507; Erratum: Plasma Phys. Control. Fusion 28, 1209, 1986.Google Scholar
Pécseli, H. L. & Trulsen, J. 1990 Wave-number-in-cell simulation of weak Langmuir turbulence. Phys. Rev. Lett. 64, 285288.Google Scholar
Pécseli, H. L. & Trulsen, J. 1992 A wavenumber-in-cell simulation of weak Langmuir turbulence. Phys. Scr. 46, 159172.Google Scholar
Perkins, F. W. & Flick, J. 1971 Parametric instabilities in inhomogeneous plasmas. Phys. Fluids 14, 20122018.Google Scholar
Petviashvili, V. I. 1975 Three-dimensional solitons of extraordinary and plasma waves. Sov. J. Plasma Phys. 1, 1516; Russian original Fiz. Plazmy 1, 28–31, 1975.Google Scholar
Píša, D., Hospodarsky, G. B., Kurth, W. S., Santolík, O., Souček, J., Gurnett, D. A., Masters, A. & Hill, M. E. 2015 Statistics of Langmuir wave amplitudes observed inside Saturn’s foreshock by the Cassini spacecraft. J. Geophys. Res. 120, 25312542.Google Scholar
Porkolab, M. 1977 Parametric instabilities due to lower-hybrid radio frequency heating of tokamak plasmas. Phys. Fluids 20, 20582075.Google Scholar
Porkolab, M. & Goldman, M. V. 1976 Upper-hybrid solitons and oscillating-two-stream instabilities. Phys. Fluids 19, 872881.Google Scholar
Pozzoli, R. & Ryutov, D. D. 1979 Modulational instability produced by Langmuir turbulence in a magnetic field. Phys. Fluids 22, 17821789.Google Scholar
Rasmussen, J. J. & Rypdal, K. 1986 Blow-up in nonlinear Schroedinger equations-I, a general review. Phys. Scr. 33, 481497.Google Scholar
Rietveld, M. T., Collis, P. N. & St-Maurice, J.-P. 1991 Naturally enhanced ion-acoustic-waves in the auroral ionosphere observed with the EISCAT 933-MHz radar. J. Geophys. Res. 96, 1929119305.Google Scholar
Schuck, P. W., Bonnell, J. W. & Kintner, P. M. 2003 A review of lower hybrid solitary structures. IEEE Trans. Plasma Sci. 31, 11251177.Google Scholar
Sedgemore-Schulthess, F. & St-Maurice, J.-P. 2001 Naturally enhanced ion-acoustic spectra and their interpretation. Surv. Geophys. 22, 5592.Google Scholar
Shatashvili, N. L. & Tsintsadze, N. L. 1982 Nonlinear Landau damping phenomenon in a strongly turbulent plasma. Phys. Scr. T2B, 511516.Google Scholar
Shukla, P. K. 1977 Nonlinear propagation of high-frequency plasma waves in a magnetized plasma. J. Plasma Phys. 18, 249256.Google Scholar
Shukla, P. K., Eliasson, B. & Stenflo, L. 2003 Nonlinearly coupled upper-hybrid and magnetoacoustic waves in collisional magnetoplasmas. Phys. Rev. E 68, 067401.Google Scholar
Shukla, P. K. & Farid, T. 1999 Nonlinear propagation of broadband upper-hybrid waves in collisional magnetoplasmas. Phys. Scr. T82, 6062.CrossRefGoogle Scholar
S̆korić, M. M. & ter Haar, D. 1980 Higher electron non-linearities in the dynamics of Langmuir collapse. Physica B + C 98, 211221.Google Scholar
Tappert, F. D. & Cole, W. J. 1971 Numerical particle-in-cell simulation of self-consistent wave kinetic equation. SIAM Rev. 13, 282283.Google Scholar
Thornhill, S. G. & ter Haar, D. 1978 Langmuir turbulence and modulational instability. Phys. Rep. 43, 4399.Google Scholar
Vedenov, A. A., Gordeev, A. V. & Rudakov, L. I. 1967 Oscillations and instability of a weakly turbulent plasma. Plasma Phys. 9, 719735.Google Scholar
Volokitin, A. & Krafft, C. 2005 Wave decay processes in a weakly magnetized plasma. Phys. Lett. A 336, 193199.Google Scholar
Vyacheslavov, L. N., Burmasov, V. S., Kandaurov, I. V., Kruglyakov, E. P., Meshkov, O. I. & Sanin, A. L. 1995 Spectra of developed Langmuir turbulence in a nonisothermal magnetized plasma. Phys. Plasmas 2, 22242230.Google Scholar
Weatherall, J. C., Goldman, M. V. & Nicholson, D. R. 1981 Parametric instabilities in weakly magnetized plasma. Astrophys. J. 246, 306313.Google Scholar
Wong, A. Y. & Quon, B. H. 1975 Spatial collapse of beam-driven plasma waves. Phys. Rev. Lett. 34, 14991502.CrossRefGoogle Scholar
Zakharov, V. E. 1972 Collapse of Langmuir waves. Sov. Phys. JETP 35, 908914; Russian original Zh. Eksp. Teor. Fiz. 62, 1745–1759, 1972.Google Scholar