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Magnetosonic solitons in space plasmas: dark or bright solitons?

Published online by Cambridge University Press:  01 December 2007

O. A. POKHOTELOV ,
O.G. ONISHCHENKO ,
M. A. BALIKHIN ,
L. STENFLO  and
P. K. SHUKLA
O. A. POKHOTELOV
Affiliation:
Department of Automatic Control and System Engineering, University of Sheffield, JSheffield S13JD, UK ([email protected])
O.G. ONISHCHENKO
Affiliation:
Institute of the Physics of the Earth, Russian Academy of Sciences, Moscow, Russia
M. A. BALIKHIN
Affiliation:
Department of Automatic Control and System Engineering, University of Sheffield, JSheffield S13JD, UK ([email protected])
L. STENFLO
Affiliation:
Department of Physics, Umea University, SE-90187 Umea, Sweden
P. K. SHUKLA
Affiliation:
Department of Physics, Umea University, SE-90187 Umea, Sweden
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Abstract

The nonlinear theory of large-amplitude magnetosonic (MS) waves in highβ space plasmas is revisited. It is shown that solitary waves can exist in the form of ‘bright’ or ‘dark’ solitons in which the magnetic field is increased or decreased relative to the background magnetic field. This depends on the shape of the equilibrium ion distribution function. The basic parameter that controls the nonlinear structure is the wave dispersion, which can be either positive or negative. A general dispersion relation for MS waves propagating perpendicularly to the external magnetic field in a plasma with an arbitrary velocity distribution function is derived.It takes into account general plasma equilibria, such as the Dory–Guest–Harris (DGH) or Kennel–Ashour-Abdalla (KA) loss-cone equilibria, as well as distributions with a power-law velocity dependence that can be modelled by κdistributions. It is shown that in a bi-Maxwellian plasma the dispersion is negative, i.e. the phase velocity decreases with an increase of the wavenumber. This means that the solitary solution in this case has the form of a ‘bright’ soliton with the magnetic field increased. On the contrary, in some non-Maxwellian plasmas, such as those with ring-type ion distributions or DGH plasmas, the solitary solution may have the form of a magnetic hole. The results of similar investigations based on nonlinear Hall–MHD equations are reviewed. The relevance of our theoretical results to existing satellite wave observations is outlined.

Type
Papers
Information
Journal of Plasma Physics , Volume 73 , Issue 6 , December 2007 , pp. 981 - 992
Copyright
Copyright © Cambridge University Press 2007

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References

Ashour-Abdalla, M. and Kennel, C. F. 1978 Nonconvective and convective electron cyclotron harmonic instabilities. J. Geophys. Res. 83, 1531.CrossRefGoogle Scholar
Balikhin, M. A., Dudok de Wit, T., Alleyne, H. St.-C., Woolliscroft, L. J. C., Walker, S. N., Krasnosels'kikh, V., Mier-Jedrzejeowicz, W. A. C. and Baumjohann, W. 1997a Experimental determination of the dispersion waves observed upstream of the quasi-perpendicular shock. Geophys. Res. Lett. 24, 787.CrossRefGoogle Scholar
Balikhin, M. A., Woolliscroft, L. J. C., Alleyne, H. St.-C., Dunlop, M. and Gedalin, M. A. 1997b Determination of the dispersion of low frequency waves downstream of the quasi-perpendicular collisionless shock. Ann. Geophys. 15, 143.CrossRefGoogle Scholar
Baumgärtel, K. 1999 Soliton approach to magnetic holes. J. Geophys. Res. 104, 28 295.CrossRefGoogle Scholar
Baumgärtel, K., Sauer, K. and Dubinin, E. 2005 Kinetic slow mode-type solitons. Nonlinear Proc. Geophys. 12, 291.CrossRefGoogle Scholar
Braginskii, S. I. 1965 Transport processes in a plasma. Reviews of Plasma Physics, Vol. 1 (ed Leontovich, M. A.). New York: Consultants Bureau, p. 205.Google Scholar
Gary, S. P. 1991 Electromagnetic ion/ion instabilities and their consequences in space plasmas: a review. Space Sci. Rev. 56, 373.CrossRefGoogle Scholar
Gosling, J. T., Asbridge, J. R., Bame, S. J., Paschmann, G. and Scopke, N. 1978 Observations of two distinct populations of bow shock ions in the upstream solar wind. Geophys. Res. Lett. 5, 957.CrossRefGoogle Scholar
Kaufman, A. N. and Stenflo, L. 1975 Upper-hybrid solitons. Phys. Scripta 11, 269.CrossRefGoogle Scholar
Kennel, C. F. and Sagdeev, R. Z. 1967 Collisionless shock waves in high beta plasmas, 2. J. Geophys. Res. 72, 3327.CrossRefGoogle Scholar
Krauss-Varban, K., Omidi, N. and Quest, K. B. 1994 Mode properties of low-frequency waves: kinetic theory versus Hall–MHD. J. Geophys. Res. 99, 5987.CrossRefGoogle Scholar
Leubner, M. P. and Schupfer, N. 2000 Mirror instability thresholds in suprathermal space plasmas. J. Geophys. Res. 105, 27 387.CrossRefGoogle Scholar
Leubner, M. P. and Schupfer, N. 2001 A general kinetic mirror instability criterion for space applications. J. Geophys. Res. 106, 12 993.CrossRefGoogle Scholar
Lucek, E. A., Constantinescu, D., Goldstein, M. L., Pickett, J., Pincon, J. L., Sahraoui, F., Treumann, R. A. and Walker, S. N. 2005 The magnetosheath. Space Sci. Rev. 118, 95.CrossRefGoogle Scholar
Ma, C.-Y. and Summers, D. 1998 Formation of power-law energy spectra in space plasmas by stochastic acceleration due to whistler-mode waves. Geophys. Res. Lett. 25, 4099.CrossRefGoogle Scholar
Macmahon, A. B. 1968 Discussion of paper by Kennel C. F. and Sagdeev R. Z. ‘Collisionless shock waves in high beta plasmas, 2’. J. Geophys. Res. 73, 7538.CrossRefGoogle Scholar
Mikhailovskii, A. B. and Smolyakov, A. I. 1985 Theory of low-frequency magnetosonic solitons. Sov. Phys.–JETP 61, 109.Google Scholar
Narita, Y., Glassmeier, K.-H., Fornaçon, K.-H., Richter, I., Schäfer, S., Motschmann, U., Dandouras, I., Rème, H. and Georgescu, E. 2006 Low-frequency wave characteristics in the upstream and downstream regime of the terrestrial bow shock. J. Geophys. Res. 111, A01203, doi:10.1029/2005JA011231.CrossRefGoogle Scholar
Perraut, S., Roux, A., Robert, P., Gendrin, R., Sauvaud, J. A., Bosqued, J. M., Kremser, G. and Korth, A. 1982 A systematic study of ULF waves above FH+ from GEOS 1 and 2 measurements and their relationship with proton ring distributions. J. Geophys. Res. 87, 6219.CrossRefGoogle Scholar
Petviashvili, V. I. and Pokhotelov, O. A. 1992 Solitary Waves in Plasmas and in the Atmosphere. London: Gordon and Breach.Google Scholar
Pokhotelov, O. A., Balikhin, M. A., Sagdeev, R. Z. and Treumann, R. A. 2005a Comment on ‘Theory and observations of slow-mode solitons in space plasmas’. Phys. Rev. Lett. 95, 129501.CrossRefGoogle ScholarPubMed
Pokhotelov, O. A., Balikhin, M. A., Sagdeev, R. Z. and Treumann, R. A. 2005b Halo and mirror instabilities in the presence of finite Larmor radius effects. J. Geophys. Res. 110, A10206, doi:10.1029/2004JA010933.CrossRefGoogle Scholar
Pokhotelov, O. A., Pilipenko, V. A. and Amata, E. 1985 Drift anisotropy instability of a finite β magnetospheric plasma. Planet. Space Sci. 33, 1229.CrossRefGoogle Scholar
Pokhotelov, O. A., Sagdeev, R. Z., Balikhin, M. A. and Treumann, R. A. 2004 Mirror instability at finite ion-Larmor radius wavelengths. J. Geophys. Res. 109, A09213, doi:10.1029/2004JA010568.CrossRefGoogle Scholar
Pokhotelov, O. A., Treumann, R. A., Sagdeev, R. Z., Balikhin, M. A., Onishchenko, O. G., Pavlenko, V. P. and Sandberg, I. 2002 Linear theory of the mirror instability in non-Maxwellian space plasmas. J. Geophys. Res. 107, 1312, doi:10.1029/2001JA009125.CrossRefGoogle Scholar
Sharma, R. P. and Shukla, P. K. 1983 Nonlinear effects at the upper-hybrid layer. Phys. Fluids 26, 87.CrossRefGoogle Scholar
Whitham, J. B. 1974 Linear and Nonlinear Waves. New York: Wiley.Google Scholar
Yu, M. Y. and Shukla, P. K. 1977 On the formation of upper-hybrid solitons. Plasma Phys. 19, 889.CrossRefGoogle Scholar