Hostname: page-component-7c8c6479df-fqc5m Total loading time: 0 Render date: 2024-03-27T10:12:41.868Z Has data issue: false hasContentIssue false

Dynamics of modulationally unstable ion-acoustic wavepackets in plasmas with negative ions

Published online by Cambridge University Press:  01 October 2008

MICHAEL S. RUDERMAN
Affiliation:
Department of Applied Mathematics, University of Sheffield, Hicks Building, Hounsfield Road, Sheffield S3 7RH, UK (m.s.ruderman@sheffield.ac.uk)
TATYANA TALIPOVA
Affiliation:
Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia
EFIM PELINOVSKY
Affiliation:
Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics, Nizhny Novgorod, Russia

Abstract

In this paper we study the propagation of nonlinear ion-acoustic waves in plasmas with negative ions. The Gardner equation governing these waves in plasmas with the negative ion concentration close to critical is derived. The weakly nonlinear theory of modulational instability based on the use of the nonlinear Schrödinger equation is discussed. The investigation of the nonlinear dynamics of modulationally unstable quasi-harmonic wavepackets is carried out by the numerical solution of the Gardner equation. The results are compared with the predictions of the weakly nonlinear theory.

Type
Papers
Copyright
Copyright © Cambridge University Press 2008

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

Benjamin, T. B. and Feir, I. F. 1967 The disintegration of wave trains on deep water. J. Fluid Mech. 27, 417430.CrossRefGoogle Scholar
Berezin, Y. A. 1987 Modelling nonlinear wave processes. Utrecht: VNU Science Press.Google Scholar
Chan, V. S. and Seshadri, S. R. 1975 Modulational stability of the ion plasma mode. Phys. Fluids 18, 12941298.CrossRefGoogle Scholar
Das, G. C. 1977 Ionic thermal effects on ion-acoustic-waves in plasmas with negative-ions. Plasma Phys. Control. Fusion 19, 363368.Google Scholar
Das, G. C. 1979 Ion-acoustic solitons and shock-waves in multicomponent plasmas. Plasma Phys. Control. Fusion 21, 257265.Google Scholar
Das, G. C. and Tagare, S. G. 1975 Propagation of ion-acoustic-waves in a multicomponent plasma. Plasma Phys. Control. Fusion 17, 10251032.Google Scholar
Engelbrecht, J. K., Fridman, V. E. and Pelinovskii, E. N. 1988 Nonlinear Evolution Equations. London: Longman Scientific and Technical Group.Google Scholar
Grimshaw, R., Pelinovsky, D., Pelinovsky, E. and Talipova, T. 2001 Wave group dynamics in weakly nonlinear long-wave models. Physica D 159, 3557.Google Scholar
Grimshaw, R., Pelinovsky, E., Talipova, T., Ruderman, M. S. and Erdélyi, R. 2005 Short-lived large-amplitude pulses in the nonlinear long-wave model described by the modified Korteweg–de Vries equation. Studi. Appl. Math. 114, 189210.CrossRefGoogle Scholar
Ikezi, H. 1973 Experiment on ion-acoustic solitary waves. Phys. Fluids 16, 16681675.Google Scholar
Kalita, B. C. and Das, G. C. 2002 Modified Korteweg–de Vries (MKdV) and Korteweg–de Vries (KdV) solitons in a warm plasma with negative ions and electrons' drift motion. J. Phys. Soc. Japan 71, 29182924.Google Scholar
Kakutani, T., Ono, H., Taniuti, T. and Wei, C. C. 1968 Reductive perturbation method in nonlinear wave propagation. II. Application to hydromagnetic waves in cold plasma. J. Phys. Soc. Japan 24, 11591166.Google Scholar
Kalita, B. C. and Barman, S. N. 1995 Solitons in a warm unmagnetized plasma with electron inertia and negative ions. J. Phys. Soc. Japan 64, 784790.CrossRefGoogle Scholar
Kalita, B. C. and Devi, N. 1993 Solitary wave in a warm plasma with negative ions and drifting effect of electrons. Phys. Fluids B 5, 440445.Google Scholar
Kalita, B. C. and Kalita, M. K. 1990 Modified Korteweg–de Vries solitons in a warm plasma with negative ions. Phys. Fluids B 2, 674676.CrossRefGoogle Scholar
Kourakis, I. and Shukla, P. K. 2003a Ion-acoustic waves in a two-electron-temperature plasma: oblique modulation and envelope excitations. J Phys. A: Math. Gen. 36, 1190111913.Google Scholar
Kourakis, I. and Shukla, P. K. 2003b Modulational instability and localized excitation of dust-ion acoustic waves. Phys. Plasmas 10, 34593470.CrossRefGoogle Scholar
Kourakis, I. and Shukla, P. K. 2005 Exact theory for localized envelope modulated electrostatic wavepackets in space and dusty plasmas. Nonlin. Processes Geophys. 12, 407423.CrossRefGoogle Scholar
Lonngren, K. E. 1983 Soliton experiments in plasma physics. Plasma Phys. Control. Fusion 25, 943982.Google Scholar
Ludwig, G. O., Ferreira, J. L. and Nakamura, Y. 1984 Observation of ion-acoustic rarefaction solitons in a multicomponent plasma with negative-ions. Phys. Rev. Lett. 52, 275278.Google Scholar
Mishra, M. K., Chhabra, R. S. and Sharma, S. R. 1994 Stability of oblique modulation of ion-acoustic waves in a multicomponent plasma. Phys. Plasmas 1, 7075.CrossRefGoogle Scholar
Nakamura, Y. 1982 Experiments on ion-acoustic solitons in plasmas. IEEE Trans. Plasma Sci. 10, 180195.Google Scholar
Nakamura, Y., Ferreira, J. L. and Ludwig, G. O. 1985 Experiments on ion-acoustic rarefactive solitons in a multi-component plasma with negative ions. J. Plasma Phys. 33, 237248.CrossRefGoogle Scholar
Nakamura, Y. and Tsukabayashi, I. 1985 Modified Korteweg–de Vries ion-acoustic solitons in a plasma. J. Plasma Phys. 34, 401415.Google Scholar
Newell, A. C. 1985 Solitons in Mathematics and Physics. Philadelphia, PA: SIAM.CrossRefGoogle Scholar
Parkes, E. J. 1987 The modulation of weakly non-linear dispersive waves near the marginal state of stability. J. Phys. A: Math. Gen. 20, 20252036.Google Scholar
Saito, M., Watanabe, S. and Tanaca, H. 1984 Modulational instability of ion wave in plasma with negative ion. J. Phys. Soc. Japan 53, 23042310.CrossRefGoogle Scholar
Su, C. H. and Gardner, C. S. 1969 Korteweg–de Vries equation and generalizations. 3. Derivation of Korteweg–de Vries equation and Burgers equation. J. Math. Phys. 10, 536539.Google Scholar
Tagare, S. G. 1973 Effect of ion temperature on propagation of ion-acoustic solitary waves of small amplitude in collisionless plasma. Plasma Phys. Control. Fusion 15, 12471252.Google Scholar
Tagare, S. G. 1986 Effect of ion temperature on ion-acoustic solitons in a two-ion warm plasma with adiabatic positive and negative ions and isothermal electrons. J. Plasma Phys. 36, 301312.Google Scholar
Taniuti, T. and Wei, C. C. 1968 Reductive perturbation method in nonlinear wave propagation. I. J. Phys. Soc. Japan 24, 941946.Google Scholar
Tappert, F. 1972 Improved Korteweg–de Vries equation for ion-acoustic waves. Phys. Fluids 15, 24462447.CrossRefGoogle Scholar
Tran, M. Q. 1979 Ion-acoustic solitons in a plasma—review of their experimental properties and related theories. Phys. Scripta 20, 317327.CrossRefGoogle Scholar
Tsuji, H. and Oikawa, M. 2004 Two-dimensional interaction of solitary waves in a modified Kadomtsev–Petviashvili equation. J. Phys. Soc. Japan 73, 30343043.Google Scholar
Verheest, F. 1988 Ion-acoustic solitons in multi-component plasmas including negative-ions at critical densities. J. Plasma Phys. 39, 7179.CrossRefGoogle Scholar
Washimi, H. and Taniuti, T. 1966 Propagation of ion-acoustic solitary waves of small amplitude. Phys. Rev. Lett. 17, 996998.Google Scholar
Watanabe, S. 1975 Ion-acoustic solitons excited by a single grid. J. Plasma Phys. 14, 353364.Google Scholar
Watanabe, S. 1978 Interpretation of experiments on ion-acoustic soliton. J. Phys. Soc. Japan 44, 611617.CrossRefGoogle Scholar
Watanabe, S. 1984 Ion acoustic soliton in plasma with negative ion. J. Phys. Soc. Japan 53, 950956.CrossRefGoogle Scholar