Abstract
The basic equations describing the nonlinear electron-acoustic waves in a plasma composed of a cold electron fluid, hot electrons obeying a trapped/vortex-like distribution, and stationary ions, in the long-wave limit, are re-examined through the use of the modified PLK method. Introducing the concept of strained coordinates and expanding the field variables into a power series of the smallness parameter ε, a set of evolution equations is obtained for various order terms in the perturbation expansion. The evolution equation for the lowest order term in the perturbation expansion is characterized by the conventional modified Korteweg–deVries (mKdV) equation, whereas the evolution equations for the higher order terms in the expansion are described by the degenerate(linearized) mKdV equation. By studying the localized traveling wave solution to the evolution equations, the strained coordinate for this order is determined so as to remove possible secularities that might occur in the solution. It is observed that the coefficient of the strained coordinate for this order corresponds to the correction term in the wave speed. The numerical results reveal that the contribution of second order term to the wave amplitude is about 20 %, which cannot be ignored.
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References
Fried B.D., Gould R.W.: Longitudinal ion oscillation in a hot plasma. Phys. Fluids 4, 139–147 (1961)
Watanabe K., Taniuti T.: Electron-acoustic mode in plasma of two-temperature electrons. J. Phys. Soc. Jpn. 43, 1819–1820 (1977)
Dubouloz N., Pottelette N., Malignre M., Truemann R.A.: Generation of broadband electrostatic noise by electron-acoustic solitons. Geophys. Res. Lett. 18, 155–158 (1972)
Schamel H.: Stationary solitary, snoidal and sinusoidal ion-acoustic waves. Plasma Phys. 14, 905–924 (1972)
Schamel H.: A modified Korteweg–deVries equation for ion-acoustic waves due to resonant electrons. J. Plasma Phys. 9, 377–387 (1973)
Abbasi H., Tsintsadze N.L., Tskhakaya D.D.: Influence of particle trapping on the propagation of ion-cyclotron waves. Phys. Plasma 6, 2373–2379 (1999)
Washimi H., Taniuti T.: Propagation of ion-acoustic solitary waves of small amplitude. Phys. Rev. Lett. 17, 996–998 (1966)
Mamun, A.A., Shukla, P.K.: Electron-acoustic solitary waves via vortex electron distribution. J. Geophys. Res. 107, A7. doi:10.1029/2001JA009131 (2002)
Taniuti T.: Reductive perturbation method and far fields of wave equations. Suppl. Progress Theor. Phys. 55, 1–35 (1974)
Sugimoto N., Kakutani T.: Note on the higher order terms in reductive perturbation theory. J. Phys. Soc. Jpn. 43, 1469–1470 (1977)
Kodama Y., Taniuti T.: Higher order perturbation in the reductive perturbation method I: weakly dispersive systems. J. Phys. Soc. Jpn. 45, 298–310 (1978)
Malfliet M., Wieers E.: Theory of ion-acoustic waves re-visited. J. Plasma Phys. 56, 441–450 (1996)
Demiray H.: A modified reductive perturbation method as applied to nonlinear ion-acoustic waves. J. Phys. Soc. Jpn. 68, 1833–1837 (1999)
Demiray H.: Contribution of higher order terms in nonlinear ion-acoustic waves: strongly dispersive case. J. Phys. Soc. Jpn. 71, 1921–1930 (2002)
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Demiray, H. Contribution of higher order terms in electron-acoustic solitary waves with vortex electron distribution. Z. Angew. Math. Phys. 65, 1223–1231 (2014). https://doi.org/10.1007/s00033-013-0394-1
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DOI: https://doi.org/10.1007/s00033-013-0394-1