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Modulation instability of obliquely propagating ion acoustic waves in a collisionless magnetized plasma consisting of nonthermal and isothermal electrons

  • Sandip Dalui
  • Anup BandyopadhyayEmail author
Original Article
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Abstract

A nonlinear Schrödinger equation is derived to investigate the amplitude modulation of ion acoustic waves propagating obliquely to the direction of the uniform static magnetic field in a collisionless plasma consisting of warm adiabatic ions and two different species of electrons at different temperatures. We have investigated the relation between two nonlinear Schrödinger equations—one describes the amplitude modulation of ion acoustic waves propagating obliquely to the direction of the magnetic field and other describes the amplitude modulation of ion acoustic waves propagating along the magnetic field. The instability conditions of the modulated wave have been investigated with respect to different parameters. We have seen that the increase in the strength of the magnetic field tends to destabilize the modulated wave when \(\omega _{c}\) lies within the interval \(\omega _{c1} < \omega _{c} < \omega _{c2}\) whereas increase in the strength of the magnetic field tends to stabilize the modulated wave when \(\omega _{c}\) is restricted by the inequalities \(0 < \omega _{c} < \omega _{c1}\) or \(\omega _{c2} < \omega _{c} < 1\), where \(\omega _{c1}\) and \(\omega _{c2}\) are two critical values of the normalized ion cyclotron frequency \(\omega _{c}\). We have investigated the dependence of different parameters on \(\omega _{c1}\) and \(\omega _{c2}\). Again, the maximum growth rate of instability increases with increasing \(\cos \theta \) and it also increases with increasing \(\beta _{e}\) upto a critical value of the wave number, where \(\beta _{e}\) is the parameter associated with the nonthermal distribution of hotter electron species and \(\theta \) is the angle of propagation of the ion acoustic wave with the magnetic field.

Keywords

Electron-ion plasma Two temperature electrons Cairns distribution Nonlinear Schrödinger equation Modulation instability 

Notes

Acknowledgements

The authors are grateful to the reviewer for his constructive comments, without which this paper could not have been written in its present form. The authors are grateful to Prof. Basudev Ghosh, Department of Physics, Jadavpur University for his helpful suggestions.

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of MathematicsJadavpur UniversityKolkataIndia

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