Ion-acoustic solitary structures at the acoustic speed in a collisionless magnetized nonthermal dusty plasma
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Debdatta Debnath
Abstract
At the acoustic speed, we have investigated the existence of ion-acoustic solitary structures including double layers and supersolitons in a collisionless magnetized plasma consisting of negatively charged static dust grains, adiabatic warm ions, and nonthermal electrons. At the acoustic speed, for negative polarity, the system supports solitons, double layers, supersoliton structures after the formation of double layer, supersoliton structures without the formation of double layer, solitons after the formation of double layer whereas the system supports solitons and supersolitons without the formation of double layer for the case of positive polarity. But it is not possible to get the coexistence of solitary structures (including double layers and supersolitons) of opposite polarities. For negative polarity, we have observed an important transformation viz., soliton before the formation of double layer → double layer → supersoliton → soliton after the formation of double layer whereas for both positive and negative polarities, we have observed the transformation from solitons to supersolitons without the formation of double layer. There does not exist any negative (positive) potential solitary structures within 0 < μ < μ c (μ c < μ < 1) and the amplitude of the positive (negative) potential solitary structure decreases for increasing (decreasing) μ and the solitary structures of both polarities collapse at μ = μ c, where μ c is a critical value of μ, the ratio of the unperturbed number density of electrons to that of ions. Similarly there exists a critical value β e2 of the nonthermal parameter β e such that the solitons of both polarities collapse at β e = β e2.
Acknowledgments
The authors are grateful to all the reviewers for their constructive comments, without which this paper could not have been written in its present form.
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Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
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Research funding: None declared.
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Conflict of interest statement: The authors declare no conflicts of interest regarding this article.
Appendix A: Derivation of Eq. (29)
From Eq. (28), we get
Substituting this expression of −M + u in Eq. (26), we get the following equation
Equation (65) can be written as
Substituting the expression of H as given by (23) into Eq. (66), we get the following equation
From Eq. (12), we see that n i is a function of ϕ and consequently we have the following results:
Using the above results, Eq. (67) can be written in the following form:
From this equation, one can easily get the following equation:
The above equation is Eq. (29).
Appendix B: Derivation of Eq. (45)
Differentiating Eq. (44) with respect to ϕ, we get:
where we have used the identity
Appendix C: Derivation of Eq. (46)
Differentiating Eq. (70) with respect to ϕ, we get:
Substituting the expression of V′(M, ϕ) as given by (70) into Eq. (71), we get the following equation
The above equation is Eq. (46).
Appendix D: Derivation of Eq. (47)
From Eqs. (12), (23), (31), (35), and (38), we get the following results:
Using the above results, from Eqs. (44)–(46), we get the following results:
The last equation is Eq. (47).
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Artikel in diesem Heft
- Frontmatter
- Dynamical Systems & Nonlinear Phenomena
- Positron nonextensivity effect on the propagation of dust ion acoustic Gardner waves
- Thermal entry flow problem for Giesekus fluid inside an axis-symmetric tube through isothermal wall condition: a comparative numerical study between exact and approximate solution
- Ion-acoustic solitary structures at the acoustic speed in a collisionless magnetized nonthermal dusty plasma
- Exact Beltrami flows in a spherical shell
- Hydrodynamics
- Insight into the dynamics of non-Newtonian carboxy methyl cellulose conveying CuO nanoparticles: significance of channel branch angle and pressure drop
- Analytical and numerical study for oscillatory flow of viscoelastic fluid in a tube with isosceles right triangular cross section
- Solid State Physics & Materials Science
- Numerical study of highly efficient tin-based perovskite solar cell with MoS2 hole transport layer
- An improved photocatalytic activity of H2 production: a hydrothermal synthesis of TiO2 nanostructures in aqueous triethanolamine
Artikel in diesem Heft
- Frontmatter
- Dynamical Systems & Nonlinear Phenomena
- Positron nonextensivity effect on the propagation of dust ion acoustic Gardner waves
- Thermal entry flow problem for Giesekus fluid inside an axis-symmetric tube through isothermal wall condition: a comparative numerical study between exact and approximate solution
- Ion-acoustic solitary structures at the acoustic speed in a collisionless magnetized nonthermal dusty plasma
- Exact Beltrami flows in a spherical shell
- Hydrodynamics
- Insight into the dynamics of non-Newtonian carboxy methyl cellulose conveying CuO nanoparticles: significance of channel branch angle and pressure drop
- Analytical and numerical study for oscillatory flow of viscoelastic fluid in a tube with isosceles right triangular cross section
- Solid State Physics & Materials Science
- Numerical study of highly efficient tin-based perovskite solar cell with MoS2 hole transport layer
- An improved photocatalytic activity of H2 production: a hydrothermal synthesis of TiO2 nanostructures in aqueous triethanolamine
