Home Ion-acoustic solitary structures at the acoustic speed in a collisionless magnetized nonthermal dusty plasma
Article
Licensed
Unlicensed Requires Authentication

Ion-acoustic solitary structures at the acoustic speed in a collisionless magnetized nonthermal dusty plasma

  • Debdatta Debnath and Anup Bandyopadhyay EMAIL logo
Published/Copyright: September 1, 2021
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 76 Issue 11

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.

Keywords: acoustic speed; electron–ion–dust plasma; ion acoustic wave; Sagdeev pseudo-potential technique; solitons, double layers, supersolitons
Corresponding author: Anup Bandyopadhyay, Department of Mathematics, Jadavpur University, Kolkata 700032, India, E-mail:

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.

  1. Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. 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

(64) − M + u = − M n i .

Substituting this expression of −M + u in Eq. (26), we get the following equation

(65) − M n i d u i z d ξ + l z d H d ξ = 0

Equation (65) can be written as

(66) d u i z d ξ − l z M n i d H d ξ = 0

Substituting the expression of H as given by (23) into Eq. (66), we get the following equation

(67) d u i z d ξ − l z M γ σ ie n i γ − 1 d n i d ξ + n i d ϕ d ξ = 0

From Eq. (12), we see that n i is a function of ϕ and consequently we have the following results:

( A ) ∫ n i d ϕ is a function of ϕ , ( B ) d d ϕ ∫ n i d ϕ = n i , ( C ) d d ξ ∫ n i d ϕ = d d ϕ ∫ n i d ϕ d ϕ d ξ = n i d ϕ d ξ , ( D ) d n i γ d ξ = γ n i γ − 1 d n i d ξ .

Using the above results, Eq. (67) can be written in the following form:

(68) d u i z d ξ − l z M σ ie d n i γ d ξ + d d ξ ∫ n i d ϕ = 0 ,

From this equation, one can easily get the following equation:

(69) d d ξ u i z − l z M σ ie n i γ + ∫ n i d ϕ = 0 .

The above equation is Eq. (29).

Appendix B: Derivation of Eq. (45)

Differentiating Eq. (44) with respect to ϕ, we get:

(70) V ′ ( M , ϕ ) = − d d ϕ ∫ 0 ϕ P ′ ( ϕ ) F ( ϕ ) d ϕ P ′ ( ϕ ) 2 = − P ′ ( ϕ ) F ( ϕ ) P ′ ( ϕ ) 2 − ∫ 0 ϕ P ′ ( ϕ ) F ( ϕ ) d ϕ   × ( − 2 ) P ″ ( ϕ ) P ′ ( ϕ ) 3 = − F ( ϕ ) P ′ ( ϕ ) + 2 P ″ ( ϕ ) P ′ ( ϕ ) ∫ 0 ϕ P ′ ( ϕ ) F ( ϕ ) d ϕ P ′ ( ϕ ) 2 = − F ( ϕ ) P ′ ( ϕ ) − 2 V ( M , ϕ ) P ″ ( ϕ ) P ′ ( ϕ ) ,

where we have used the identity d d ϕ ∫ 0 ϕ P ′ ( ϕ ) F ( ϕ ) d ϕ = P ′ ( ϕ ) F ( ϕ ) to simplify (70). The above equation is Eq. (45).

Appendix C: Derivation of Eq. (46)

Differentiating Eq. (70) with respect to ϕ, we get:

(71) V ″ ( M , ϕ ) = d d ϕ − F ( ϕ ) P ′ ( ϕ ) − 2 V ( M , ϕ ) P ″ ( ϕ ) P ′ ( ϕ ) = − F ′ ( ϕ ) P ′ ( ϕ ) + F ( ϕ ) P ″ ( ϕ ) P ′ ( ϕ ) 2 − 2 V ( M , ϕ ) P ′ ′ ′ ( ϕ ) P ′ ( ϕ ) + 2 V ( M , ϕ ) P ″ ( ϕ ) 2 P ′ ( ϕ ) 2 − 2 V ′ ( M , ϕ ) P ″ ( ϕ ) P ′ ( ϕ )

Substituting the expression of V′(M, ϕ) as given by (70) into Eq. (71), we get the following equation

V ″ ( M , ϕ ) = − F ′ ( ϕ ) P ′ ( ϕ ) + 3 F ( ϕ ) P ″ ( ϕ ) P ′ ( ϕ ) 2 + 2 V ( M , ϕ ) 3 P ″ ( ϕ ) 2 P ′ ( ϕ ) 2 − P ′ ′ ′ ( ϕ ) P ′ ( ϕ )

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:

(72) n i ( 0 ) = 1 ,

(73) n i ′ ( 0 ) = μ ( 1 − β e ) ,

(74) H ( 0 ) = γ γ − 1 σ ie ,

(75) H ′ ( 0 ) = γ σ ie μ ( 1 − β e ) + 1 ,

(76) G ( 0 ) = 0 ,

(77) G ′ ( 0 ) = 1 + γ σ ie μ ( 1 − β e ) ,

(78) P ( 0 ) = M 2 2 + γ γ − 1 σ ie ,

(79) P ′ ( 0 ) = − M 2 + γ σ ie μ ( 1 − β e ) + 1 ,

(80) F ( 0 ) = 0 ,

(81) F ′ ( 0 ) = μ ( 1 − β e ) − l z 2 M 2 1 + γ σ ie μ ( 1 − β e ) .

Using the above results, from Eqs. (44)–(46), we get the following results:

V ( M , 0 ) = 0 V ′ ( M , 0 ) = 0 V ″ ( M , 0 ) = − μ ( 1 − β e ) − l z 2 M 2 γ σ ie μ ( 1 − β e ) + 1 ( − M 2 + γ σ ie ) μ ( 1 − β e ) + 1

The last equation is Eq. (47).

References

[1] P. Shukla and M. Yu, “Exact solitary ion acoustic waves in a magnetoplasma,” J. Math. Phys., vol. 19, p. 2506, 1978. https://doi.org/10.1063/1.523632.Search in Google Scholar

[2] A. Hasegawa and T. Sato, “Existence of a negative potential solitary-wave structure and formation of a double layer,” Phys. Fluids, vol. 25, p. 632, 1982. https://doi.org/10.1063/1.863785.Search in Google Scholar

[3] S. Baboolal, R. Bharuthram, and M. Hellberg, “Arbitrary-amplitude rarefactive ion-acoustic double layers in warm multi-fluid plasmas,” J. Plasma Phys., vol. 40, p. 163, 1988. https://doi.org/10.1017/s0022377800013180.Search in Google Scholar

[4] R. Bharuthram and P. K. Shukla, “Large amplitude ion-acoustic solitons in a dusty plasma,” Planet. Space Sci., vol. 40, p. 973, 1992. https://doi.org/10.1016/0032-0633(92)90137-d.Search in Google Scholar

[5] R. A. Cairns, A. A. Mamum, R. Bingham, et al.., “Electrostatic solitary structures in non-thermal plasmas,” Geophys. Res. Lett., vol. 22, p. 2709, 1995. https://doi.org/10.1029/95gl02781.Search in Google Scholar

[6] R. A. Cairns, R. Bingham, R. O. Dendy, C. M. C. Nairn, P. K. Shukla, and A. A. Mamun, “Ion sound solitary waves with density depressions,” J. Phys. IV, vol. 5, p. C6, 1995. https://doi.org/10.1051/jp4:1995608.10.1051/jp4:1995608Search in Google Scholar

[7] S. Popel, M. Yu, and V. Tsytovich, “Shock waves in plasmas containing variable‐charge impurities,” Phys. Plasmas, vol. 3, p. 4313, 1996. https://doi.org/10.1063/1.872048.Search in Google Scholar

[8] A. Mamun, R. Cairns, and P. Shukla, “Solitary potentials in dusty plasmas,” Phys. Plasmas, vol. 3, p. 702, 1996. https://doi.org/10.1063/1.871905.Search in Google Scholar

[9] A. A. Mamun, “Effects of ion temperature on electrostatic solitary structures in nonthermal plasmas,” Phys. Rev. E, vol. 55, p. 1852, 1997. https://doi.org/10.1103/physreve.55.1852.Search in Google Scholar

[10] T. S. Gill, P. Bala, H. Kaur, N. S. Saini, S. Bansal, and J. Kaur, “Ion-acoustic solitons and double-layers in a plasma consisting of positive and negative ions with non-thermal electrons,” Eur. Phys. J. D, vol. 31, p. 91, 2004. https://doi.org/10.1140/epjd/e2004-00121-4.Search in Google Scholar

[11] S. Maharaj, S. Pillay, R. Bharuthram, S. Singh, and G. Lakhina, “The effect of dust grain temperature and dust streaming on electrostatic solitary structures in a non-thermal plasma,” Phys. Scripta, vol. 2004, p. 135, 2004. https://doi.org/10.1088/0031-8949/2004/t113/034.Search in Google Scholar

[12] C. R. Choi, C.-M. Ryu, N. C. Lee, and D.-Y. Lee, “Ion acoustic solitary waves in a dusty plasma obliquely propagating to an external magnetic field,” Phys. Plasmas, vol. 12, 2005, Art no. 022304. https://doi.org/10.1063/1.1843820.Search in Google Scholar

[13] C. R. Choi, C.-M. Ryu, N. C. Lee, D.-Y. Lee, and Y. Kim, “Ion thermal pressure effects on dust ion acoustic solitary waves in a dusty plasma obliquely propagating to an external magnetic field,” Phys. Plasmas, vol. 12, 2005, Art no. 072301. https://doi.org/10.1063/1.1943367.Search in Google Scholar

[14] S. Maitra and R. Roychoudhury, “Obliquely propagating ion acoustic solitary waves in a dusty plasma in the presence of an external magnetic field,” Phys. Plasmas, vol. 13, p. 112302, 2006. https://doi.org/10.1063/1.2364140.Search in Google Scholar

[15] M. Marklund, B. Eliasson, and P. K. Shukla, “Magnetosonic solitons in a fermionic quantum plasma,” Phys. Rev. E, vol. 76, 2007, Art no. 067401. https://doi.org/10.1103/PhysRevE.76.067401.10.1103/PhysRevE.76.067401Search in Google Scholar PubMed

[16] S. Ali, W. M. Moslem, P. K. Shukla, and R. Schlickeiser, “Linear and nonlinear ion-acoustic waves in an unmagnetized electron–positron–ion quantum plasma,” Phys. Plasmas, vol. 14, 2007, Art no. 082307. https://doi.org/10.1063/1.2750649.Search in Google Scholar

[17] C. R. Choi, C.-M. Ryu, D.-Y. Lee, N. C. Lee, and Y.-H. Kim, “Dust ion acoustic solitary waves in a magnetized dusty plasma with anisotropic ion pressure,” Phys. Lett. A, vol. 364, p. 297, 2007. https://doi.org/10.1016/j.physleta.2006.12.014.Search in Google Scholar

[18] W. F. El-Taibany and M. Wadati, “Sagdeev potential analysis for positively charged dust grains in nonthermal dusty plasma near Mars,” Phys. Plasmas, vol. 14, p. 103703, 2007. https://doi.org/10.1063/1.2784764.Search in Google Scholar

[19] S. Ghosh and R. Bharuthram, “Ion acoustic solitons and double layers in electron–positron–ion plasmas with dust particulates,” Astrophys. Space Sci., vol. 314, p. 121, 2008. https://doi.org/10.1007/s10509-008-9748-0.Search in Google Scholar

[20] P. Chatterjee and K. Roy, “Large amplitude solitary waves in a four-component dusty plasma with nonthermal ions,” Z. Naturforsch. A, vol. 63, p. 393, 2008. https://doi.org/10.1515/zna-2008-7-802.Search in Google Scholar

[21] M. Djebli and H. Marif, “Large amplitude double layers in a positively charged dusty plasma with nonthermal electrons,” Phys. Plasmas, vol. 16, 2009, Art no. 063708. https://doi.org/10.1063/1.3152324.Search in Google Scholar

[22] H. R. Pakzad, “Ion acoustic solitary waves in plasma with nonthermal electron and positron,” Phys. Lett. A, vol. 373, p. 847, 2009. https://doi.org/10.1016/j.physleta.2008.12.066.Search in Google Scholar

[23] E. I. El-Awady, S. A. El-Tantawy, W. M. Moslem, and P. K. Shukla, “Electron-positron-ion plasma with kappa distribution: Ion acoustic soliton propagation,” Phys. Lett. A, vol. 374, p. 3216, 2010. https://doi.org/10.1016/j.physleta.2010.05.053.Search in Google Scholar

[24] M. Tribeche and L. Djebarni, “Electron-acoustic solitary waves in a nonextensive plasma,” Phys. Plasmas, vol. 17, p. 124502, 2010. https://doi.org/10.1063/1.3522777.Search in Google Scholar

[25] H. R. Pakzad and M. Tribeche, “Electron-acoustic solitons in plasma with nonthermal electrons,” Astrophys. Space Sci., vol. 330, p. 95, 2010. https://doi.org/10.1007/s10509-010-0367-1.Search in Google Scholar

[26] M. Tribeche and A. Merriche, “Nonextensive dust-acoustic solitary waves,” Phys. Plasmas, vol. 18, 2011, Art no. 034502. https://doi.org/10.1063/1.3561789.Search in Google Scholar

[27] O. R. Rufai, R. Bharuthram, S. V. Singh, and G. S. Lakhina, “Low frequency solitons and double layers in a magnetized plasma with two temperature electrons,” Phys. Plasmas, vol. 19, p. 122308, 2012. https://doi.org/10.1063/1.4771574.Search in Google Scholar

[28] A. E. Dubinov and D. Y. Kolotkov, “Ion-acoustic supersolitons in plasma,” Plasma Phys. Rep., vol. 38, p. 909, 2012. https://doi.org/10.1134/s1063780x12100054.Search in Google Scholar

[29] A. E. Dubinov and D. Y. Kolotkov, “Ion-acoustic super solitary waves in dusty multispecies plasmas,” IEEE Trans. Plasma Sci., vol. 40, p. 1429, 2012. https://doi.org/10.1109/tps.2012.2189026.Search in Google Scholar

[30] A. E. Dubinov and D. Y. Kolotkov, “Ion-acoustic supersolitons in plasma,” Plasma Phys. Rep., vol. 38, p. 909, 2012. https://doi.org/10.1134/s1063780x12100054.Search in Google Scholar

[31] A. Das, A. Bandyopadhyay, and K. P. Das, “Dust ion-acoustic solitary structures in non-thermal dusty plasma,” J. Plasma Phys., vol. 78, p. 149, 2012. https://doi.org/10.1017/s002237781100050x.Search in Google Scholar

[32] A. E. Dubinov and D. Y. Kolotkov, “Interpretation of ion-acoustic solitons of unusual form in experiments in SF6-Ar plasma,” High Energy Chem., vol. 46, p. 349, 2012. https://doi.org/10.1134/s0018143912060033.Search in Google Scholar

[33] S. V. Singh, S. Devanandhan, G. S. Lakhina, and R. Bharuthram, “Effect of ion temperature on ion-acoustic solitary waves in a magnetized plasma in presence of superthermal electrons,” Phys. Plasmas, vol. 20, 2013, Art no. 012306. https://doi.org/10.1063/1.4776710.Search in Google Scholar

[34] M. A. Hellberg, T. K. Baluku, F. Verheest, and I. Kourakis, “Dust-acoustic supersolitons in a three-species dusty plasma with kappa distributions,” J. Plasma Phys., vol. 79, p. 1039, 2013. https://doi.org/10.1017/s0022377813001153.Search in Google Scholar

[35] O. R. Rufai, R. Bharuthram, S. V. Singh, and G. S. Lakhina, “Ion acoustic solitons and supersolitons in a magnetized plasma with nonthermal hot electrons and Boltzmann cool electrons,” Phys. Plasmas, vol. 21, 2014, Art no. 082304. https://doi.org/10.1063/1.4891877.Search in Google Scholar

[36] S. V. Singh and G. S. Lakhina, “Ion-acoustic supersolitons in the presence of non-thermal electrons,” Commun. Nonlinear Sci. Numer. Simulat., vol. 23, p. 274, 2015. https://doi.org/10.1016/j.cnsns.2014.11.017.Search in Google Scholar

[37] A. Paul and A. Bandyopadhyay, “Dust ion acoustic solitary structures in presence of nonthermal electrons and isothermal positrons,” Astrophys. Space Sci., vol. 361, p. 172, 2016. https://doi.org/10.1007/s10509-016-2758-4.Search in Google Scholar

[38] O. R. Rufai, R. Bharuthram, S. V. Singh, and G. S. Lakhina, “Nonlinear low frequency electrostatic structures in a magnetized two-component auroral plasma,” Phys. Plasmas, vol. 23, 2016, Art no. 032309. https://doi.org/10.1063/1.4944669.Search in Google Scholar

[39] A. Paul, A. Das, and A. Bandyopadhyay, “Dust ion acoustic solitary structures in the presence of isothermal positrons,” Plasma Phys. Rep., vol. 43, p. 218, 2017. https://doi.org/10.1134/s1063780x1702012x.Search in Google Scholar

[40] A. Paul, A. Bandyopadhyay, and K. P. Das, “Dust ion acoustic solitary structures in presence of nonthermally distributed electrons and positrons,” Phys. Plasmas, vol. 24, 2017, Art no. 013707. https://doi.org/10.1063/1.4975089.Search in Google Scholar

[41] A. Paul and A. Bandyopadhyay, “Ion acoustic solitons, double layers and supersolitons in a collisionless unmagnetized plasma consisting of nonthermal electrons and isothermal positrons,” Indian J. Phys., vol. 92, p. 1187, 2018. https://doi.org/10.1007/s12648-018-1180-x.Search in Google Scholar

[42] D. Debnath, A. Bandyopadhyay, and K. P. Das, “Ion acoustic solitary structures in a magnetized nonthermal dusty plasma,” Phys. Plasmas, vol. 25, 2018, Art no. 033704. https://doi.org/10.1063/1.5021127.Search in Google Scholar

[43] D. Debnath and A. Bandyopadhyay, “Combined effect of Kappa and Cairns distributed electrons on ion acoustic solitary structures in a collisionless magnetized dusty plasma,” Astrophys. Space Sci., vol. 365, Art no. 72, 2020. https://doi.org/10.1007/s10509-020-03786-6.Search in Google Scholar

[44] S. Dalui, S. Sardar, and A. Bandyopadhyay, “Arbitrary amplitude ion acoustic solitons, double layers and supersolitons in a collisionless magnetized plasma consisting of non-thermal and isothermal electrons,” Z. Naturforsch. A, vol. 76, pp. 455–468, 2021. https://doi.org/10.1515/zna-2020-0296.Search in Google Scholar

[45] F. Verheest and M. A. Hellberg, “Nonthermal effects on existence domains for dust-acoustic solitary structures in plasmas with two-temperature ions,” Phys. Plasmas, vol. 17, 2010, Art no. 023701. https://doi.org/10.1063/1.3299356.Search in Google Scholar

[46] T. Baluku, M. Hellberg, I. Kourakis, and N. Saini, “Dust ion acoustic solitons in a plasma with kappa-distributed electrons,” Phys. Plasmas, vol. 17, 2010, Art no. 053702. https://doi.org/10.1063/1.3400229.Search in Google Scholar

[47] T. K. Baluku, M. A. Hellberg, and F. Verheest, “New light on ion acoustic solitary waves in a plasma with two-temperature electrons,” Europhys. Lett., vol. 91, p. 15001, 2010. https://doi.org/10.1209/0295-5075/91/15001.Search in Google Scholar

[48] A. Das, A. Bandyopadhyay, and K. P. Das, “An analytical study on the existence of solitary structure at M = Mc,” J. Plasma Phys., vol. 78, p. 565, 2012. https://doi.org/10.1017/s0022377812000372.Search in Google Scholar

[49] F. Verheest and M. A. Hellberg, “Electrostatic supersolitons and double layers at the acoustic speed,” Phys. Plasmas, vol. 22, 2015, Art no. 012301. https://doi.org/10.1063/1.4905518.Search in Google Scholar

[50] A. Paul, A. Bandyopadhyay, and K. P. Das, “Dust ion acoustic solitary structures at the acoustic speed in the presence of nonthermal electrons and isothermal positrons,” Plasma Phys. Rep., vol. 45, p. 466, 2019. https://doi.org/10.1134/s1063780x19050088.Search in Google Scholar

[51] J. H. Binsack, Ph.D. Thesis, Massachusetts Institute of Technology, 1966.Search in Google Scholar

[52] S. Olbert, “Summary of Experimental Results from M.I.T. Detector on IMP-1,” in Physics of the Magnetosphere, vol. 10, Dordrecht, Springer, 1968, p. 641.10.1007/978-94-010-3467-8_23Search in Google Scholar

[53] V. M. Vasyliunas, “A survey of low-energy electrons in the evening sector of the magnetosphere with OGO 1 and OGO 3,” J. Geophys. Res., vol. 73, p. 2839, 1968. https://doi.org/10.1029/ja073i009p02839.Search in Google Scholar

[54] F. Verheest and S. Pillay, “Large amplitude dust-acoustic solitary waves and double layers in nonthermal plasmas,” Phys. Plasmas, vol. 15, 2008, Art no. 013703. https://doi.org/10.1063/1.2831025.Search in Google Scholar

[55] P. O. Dovner, A. I. Eriksson, R. Boström, and B. Holback, “Freja multiprobe observations of electrostatic solitary structures,” Geophys. Res. Lett., vol. 21, p. 1827, 1994. https://doi.org/10.1029/94gl00886.Search in Google Scholar

[56] R. Boström, G. Gustafsson, B. Holback, G. Holmgren, H. Koskinen, and P. Kintner, “Characteristics of Solitary Waves and Weak Double Layers in the Magnetospheric Plasma,” Phys. Rev. Lett., vol. 61, p. 82, 1988. https://doi.org/10.1103/physrevlett.61.82.Search in Google Scholar PubMed

[57] R. Boström, “Observations of weak double layers on auroral field lines,” IEEE Trans. Plasma Sci., vol. 20, p. 756, 1992. https://doi.org/10.1109/27.199524.Search in Google Scholar

[58] R. E. Ergun, C. W. Carlson, J. P. McFadden, et al.., “FAST satellite observations of electric field structures in the auroral zone,” Geophys. Res. Lett., vol. 25, p. 2025, 1998. https://doi.org/10.1029/98gl00635.Search in Google Scholar

[59] R. E. Ergun, C. W. Carlson, J. P. McFadden, et al.., “FAST satellite wave observations in the AKR source region,” Geophys. Res. Lett., vol. 25, p. 2061, 1998. https://doi.org/10.1029/98gl00570.Search in Google Scholar

[60] G. T. Delory, R. E. Ergun, C. W. Carlson, et al.., “FAST observations of electron distributions within AKR source regions,” Geophys. Res. Lett., vol. 25, p. 2069, 1998. https://doi.org/10.1029/98gl00705.Search in Google Scholar

[61] R. Pottelette, R. E. Ergun, R. A. Treumann, et al.., “Modulated electron-acoustic waves in auroral density cavities: FAST observations,” Geophys. Res. Lett., vol. 26, p. 2629, 1999. https://doi.org/10.1029/1999gl900462.Search in Google Scholar

[62] J. P. McFadden, C. W. Carlson, R. E. Ergun, et al., “FAST observations of ion solitary waves,” J. Geophys. Res., vol. 108, p. 8018, 2003. https://doi.org/10.1029/2002JA009485.Search in Google Scholar

[63] H. Matsumoto, H. Kojima, T. Miyatake, et al.., “Electrostatic solitary waves (ESW) in the magnetotail: BEN wave forms observed by GEOTAIL,” Geophys. Res. Lett., vol. 21, p. 2915, 1994. https://doi.org/10.1029/94gl01284.Search in Google Scholar

[64] J. R. Franz, P. M. Kintner, and J. S. Pickett, “POLAR observations of coherent electric field structures,” Geophys. Res. Lett., vol. 25, p. 1277, 1998. https://doi.org/10.1029/98gl50870.Search in Google Scholar

[65] C. A. Cattell, J. Dombeck, J. R. Wygant, et al.., “Comparisons of Polar satellite observations of solitary wave velocities in the plasma sheet boundary and the high altitude cusp to those in the auroral zone,” Geophys. Res. Lett., vol. 26, p. 425, 1999. https://doi.org/10.1029/1998gl900304.Search in Google Scholar

[66] J. R. Asbridge, S. J. Bame, and I. B. Strong, “Outward flow of protons from the Earth’s bow shock,” J. Geophys. Res., vol. 73, p. 5777, 1968. https://doi.org/10.1029/ja073i017p05777.Search in Google Scholar

[67] W. Feldman, R. Anderson, S. Bame, et al.., “Electron velocity distributions near the Earth’s bow shock,” J. Geophys. Res., vol. 88, p. 96, 1983. https://doi.org/10.1029/ja088ia01p00096.Search in Google Scholar

[68] R. Lundin, A. Zakharov, R. Pellinen, et al.., “First measurements of the ionospheric plasma escape from Mars,” Nature, vol. 341, p. 609, 1989. https://doi.org/10.1038/341609a0.Search in Google Scholar

[69] F. Verheest, Waves in Dusty Space Plasmas, Dordrecht, Netherlands, Kluwer Academic, 2000.10.1007/978-94-010-9945-5Search in Google Scholar

[70] P. K. Shukla and A. A. Mamun, Introduction to Dusty Plasma Physics, Bristol, UK, IoP, 2002.10.1887/075030653XSearch in Google Scholar

[71] Y. Futaana, S. Machida, Y. Saito, A. Matsuoka, and H. Hayakawa, “Moon-related nonthermal ions observed by Nozomi: Species, sources, and generation mechanisms,” J. Geophys. Res., vol. 108, p. 1025, 2003. https://doi.org/10.1029/2002ja009366.Search in Google Scholar

[72] R. Z. Sagdeev, Reviews of Plasma Physics, vol. 4, M. A. Leontovich, Ed., New York, NY, Consultant Bureau, 1966.Search in Google Scholar

[73] H. Alfvén, Cosmic Plasma, vol. 82, Dordrecht, Holland, D. Reidel Publishing Company, 1981.10.1007/978-94-009-8374-8Search in Google Scholar

[74] A. E. Dubinov and D. Y. Kolotkov, “Above the weak nonlinearity: super-nonlinear waves in astrophysical and laboratory plasmas,” Rev. Mod. Plasma Phys., vol. 2, 2018, Art no. 2. https://doi.org/10.1007/s41614-018-0014-9.Search in Google Scholar

[75] M. Temerin, K. Cerny, W. Lotko, and F. Mozer, “Observations of double layers and solitary waves in the auroral plasma,” Phys. Rev. Lett., vol. 48, p. 1175, 1982. https://doi.org/10.1103/physrevlett.48.1175.Search in Google Scholar

[76] F. Mozer, R. Ergun, M. Temerin, C. Cattell, J. Dombeck, and J. Wygant, “New features of time domain electric-field structures in the auroral acceleration region,” Phys. Rev. Lett., vol. 79, p. 1281, 1997. https://doi.org/10.1103/physrevlett.79.1281.Search in Google Scholar

[77] R. Ergun, C. Carlson, J. McFadden, et al.., “Debye-scale plasma structures associated with magnetic-field-aligned electric fields,” Phys. Rev. Lett., vol. 81, p. 826, 1998. https://doi.org/10.1103/physrevlett.81.826.Search in Google Scholar
Received: 2021-04-29
Revised: 2021-07-23
Accepted: 2021-08-12
Published Online: 2021-09-01
Published in Print: 2021-11-25

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Positron nonextensivity effect on the propagation of dust ion acoustic Gardner waves
  4. 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
  5. Ion-acoustic solitary structures at the acoustic speed in a collisionless magnetized nonthermal dusty plasma
  6. Exact Beltrami flows in a spherical shell
  7. Hydrodynamics
  8. Insight into the dynamics of non-Newtonian carboxy methyl cellulose conveying CuO nanoparticles: significance of channel branch angle and pressure drop
  9. Analytical and numerical study for oscillatory flow of viscoelastic fluid in a tube with isosceles right triangular cross section
  10. Solid State Physics & Materials Science
  11. Numerical study of highly efficient tin-based perovskite solar cell with MoS2 hole transport layer
  12. An improved photocatalytic activity of H2 production: a hydrothermal synthesis of TiO2 nanostructures in aqueous triethanolamine
https://doi.org/10.1515/zna-2021-0120
Keywords for this article
acoustic speed; electron–ion–dust plasma; ion acoustic wave; Sagdeev pseudo-potential technique; solitons, double layers, supersolitons

Articles in the same Issue

  1. Frontmatter
  2. Dynamical Systems & Nonlinear Phenomena
  3. Positron nonextensivity effect on the propagation of dust ion acoustic Gardner waves
  4. 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
  5. Ion-acoustic solitary structures at the acoustic speed in a collisionless magnetized nonthermal dusty plasma
  6. Exact Beltrami flows in a spherical shell
  7. Hydrodynamics
  8. Insight into the dynamics of non-Newtonian carboxy methyl cellulose conveying CuO nanoparticles: significance of channel branch angle and pressure drop
  9. Analytical and numerical study for oscillatory flow of viscoelastic fluid in a tube with isosceles right triangular cross section
  10. Solid State Physics & Materials Science
  11. Numerical study of highly efficient tin-based perovskite solar cell with MoS2 hole transport layer
  12. An improved photocatalytic activity of H2 production: a hydrothermal synthesis of TiO2 nanostructures in aqueous triethanolamine
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 2.12.2025 from https://www.degruyterbrill.com/document/doi/10.1515/zna-2021-0120/html?lang=en
Scroll to top button