Effect of non-thermal and trapped electrons on solitary waves and chaos in auroral acceleration regions

Document Type : Research Article

Author

Assistant Professor, Department of Plasma Physics and Basic Particle, Faculty of Physics, Shahrood University of Technology, Shahrood, Iran

Abstract

In this paper, using the reductive perturbation method, the propagation of nonlinear solitary waves and chaos phenomenon and its stability were studied in auroral acceleration regions in the presence of electrons with the Cairns-Gurevich distribution function. Using the continuity, momentum transfer, and Poisson equations, and considering the density of electrons as the Cairns-Gurovich distribution function, and using two different models, Korteweg–De Vries (KdV) and modified KdV equations were obtained. It was shown that the solutions of these equations are in the form of solitary waves. The effect of non-thermal and trapped electrons and wave velocity on these waves were studied. In the next section, pseudo-potentials and total mechanical energy are obtained. Considering a quasi-periodic factor, KdV and modified KdV equations were reviewed and the chaos and its stability were studied in the auroral acceleration regions. Results showed that by increasing the wave velocity and non-thermal and trapped parameters, the size of the field increased, and the depth of the potential well was also increased. These results confirmed each other. It was indicated that in the case of b=0, this distribution function became as the Maxwellian distribution function. In the case b>0, in addition to free particles, the trapped and non-thermal particles also affect the distribution function. In this case, the width of the distribution function became larger, which indicated that the more energetic electrons existed in this case. It is also concluded that for both nonlinear equations, the solutions can exist in the form of rarefactive and compressive solitons. Three-dimensional graphs of total mechanical energy were also plotted for different values of the wave velocity and non-thermal and trapped parameters. Results for this case also showed that for the total energy of E1, by increasing the b parameter, the energy deviated from the uniform function and reached the saddle state. It was also shown that the wave velocity was similar to the b parameter. It was found that for different values of U and b parameters, the behavior of the total energy of E2 was different from the total energy diagram of E1. Poincaré return mapping diagrams confirmed the existence of a closed cycle indicating chaos in these plasmas. Results of this section also showed that for solitons with function ψ1, by increasing the U parameter, the Poincaré return mapping cycle region increased. Poincaré return mapping lines were also more focused in this case. For solitons with ψ1 functions, by increasing the wave velocity, Poincaré's return map goes from a quasi-stable state to a stable state. By increasing the quasi-periodic frequency, the Poincaré return map goes from steady-state to quasi-steady state so that a cycle converts to two cycles with a certain overlap. Finally, it was concluded that using real parameters, the wave velocity was in the interval 13km/s<v'<52km/s and the electric field was approximately 5mV/m and the Debye length became 15m. It was also concluded that the results of the recent work were in good agreement with the results obtained from the Viking, Freja and S3-3 satellites.

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References

سلمانپور، ح. و شریفیان، م.، 1397، امواج سالیتونی در پلاسمای میان ستاره‌ای با الکترون‌های دارای توزیع کرنز در حضور یون‌های منفی، م. فیزیک زمین و فضا، 44(2)، 351-361.
صابریان، ا.، 1398، سالیتون‌های یون-صوتی در پلاسمای دور از تعادل بادهای خورشیدی، م. فیزیک زمین و فضا، 45(1)، 235-246.
صابریان ا. و خوشه‌شاهی، ر.، 1399، امواج سالیتونی غبار-صوتی در پلاسماهای غباری فضایی با توزیع غیرتعادلی، م. فیزیک زمین و فضا، 46(2)، 377-394.
Abdikian, A., 2017, Modulational instability of ion-acoustic waves in magnetoplasma with pressure of relativistic electrons. Phys. Plasmas 24, 052123.
Abdikian, A. R., Saha A. and Alimirzaei, S., 2020, Bifurcation analysis of ion-acoustic waves in an adiabatic trapped electron and warm ion plasma. J. Taibah Univers. Sci. 14, 1051-1058.
Annou, K., 2015, Ion-acoustic solitons in plasma: an application to Saturn’s magnetosphere. Astrophys. Space Sci. 357, 163.
Bara, D., Djebli, M. and Bennaceur-Doumaz, D., 2014, Combined effects of electronic trapping and non-thermal electrons on the expansion of laser produced plasma into vacuum. Laser Part. Beams 32, 391-398.
Bernstein, I. B., Green, J. M. and Kruskal, M. D., 1957, Exact nonlinear plasma oscillations. Phys. Rev. 108, 546-550.
Bostrom, R., 1992, Observations of weak double layers on auroral field lines. IEEE Trans. Plasma Sci. 20, 756-763.
Cairns, R. A., Mamum, A. A., Bingham, R., Boström, R., Dendy, R. O., Nairn, C. M. and Shukla, P. K., 1995, Electrostatic solitary structures in non-thermal plasmas. Geophys. Res. Lett. 22, 2709-2712.
Choi, C. R., Lee, D.-Y. and Kim, Y., 2006, The ion acoustic solitary waves and double layers in the solar wind plasma. J. Astron. Space Sci. 23, 209-216.
Das, G. C. and Paul, S. N., 1985, Ion‐acoustic solitary waves in relativistic plasmas. Phys. Fluids, 28, 823-825.
Das, T. K., Ali, R. and Chatterjee, P., 2017, Effect of dust ion collision on dust ion acoustic waves in the framework of damped Zakharov-Kuznetsov equation in presence of external periodic force. Phys. Plasmas 24, 103703.
Dovner, P. O., Eriksson, A. I. , Bostrom, R. and B. Holback, 1994, Freja Multiprobe observations of electrostatic solitary structure. Geophys. Res. Lett. 21, 1827-1830.
El-Labany, S. K., El-Taibany, W. F. and Zedan, N. A., 2017, Modulated ion acoustic waves in a plasma with Cairns-Gurevich distribution. Phys. Plasmas 24, 112118.
Esfandyari-Kalejahi, A., Kourakis, I. and Shukla, P. K., 2008, Ion-acoustic waves in a plasma consisting of adiabatic warm ions, nonisothermal electrons, and a weakly relativistic electron beam: linear and higher-order nonlinear effects. Phys. Plasmas 15, 022303.
Ghosh, B., 1989, A second-order theory for electron plasma solitary waves in a cylindrical waveguide. Contrib. Plasma Phys. 29, 125-134.
Ghosh, S. S. and Lakhina, G. S., 2004, Anomalous width variation of rarefactive ion acoustic solitary waves in the context of auroral plasmas. Nonlinear Proc. Geoph. 11, 219-228.
Gurevich, A. V., 1968, Distribution of captured particles in a potential well in the absence of collisions. Sov. Phys. JETP 26, 575-580.
Hakimi Pajouh, H. and Abbasi, H., 2002, Modulational instability of the electron cyclotron waves in an adiabatic wave-particle interaction. Plasma Phys. 7, 112-114.
Hasselblatt, B. and Anatole K., 2003, A First Course in Dynamics: With a Panorama of Recent Developments. Cambridge University Press.
Hossen, M. R. and Mamun, A. A., 2014, Electrostatic solitary structures in a relativistic degenerate multispecies plasma Braz. J. Phys. 44, 673-681.
Hossen, M. R., Ema, S. A. and Mamun, A. A., 2014, Nonplanar shock structures in a relativistic degenerate multi-species plasma. Commun. Theor. Phys. 62, 888–894.
Hosen, B., Shah, M. G., Hossen, M. R. and Mamun, A. A., 2017, Ion-acoustic solitary waves and double layers in a magnetized degenerate quantum plasma. IEEE Trans. Plasma Sci. 45, 3316-3327.
Louarn, P., Roux, A., de Feraudy, H. and Le Queau, D., 1990, Trapped electrons as a free energy source for the auroral kilometric radiation. J. Geophys. Res. 95, 5983-5995.
Mahmood, S. and Akhtar, N., 2008, Ion acoustic solitary waves with adiabatic ions in magnetized electron-positron-ion plasmas. Eur. Phys. J. D 49, 217-222.
Main, D. S., Newman, D. L. and Ergun, R. E., 2006, Double layers and ion phase-space holes in the auroral upward-current region, Phys. Rev. Let., 97, 185001.
Main, D. S., Newman, D. L., Scholz, C., and Ergun, R. E., 2012, Ion acoustic solitons in Earth’s upward-current region. Phys. Plasmas 19, 072905.
Naeem, I., Ali, S., Irfan, M. and Mirza, A. M., 2020, Ion-acoustic shocklets in F-region of ionosphere with non-Maxwellian electrons. Phys. Lett. A 384, 126568.
Ouazene, M. and Amour, R., 2019, Dust acoustic solitons in a dusty plasma with Cairns–Gurevich distributed ions. Astrophys. Space Sci. 364, 1-8.
Pakzad, H. R., 2011, Ion acoustic solitons of KdV and modified KdV equations in weakly relativistic plasma containing nonthermal electron, positron and warm ion. Astrophys. Space Sci. 332, 269–277.
Reddy, R. V. and Lakhina, G. S., 1991, Ion acoustic double layers and solitons in auroral plasma. Planet. Space Sci. 39, 1343-1350.
Reddy, R. V., Lakhina, G. S. and Verheest, F., 1992, Ion-acoustic double layers and solitons in multispecies auroral beam-plasmas. Planet. Space Sci. 40, 1055-1062.
Rufai, O. R., Bharuthram, R., Singh, S. V. and Lakhina, G. S., 2014, Ion acoustic solitons and supersolitons in a magnetized plasma with nonthermal hot electrons and Boltzmann cool electrons. Phys. Plasmas 21, 082304.
Rufai, O. R., Bharuthram, R., Singh, S. V. and Lakhina, G. S., 2015, Effect of excess superthermal hot electrons on finite amplitude ion-acoustic solitons and supersolitons in a magnetized auroral plasma. Phys. Plasmas 22, 102305.
Rufai, O. R., Bharuthram R., Singh, S. V. and Lakhina, G. S., 2016, Obliquely propagating ion-acoustic solitons and supersolitons in four-component auroral plasmas. Adv. Space Res. 57, 813-820.
Saha, A. and Chatterjee, P., 2014a, Bifurcations of ion acoustic solitary waves and periodic waves in an unmagnetized plasma with kappa distributed multi-temperature electrons, Astrophys. Space Sci., 350, 631-636.
Saha, A. and Chatterjee, P., 2014b, Bifurcations of ion acoustic solitary and periodic waves in an electron-positron-ion plasma through non-perturbative approach, J. Plasma Phys., 80, 553-563.
Saha, A. and Tamang, J., 2017, Qualitative analysis of the positron-acoustic waves in electron-positron-ion plasmas with κ deformed Kaniadakis distributed electrons and hot positrons. Phys. Plasmas 24, 082101.
Saha, A., Ali, R. and Chatterjee, P., 2017, Nonlinear excitations for the positron acoustic waves in auroral acceleration regions. Adv. Space Res. 60, 1220-1236.
Sahu, B., 2010, Positron acoustic shock waves in planar and nonplanar geometry. Phys. Scr. 82, 065504.
Schamel, H., 1979, Role of trapped particles and waves in plasma solitons-theory and application. Phys. Scr. 20, 306-316.
Sultana, S., 2018, Ion acoustic solitons in magnetized collisional non-thermal dusty plasmas. Phys. Lett. A 382, 1368-1373.
Temerin, M., Cerny, K., Lotko, W. and Mozer, F. S., 1982, Observations of double layers and solitary waves in the auroral plasma. Phys. Rev. Lett. 48, 1175-1179.
Tribeche, M., Aoutou, K., Younsi, S. and Amour, R., 2009, Nonlinear positron acoustic solitary waves. Phys. Plasmas 16, 072103.
Tsallis, C., 1988, Possible generalization of Boltzmann-Gibbs statistics. J. Stat. Phys. 52, 479–487.
Washimi H. and Taniuti T., 1966, Propagation of ion-acoustic solitary waves of small amplitude. Phys. Rev. Lett. 17, 996-998.
Journal of the Earth and Space Physics
Volume 48, Issue 2
online publication date: 31 August 2022
August 2022
Pages 453-475

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