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本文研究了同时含有非热(nonthermal)电子和陷俘(trapped)离子分布的复杂等离子体系统中非线性尘埃声波的传播特征. 首先, 利用线性化方法推导得到非线性尘埃声波的色散关系. 接着, 借助Sagdeev势方法推导得到表征非线性尘埃声波运动的二维自治系统、Sagdeev势方程和Sagdeev势函数的具体表达式. 然后, 依据数值模拟的方法分析了多种系统因素对二维自治系统相图的重要影响. 结果表明: 含有nonthermal电子和trapped离子的复杂等离子体系统中同时存在线性周期波、非线性周期波和孤立波. 接下来, 通过讨论Sagdeev势函数随系统参数的变化规律发现: 该复杂等离子体系统中仅存在振幅大于零的压缩型孤立波. 最后, 探讨多种系统因素对非线性尘埃声孤波的振幅、宽度和波形等传播特征的重要影响. 结果显示: 马赫数、nonthermal电子和trapped离子以及尘埃颗粒未扰动的数密度、温度及荷电量等参数对该复杂等离子体系统中非线性尘埃声孤波的振幅、宽度和波形等传播特性均具有显著影响, 且该结果与Sagdeev势函数的分析结果保持一致.
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关键词:
- 非线性尘埃声孤波 /
- Sagdeev势方法 /
- 非热电子分布 /
- 陷俘离子分布
The propagation characteristics of nonlinear dust acoustic solitary waves in a complex plasma system with nonthermal electrons and trapped ions are investigate in this work. The nonlinear dispersion relation of dust acoustic waves is obtained by using the linear method, and the two-dimensional autonomous system governing the motion of nonlinear dust acoustic waves is derived by using the Sagdeev potential method. At the same time, the specific expression of the Sagdeev potential function is obtained based on the Sagdeev potential equation. The numerical simulations are used to analyze the phase portraits of the two-dimensional autonomous system, revealing the linear periodic wave orbits, nonlinear periodic wave orbits, and homoclinic orbits co-existing in the complex dusty plasma system with nonthermal electrons and trapped ions. Furthermore, from the variations of the Sagdeev potential function with different system parameters it follows that only the compressive solitary waves exist in this complex plasma system. The significant influences of various system parameters on the amplitude, width, and waveform of the nonlinear dust acoustic solitary wave in the complex plasma system are discussed in detail. The results demonstrate that the Mach number, the nonthermal electrons and trapped ions, undisturbed dust particle number density, temperature, and charge have important effects on the propagating characteristics of the nonlinear dust acoustic solitary waves in a complex plasma with nonthermal electrons and trapped ions.-
Keywords:
- nonlinear dust acoustic solitary waves /
- Sagdeev potential method /
- nonthermal electron distribution /
- trapped ions distribution
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Google Scholar
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Google Scholar
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图 1 色散关系随不同参数的变化规律
Fig. 1. Variations of dispersion relation with different parameters.
图 2 系统相图随马赫数M的变化 (a) M = 1.3; (b) M = 1.4; (c) M = 1.5
Fig. 2. Variations of system phase diagram with different M: (a) M = 1.3; (b) M = 1.4; (c) M = 1.5.
图 3 系统相图随nonthermal电子数$ \alpha $的变化 (a) α = 0; (b) α = 0.4; (c) α = 0.8
Fig. 3. Variations of system phase diagram with different $ \alpha $: (a) α = 0; (b) α = 0.4; (c) α = 0.8.
图 4 系统相图随trapped离子数b的变化 (a) b = 0.7; (b) b = 0.8; (c) b = 0.9
Fig. 4. Variations of system phase diagram with different b: (a) b = 0.7; (b) b = 0.8; (c) b = 0.9.
图 5 系统相图随参数$ {\sigma _{\mathrm{i}}} $的变化 (a) σi = 0.4; (b) σi = 0.5; (c) σi = 0.6
Fig. 5. Variations of system phase diagram with different $ {\sigma _{\mathrm{i}}} $: (a) σi = 0.4; (b) σi = 0.5; (c) σi = 0.6.
图 6 系统相图随参数$ {\sigma _{\mathrm{d}}} $的变化 (a) σd = 0. 02; (b) σd = 0.05; (c) σd = 0.08
Fig. 6. Variations of system phase diagram with different $ {\sigma _{\mathrm{d}}} $: (a) σd = 0.02; (b) σd = 0.05; (c) σd = 0.08.
图 7 系统相图随参数$ \delta $的变化 (a) δ = 2; (b) δ = 3; (c) δ = 4
Fig. 7. Variations of system phase diagram with different $ \delta $: (a) δ = 2; (b) δ = 3; (c) δ = 4.
图 8 Sagdeev势函数$ V\left( \phi \right) $随不同系统参数的变化规律 (a) α = 0.4, b = 0.8, σi = 0.5, σd = 0.02, δ = 2; (b) M = 1.3, b = 0.8, σi = 0.5, σd = 0.02, δ = 2; (c) M = 1.3, α = 0.4, σi = 0.5, σd = 0.02, δ = 2; (d) M = 1.3, α = 0.4, b = 0.8, σd = 0.02, δ = 2; (e) M = 1.3, α = 0.4, b = 0.8, σi = 0.5, δ = 2; (f) M = 1.3, α = 0.4, b = 0.8, σi = 0.5, σd = 0.02
Fig. 8. Variations of Sagdeev potential $ V\left( \phi \right) $ with different parameters: (a) α = 0.4, b = 0.8, σi = 0.5, σd = 0.02, δ = 2; (b) M = 1.3, b = 0.8, σi = 0.5, σd = 0.02, δ = 2; (c) M = 1.3, α = 0.4, σi = 0.5, σd = 0.02, δ = 2; (d) M = 1.3, α = 0.4, b = 0.8, σd = 0.02, δ = 2; (e) M = 1.3, α = 0.4, b = 0.8, σi = 0.5, δ = 2; (f) M = 1.3, α = 0.4, b = 0.8, σi = 0.5, σd = 0.02.
图 9 孤立波$ \phi $的波形随不同参数的变化规律 (a) α = 0.4, b = 0.8, σi = 0.5, σd = 0.02, δ = 2; (b) M = 1.3, b = 0.8, σi = 0.5, σd = 0.02, δ = 2; (c) M = 1.3, α = 0.4, σi = 0.5, σd = 0.02, δ = 2; (d) M = 1.3, α = 0.4, b = 0.8, σd = 0.02, δ = 2; (e) M = 1.3, α = 0.4, b = 0.8, σi = 0.5, δ = 2; (f) M = 1.3, α = 0.4, b = 0.8, σi = 0.5, σd = 0.02
Fig. 9. Waveform variations of the solitary waves $ \phi $ with different parameters: (a) α = 0.4, b = 0.8, σi = 0.5, σd = 0.02, δ = 2; (b) M = 1.3, b = 0.8, σi = 0.5, σd = 0.02, δ = 2; (c) M = 1.3, α = 0.4, σi = 0.5, σd = 0.02, δ = 2; (d) M = 1.3, α = 0.4, b = 0.8, σd = 0.02, δ = 2; (e) M = 1.3, α = 0.4, b = 0.8, σi = 0.5, δ = 2; (f) M = 1.3, α = 0.4, b = 0.8, σi = 0.5, σd = 0.02.
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[1] Gill T S, Bains A S, Bedi C 2010 Phys. Plasmas. 17 013701
Google Scholar
[2] Zahed H, Emadi E 2016 Phys. Plasmas. 23 083706
Google Scholar
[3] Singh K, Kaur N, Saini N S 2017 Phys. Plasmas. 24 063703
Google Scholar
[4] Akhter T, Mannan A, Mamun A A 2013 Plasma. Phys. Rep. 39 548
Google Scholar
[5] Anowarm G M, Mamuna A 2008 Phys. Lett. 372 5896
Google Scholar
[6] Rasheed A, Tsintsadze N L, Murtaza G 2011 Phys. Plasmas. 18 112701
Google Scholar
[7] Rao N N, Shukla P K, Yu M Y 1990 Planet. Space. Sci. 38 543
Google Scholar
[8] Barkan A, Merlino R L, N D Angelo 1995 Phys. Plasmas 2 3563
Google Scholar
[9] Xie B S, He K F, Huang Z Q 1998 Chin. Phys. Lett. 15 892
Google Scholar
[10] Lin M M, Duan W S 2005 Commun. Theor. Phys. 44 719
Google Scholar
[11] Murad A, Zakir U, Haque Q 2019 Braz. J. Phys. 49 79
Google Scholar
[12] Sarmah B, Devi A, Sarma J 2019 InfoKara 8 115
Google Scholar
[13] Soni P K, Aravindakshan H, Kakad B, Kakad A 2021 Phys. Scr. 96 105604
Google Scholar
[14] Jahan S, Banik S, Chowdhury N A, Mannan A, Mamun A A 2022 Gases 2 22
Google Scholar
[15] 林麦麦, 付颖捷, 宋秋影, 于腾萱, 文惠珊, 蒋蕾 2022 物理学报 71 095203
Google Scholar
Lin M M, Fu Y J, Song Q Y, Yu T X, Wen H S, Jiang L 2022 Acta Phys. Sin. 71 095203
Google Scholar
[16] 林麦麦, 王明月, 蒋蕾 2023 物理学报 72 035201
Google Scholar
Lin M M, Wang M Y, Jiang L 2023 Acta Phys. Sin. 72 035201
Google Scholar
[17] Mamani C 2023 Braz. J. Phys. 53 110
Google Scholar
[18] Saha T, Chatterjee P 2009 Phys. Plasmas 16 013707
Google Scholar
[19] Mamun A A, Shukla P K 2009 Phys. Rev. E 80 037401
Google Scholar
[20] Selim M M 2016 Eur. Phys. J. Plus 131 93
Google Scholar
[21] Gill T S, Kaur H, Bansal S, Saini N S, Bala P 2007 Eur. Phys. J. D 41 151
Google Scholar
[22] Mamun A A, Alam M N, Azad A K 1998 Phys. Plasmas 5 1212
Google Scholar
[23] Mandal D, Lesur M, Gravier E, Sama J N, Guillevic A, Sarazin Y 2023 Plasma Phys. Controlled Fusion 65 055001
Google Scholar
[24] Kaniadakis G, Lavagno A, Quarati P 1996 Phys. Lett. B 369 308
Google Scholar
[25] El-Labany S K, El-Taibany W F, El-Abbasy O M 2007 Chaos, Solitons Fractals 33 813
Google Scholar
[26] Salam M A, Akbar M A, Ali M Z 2021 Results Phys. 26 104376
Google Scholar
[27] Kian R B, Mahdieh M H 2023 Fluid Dyn. Res. 55 35503
Google Scholar
[28] Taylor H A, Daniell R E, Hartle R E, Brinton H C, Bauer S J, Scarf F L 1981 Adv. Space Res. 1 247
Google Scholar
[29] Sabry R, Moslem W M, Shukla P K 2009 Phys. Plasmas 16 032302
Google Scholar
[30] Amour R, Tribeche M 2010 Plasma Phys. 17 063702
Google Scholar
[31] Haider M M, Ferdous T, Duha S S 2014 Cent. Eur. J. Phys. 12 701
Google Scholar
[32] Ghai Y, Saini S N 2017 Astrophys. Space Sci. 362 3
Google Scholar
[33] Annou K, Bahamida S, Annou R 2011 Pramana-J. Phys. 76 513
Google Scholar
[34] Mamun A A 1998 Phys. Scr. 57 258
Google Scholar
[35] Demiray H, Abdikian A 2019 Chaos, Solitons Fractals 121 50
Google Scholar
[36] Rasheed A, Murtaza G, Tsintsadze NL 2010 Phys. Rev. E 82 016403
Google Scholar
[37] El-Shamy E, Al-Chouikh R, El-Depsy A, Al-Wadie N 2016 Phys. Plasmas 23 122122
Google Scholar
[38] Cairns R A, Mamum A A, Bingham R, Boström R, Dendy R O, Nairn C M C, Shukla P K 1995 Geophys. Res. Lett. 22 2709
Google Scholar
[39] Misra A P, Wang Y L 2015 Commun. Nonlinear Sci. Numer. Simul. 22 1360
Google Scholar
[40] Pakzad H R, Tribeche M 2012 J. Fusion Energy 31 611
Google Scholar
[41] El-Labany S K, El-Taibany W F, El-Bedwehy N A, Zedan N A 2017 Plasmas Phys. Rep. 43 756
Google Scholar
[42] Nejoh Y 1992 IEEE Trans. Plasmas Sci. 20 80
Google Scholar
[43] Saha A, Tamang J 2019 Adv. Space Res. 63 1596
Google Scholar
[44] Saha A, Chatterjee P 2014 Astrophys. Space Sci. 350 631
Google Scholar
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