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研究了由尘埃颗粒、电子和非热离子所组成的非磁化热尘埃等离子体中(2 + 1)维非线性尘埃声孤波的传播特征. 首先, 利用约化摄动法推导得到了用来描述(2 + 1)维非线性尘埃声孤波的Kadomtsev-Petviashvili (KP)方程, 并采用行波解法进行了定性分析, 从而获得了该系统的相图及Sagdeev势方程; 然后, 利用数学软件的数值模拟分析方法讨论了等温和绝热两种状态下, 热尘埃等离子体系统中不同参数对KP方程的非线性系数、色散系数、系统相图、Sagdeev势函数及孤立波解的影响. 最终, 研究结果表明: 等温和绝热状态下, 尘埃颗粒的质量、电子和非热离子的温度、数密度及分布状态等多种系统参数对非线性尘埃声孤波的振幅、宽度及波形等传播特征均存在重要影响.
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关键词:
- 非热离子 /
- 约化摄动法 /
- Sagdeev势方法 /
- 尘埃声孤波
The propagation characteristics of (2 + 1) dimensional nonlinear dust acoustic solitary wave in an unmagnetized hot dusty plasma composed of dust particles, electrons and nonthermal ions are studied in the paper. Firstly, the Kadomtsev-Petviashvili (KP) equation, which is used to describe the (2 + 1) dimensional nonlinear dust acoustic solitary wave, is derived by the reduced perturbation method, and the phase diagram and the Sagdeev potential equation of the system are obtained by using the traveling wave solution method. Then, the effects of different parameters in the hot dusty plasma system on the nonlinear coefficient, dispersion coefficient of the KP equation, system phase diagrams, Sagdeev potential function and the solitary wave solution in isothermal and adiabatic states are discussed by using numerical simulation and analysis method of mathematical software. Finally, the results show that the mass of dust particles, temperature, number density and distribution state of electrons and nonthermal ions have important effects on the amplitude, width and waveform of the nonlinear dust acoustic solitary wave under isothermal and adiabatic conditions.-
Keywords:
- nonthermal ions /
- reductive perturbation method /
- Sagdeev potential method /
- dust acoustic solitary wave
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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Google Scholar
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图 1
${\sigma _{\rm{d}}}$ 取值不同时, 非线性系数A随参数α的变化 (a) 等温状态,$\gamma = 1$ ; (b) 绝热状态,$\gamma = 3$ Fig. 1. Nonlinear coefficient A with respect to the parameter α for different values of
${\sigma _{\rm{d}}}$ : (a) Isothermal state; (b) adiabatic state.
图 2 (a)—(c)
${m_{\rm{d}}}, \;\mu, \;{\sigma _{\rm{i}}}$ 取值不同时, 等温状态($\gamma = 1$ )下非线性系数A随参数α的变化Fig. 2. Nonlinear coefficient A with respect to the parameter α in isothermal state under the condition of different values of (a)−(c)
${m_{\rm{d}}}, \;\mu, \;{\sigma _{\rm{i}}}$ .
图 3 (a)—(c)
${m_{\rm{d}}}, \;\mu, \;{\sigma _{\rm{i}}}$ 取值不同时, 绝热状态($\gamma = 3$ )下非线性系数A随参数α的变化Fig. 3. Nonlinear coefficient A with respect to the parameter α in adiabatic state under the condition of different values of (a)−(c)
${m_{\rm{d}}}, \;\mu, \;{\sigma _{\rm{i}}}$ .
图 4 色散系数B随参数
${v_0}$ 的变化 (a), (b) 等温状态,$\gamma = 1$ ; (c), (d) 绝热状态,$\gamma = 3$ Fig. 4. Dispersion coefficient A with respect to the parameter
${v_0}$ in (a), (b) isothermal state and (c), (d) adiabatic state, respectively.
图 5 相平面
$\left( {{\phi _1}, \;\psi } \right)$ 及轨线分布图 (a)$ \gamma = 1 $ ; (b)$ \gamma = 3 $ Fig. 5. Track of phase plane: (a)
$ \gamma = 1 $ ; (b)$ \gamma = 3 $ .
图 6
${\sigma _{\rm{d}}}$ 取不同值时, 等温状态($\gamma = 1$ )下Sagdeev势$V\left( {{\phi _1}} \right)$ 随${\phi _1}$ 的变化Fig. 6. The Sagdeev potential
$V\left( {{\phi _1}} \right)$ with respect to${\phi _1}$ in isothermal state for different values of${\sigma _{\rm{d}}}$ .
图 7
${\sigma _{\rm{d}}}$ 取不同值时, 绝热状态($\gamma = 3$ )下Sagdeev势$V\left( {{\phi _1}} \right)$ 随${\phi _1}$ 的变化Fig. 7. The Sagdeev potential
$V\left( {{\phi _1}} \right)$ with respect to${\phi _1}$ in adiabatic state for different values of${\sigma _{\rm{d}}}$ .
图 8 (a)—(d)
$\alpha, \;{\sigma _{\rm{i}}}, \;\mu, \;{m_{\rm{d}}}$ 取不同值, 等温状态($\gamma = 1$ )下Sagdeev势$V\left( {{\phi _1}} \right)$ 随$ {\phi _1} $ 的变化Fig. 8. The Sagdeev potential
$V\left( {{\phi _1}} \right)$ with respect to$ {\phi _1} $ in isothermal state under the condition of different values of (a)−(d)$\alpha, \;{\sigma _{\rm{i}}}, \;\mu, \;{m_{\rm{d}}}$ .
图 9 (a)—(d)
$\alpha, \;{\sigma _{\rm{i}}}, \;\mu, \;{m_{\rm{d}}}$ 取不同值, 绝热状态($\gamma = 3$ )下Sagdeev势$V\left( {{\phi _1}} \right)$ 随$ {\phi _1} $ 的变化Fig. 9. The Sagdeev potential
$V\left( {{\phi _1}} \right)$ with respect to$ {\phi _1} $ in adiabatic state under the condition of different values of (a)−(d)$\alpha, \;{\sigma _{\rm{i}}}, \;\mu, \;{m_{\rm{d}}}$ .
图 10 α取值不同时, 孤立波
$ {\phi _1} $ 的波形变化 (a) 等温状态,$\gamma = 1$ ; (b) 绝热状态,$\gamma = 3$ Fig. 10. Waveform of solitary waves
$ {\phi _1} $ for different values of α: (a) Isothermal state; (b) adiabatic state, respectively.
图 11 (a)—(d)
${\sigma _{\rm{d}}}, \;{\sigma _{\rm{i}}}, \;\mu, \;{m_{\rm{d}}}$ 取不同值时, 等温状态($\gamma = 1$ )下孤立波$ {\phi _1} $ 的波形变化Fig. 11. Waveform of solitary waves
$ {\phi _1} $ in isothermal state under the condition of different values of (a)−(d)${\sigma _{\rm{d}}}, \;{\sigma _{\rm{i}}}, \;\mu, \;{m_{\rm{d}}}$ .
图 12 (a)—(d)
${\sigma _{\rm{d}}}, \;{\sigma _{\rm{i}}}, \;\mu, \;{m_{\rm{d}}}$ 取不同值时, 绝热状态($\gamma = 3$ )下孤立波$ {\phi _1} $ 的波形变化Fig. 12. Waveform of solitary waves
$ {\phi _1} $ in adiabatic state under the condition of different values of (a)−(d)${\sigma _{\rm{d}}}, \;{\sigma _{\rm{i}}}, \;\mu, \;{m_{\rm{d}}}$ . -
[1] Rosenberg M, Kalman G 1997 Phys. Rev. E 56 7166
Google Scholar
[2] Gill T S, Bains A S, Bedi C 2010 Phys. Plasmas 17 013701
Google Scholar
[3] El-Taibany W F, El-Bedwehy N A, El-Shamy E F 2011 Phys. Plasmas 18 033703
Google Scholar
[4] Sabry R, Moslem W M, Shukla P K 2009 Phys. Plasmas 16 032302
Google Scholar
[5] Singh K, Kaur N, Saini N S 2017 Phys. Plasmas 24 063703
Google Scholar
[6] Melandsø F, Goree J 1995 Phys. Rev. E 52 5312
[7] Gurnett D A, Ansher J A, Kurth W S, Granroth L J 1997 Geophys. Res. Lett. 24 3125
[8] Rao N N, Shukla P K, Yu M Y 1990 Planet. Space Sci. 38 543
Google Scholar
[9] Barkan A, Merlino R L, Angelo D N 1995 Phys. Plasmas 2 3563
Google Scholar
[10] Ma J X, Liu J 1997 Phys. Plasmas 4 253
Google Scholar
[11] Xie B S, He K F, Huang Z Q 1998 Chin. Phys. Lett. 15 892
Google Scholar
[12] El-Taibany W F 2013 Phys. Plasmas 20 093701
Google Scholar
[13] Paul A, Mandal G, Mamun A A, Amin M R 2013 Phys. Plasmas 20 104505
Google Scholar
[14] El-Labany S K, El-Taibany W F, El-Tantawy A A, Zedan N A 2020 Contrib. Plasma Phys. 60 e202000049
[15] Schamel H 1986 Phys. Rep. 140 161
Google Scholar
[16] Ghosh S, Bharuthram R, Khan M, Gupta M R 2004 Phys. Plasmas 11 3602
Google Scholar
[17] El-Taibany W F, Wadati Miki, Sabry R 2007 Phys. Plasmas 14 032304
[18] Ghosh U N, Chatterjee P 2012 Indian J. Phys. 86 407
Google Scholar
[19] Bliokh P V, Yaroshenko V V 1985 Sov. Astron. 29 330
[20] Seadawy A R, Lu D 2016 Results Phys. 6 590
Google Scholar
[21] Bhakta S, Ghosh U, Sarkar S 2017 Phys. Plasmas 24 023704
Google Scholar
[22] Iqbal M, Seadawy A R, Lu D, Xia X 2019 Mod. Phys. Lett. A 34 1950309
Google Scholar
[23] El-Bedwehy N A, El-Taibany W F 2020 Phys. Plasmas 27 012107
Google Scholar
[24] Tasnim I, Masud M M, Mamun A A 2014 J. Korean Phys. Soc. 64 987
Google Scholar
[25] Emamuddin M, Mamun A A 2018 Phys. Plasmas 25 013708
Google Scholar
[26] Mendoza-Briceño C A, Russel S M, Mamun A A 2000 Planet. Space Sci. 48 599
Google Scholar
[27] 王红艳, 段文山 2007 物理学报 56 3977
Google Scholar
Wang H Y, Duan W S 2007 Acta Phys. Sin. 56 3977
Google Scholar
[28] Mamun A A, Cairns R A, Shukla P K 1996 Phys. Plasmas 3 2610
Google Scholar
[29] Cairns R A, Mamun A A, Bingham R, Bostrom R, Dendy R O, Nairn C M C, Shukla P K 1995 Geophys. Res. Lett. 22 2709
Google Scholar
[30] Mamuna A A, Russell S M, Cesar A, Mendoza-Briceño C A, Alamb M N, Datta T K, Das A K 2000 Planet. Space Sci. 48 163
Google Scholar
[31] Kotsarenko N Ya, Koshevaya S V, Stewart G A, Maravilla D 1998 Planet. Space Sci. 46 429
Google Scholar
[32] Wang Z, Gurnett D A, Averkamp T F, Persoon A M, Kurth W S 2006 Planet. Space Sci. 54 957
Google Scholar
[33] Pickett J S, Kurth W S, Gurnett D A, Huff R L, Faden J B, Averkamp T F, Píša D, Jones G H 2015 J. Geophys. Res. Space Phys. 120 6569
Google Scholar
[34] El-Labany S K, Safi F M, Moslem W M 2007 Planet. Space Sci. 55 2192
Google Scholar
[35] Mamun A A, Shukla P K 2011 J. Plasma Phys. 77 437
Google Scholar
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