有界空间中放电尘埃等离子体稳定性的研究
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摘要
近年来,人们对尘埃等离子体的研究产生了浓厚的兴趣,如各种低频波的不稳定性和非线性相干结构(孤波)的特点等。在尘埃等离子体中,尘埃放电现象会引起耗散等效应,这对等离子体系统的稳定性会产生很大影响。目前,尘埃电荷扰动是等离子体的热门研究课题之一。然而,绝大多数此类研究仅限于无界尘埃等离子体。众所周知,有界性是实验室等离子体的显著特点,而且空间等离子体环境中也能自动形成各种局域化结构。在边界效应的影响下,等离子波谱将被离散化。因此,边界效应又是等离子体的另一研究热点。
本文运用正交模分析法研究了尘埃电荷扰动等因素对尘埃等离子体中静电低频波色散关系的影响。同时,也运用约化摄动法分析了尘埃等离子体中一三维尘埃声孤立波的特点。
本文首先研究了无界尘埃等离子体中低频波的色散关系,发现尘埃绝热电荷扰动、外磁场、粒子碰撞和斜传效应对尘埃低频波都有强烈影响。接着,本文讨论了一有界尘埃等离子体中尘埃声波的色散关系,结果表明,边界效应使径向波数离散化,绝热电荷扰动、粒子碰撞和尘埃大小等因素对尘埃声波都有明显影响。后来,我们又分析了边界效应、非绝热电荷扰动、外磁场和快离子效应对一尘埃等离子体稳定性的影响,数值结果显示产生了两种不同模式的低频波。最后,我们对一三维尘埃声孤波的性质进行了详细的探讨,发现只存在稀疏型孤波,而且外磁场和粒子碰撞只对波宽有影响。
In recent years, there has been great interesting in studying dusty plasmas, such as the stability of low frequency waves and the properties of nonlinear coherent structures (solitary wave) et al. The effects of dissipation et al. are produced by the dust charging in a dusty plasmas, this will strongly influence the stability of the dusty plasmas. Nowadays, dust charge fluctuation is one of interesting topics in studying plasmas. However, most of these investigations are only concerned with a dusty plasmas of infinite extent. As is well known, the boundary is the distinct character in experiment plasmas, moreover, various localized structures are automatically formed in space plasmas environments. Plasmas wave spectrum is discrete due to the boundary effect. So the boundary effect is another focus in studying plasmas.
In this paper, by carrying out a normal mode analysis, the effects of dust charge fluctuation et al. on the dispersion relation of low frequency electrostatic waves are investigated. Moreover, the features of a 3-D dust acoustic solitary waves in a dusty plasmas are also studied by using the reductive perturbation method.
In the present thesis, firstly, the dispersion relation of an infinite dusty plasmas is studied, it is found that the effects of adiabatic variation, the external magnetic field, the particle collisions and the obliqueness have strong influence on dusty low frequency waves. Secondly, the dispersion relation of dust acoustic wave in a bounded dusty plasmas is discussed, it is shown that the radial wave number is discrete because of the boundary effect, and the dust acoustic wave is obviously affected by the effects of adiabatic dust charge fluctuation, the particle collisions and the dust grain size. Furthermore, the influence of the boundary effect, nonadiabatic dust charge fluctuation, magnetized field and fast ions etc on the low frequency waves in a dusty plasmas is analyzed. It is observed that there exist two different wave modes. Lastly, we studied the properties of a 3-D dust acoustic solitary waves in a dusty plasmas. It is clear that the rarefactive solitary waves only exist, arid the external magnetic field and collisional frequency just modified the width of the waves.
本文运用正交模分析法研究了尘埃电荷扰动等因素对尘埃等离子体中静电低频波色散关系的影响。同时,也运用约化摄动法分析了尘埃等离子体中一三维尘埃声孤立波的特点。
本文首先研究了无界尘埃等离子体中低频波的色散关系,发现尘埃绝热电荷扰动、外磁场、粒子碰撞和斜传效应对尘埃低频波都有强烈影响。接着,本文讨论了一有界尘埃等离子体中尘埃声波的色散关系,结果表明,边界效应使径向波数离散化,绝热电荷扰动、粒子碰撞和尘埃大小等因素对尘埃声波都有明显影响。后来,我们又分析了边界效应、非绝热电荷扰动、外磁场和快离子效应对一尘埃等离子体稳定性的影响,数值结果显示产生了两种不同模式的低频波。最后,我们对一三维尘埃声孤波的性质进行了详细的探讨,发现只存在稀疏型孤波,而且外磁场和粒子碰撞只对波宽有影响。
In recent years, there has been great interesting in studying dusty plasmas, such as the stability of low frequency waves and the properties of nonlinear coherent structures (solitary wave) et al. The effects of dissipation et al. are produced by the dust charging in a dusty plasmas, this will strongly influence the stability of the dusty plasmas. Nowadays, dust charge fluctuation is one of interesting topics in studying plasmas. However, most of these investigations are only concerned with a dusty plasmas of infinite extent. As is well known, the boundary is the distinct character in experiment plasmas, moreover, various localized structures are automatically formed in space plasmas environments. Plasmas wave spectrum is discrete due to the boundary effect. So the boundary effect is another focus in studying plasmas.
In this paper, by carrying out a normal mode analysis, the effects of dust charge fluctuation et al. on the dispersion relation of low frequency electrostatic waves are investigated. Moreover, the features of a 3-D dust acoustic solitary waves in a dusty plasmas are also studied by using the reductive perturbation method.
In the present thesis, firstly, the dispersion relation of an infinite dusty plasmas is studied, it is found that the effects of adiabatic variation, the external magnetic field, the particle collisions and the obliqueness have strong influence on dusty low frequency waves. Secondly, the dispersion relation of dust acoustic wave in a bounded dusty plasmas is discussed, it is shown that the radial wave number is discrete because of the boundary effect, and the dust acoustic wave is obviously affected by the effects of adiabatic dust charge fluctuation, the particle collisions and the dust grain size. Furthermore, the influence of the boundary effect, nonadiabatic dust charge fluctuation, magnetized field and fast ions etc on the low frequency waves in a dusty plasmas is analyzed. It is observed that there exist two different wave modes. Lastly, we studied the properties of a 3-D dust acoustic solitary waves in a dusty plasmas. It is clear that the rarefactive solitary waves only exist, arid the external magnetic field and collisional frequency just modified the width of the waves.
引文
铩颷1]杜世刚.等离子体物理[M],原子能出版社(1998)2.
[2]杜世刚.等离子体物理[M],原子能出版社(1998)91.
[3]Vladimirov S V,Ostrikov K.2004 Physics Reports.393 175.
[4]Lin I,Ying-Ju Lai,Wen-Tau Juan,Ming-Hua Chang,Hong-Yu Chue.2002 Vacuum66 285.
[5]Melandso F,Goree J.1995 Phys.Rev.E 52 5312.
[6]Lin I,Juan W T,Chiang C H.2002 Science 272 1626.
[7]Barkan A,D'Angelo N,Merlino R L.1994 Phys.Rev.Lett.73 3093.
[8]Rosenberg M,Mendis D A.1995 IEEE Trans.Plasmas Sci.23 177.
[9]Sickafoose A A,Colwell J E,Horanyi M,Robertson S.2000 Phys.Rev.Lett.84 6034.
[10]Sodha M S,Guha S,1971 Adv.Plasma Phys.4 219.
[11]Yakubov I T,Khrapak A G.1989 Sov.Technol.Rev.B 2 269.
[12]Feuerbacher B,Fitton B.1972 J.Appl.Phys.43 1563.
[13]Chow V W,Rosenberg M.1994 IEEE Trans.Plasma Sci.22 179.
[14]Havnes O,Goertz C K,Morrill G E,Lp W.1987 J.Geophys.Res.92 2281.
[15]Ma J X,Liu J.1997 Phys.Plasmas 4 253.
[16]Fortov V E,Nefedov A P,Petrov OF,Samarian A A,Chernyschev A V.1996 Phys.Rev.E 54 R2236.
[17]Khodataev Y K,Khrapak S A,Nefedov A P,Petrov O F.1998.Phys.Rev.(?)57 7886.
[18]Nejoh Y N.1997 Phys.Plasmas 4 2813.
[19]Geortz C K.1989 Rev.Geophys 27 271.
[20]Samarian A A,Vaulina O S,Nefedov A P,Fortov V E,James B W,Petrov O F.2001Phys.Rev.E 64 056407-1.
[21]Chang J S,Spariosu K.1993 J.Phys.Soc.Jpn.62 97.
[22]Barkan A,Merlino R L.Angelo N D.1995 Phys.Plasmas 2 3563.
[23]Barkan A,D'Angelo N,Merlino R L.1995 Planet.Space Sci.43 905.
[24]Barkan A,D'Angelo N,Merlino R L.1996 Planet.Space Sci.44 239.
[25]Merlino R L,Barkan A,Thompson C,D'Angelo N.1998 Phys.Plasmas 5 1637.
[26]Molotokov V I,Nefedov A P,Torchinskii V M etc..1999 JETP 89 477.
[27]Nakamura Y,Bailung H,Shukla P K.1999 Phys,Rev.Lett.83 1602.
[28]Pieper J B,Goree J.1996 Phys,Rev.Lett.77 3137.
[29]Prabhakara H R,Tana P L.1996 Phys.Plasmas 3 3176.
[30]Thomas E Jr,Watson M.1999 Phys.Plasmas 6 4111.
[31]Thompson C,Barkan A,D'Angelo,Merlino R L.1997 Phys.Plasmas 4 2331.
铩颷32]Heydari-Malayeri M,Rosa M R,Zinnecker H etc.1999 Astwn.Astrophys.344 848.
[33]Carlquist P,Gahm G F,Kirsten H.2003 Astron.Astrophys.403 399.
[34]Ellis R F,Marden-Marshall E.1979 Phys.Fluids 22 2137.
[35]Marden-Marshall E,Ellis R F,Walsh J E.1986 Plasma Phys.Controlled Fusion 281461.
[36]Vranjes J,Okamoto A,Yoshimura S,Poedts S,Kono M,Tanaka M Y.2002 Phys.Rev.Lett.89 265002.
[37]Zhang L.1992 Plasma Phys.Controlled Fusion 34 501.
[38]Perkins F W,Jassby D L.1971 Phys.fluids 14 102.
[39]Jassby D L.1972 Phys.fluids 15 1590.
[40]Kent G I.1969 Phys.fluids 12 2140.
[41]Rao N N,Shukla P K,Yu M Y.1990 Planet.Space Sci.38 543.
[42]Shulda P K,Silin V P.1992 Phys.Scr.45 508.
[43]D'Angelo N,Merlino R L.1996 Planet.Space Sci.44 1593.
[44]D'Angelo N.2002 Phys.Lett.A 304 102.
[45]D'Angelo N.1998 Planet.Space Sci.46 1671.
[46]D'Angelo N.2001 Phys.Lett.A 292 195.
[47]Ghosh S,Bharuthram R,Khan M et al.2004 Phys.Plasmas 11 3602.
[48]Zhang Li-ping,Xue Ju-kui.2005 Chin.Phys.14 2052.
[49]Cairns R A,Mamun A A,Bingham R,Dendy R O,Bostrom R,Shukla P K,Nai(?)OM C.1995 Geophys.Res.Lett.22 2709.
[50]Zhang Li-ping,Xue Ju-kui.2005 Chaos,Solitons and Fractals 23 543.
[51]Chu J H,Du J B,Lin I.1994 J.Phys.D 27 296.
[52]Vranjes J,Poedts S.2004 Phys.Plasmas 11 891.
[53]Vranjes J,Poedts S.2004 Phys.Plasmas 11 2178.
[54]Shukla P K,Rosenberg M.1999 Phys.Plasmas 6 1038.
[55]Shukla P K,Mamun A A.2001 J.Plasma Phys.65 97.
[56]Baines M F,Williams I P,Asebiomo R L.1965 Mon.Not.R.Astron.Soc.130 63.
[57]Melandso F,Askalsen F T,Haynes O.1993 Plant Space Sci.41 312.
[58]Winske D,Jones M E.1995 IEEE Trans.Plasmas Sci.23 188.
[59]Melandso F.1996 Phys.Plasmas 3 3890.
[60]Barnes M S.1992 Phys.Rev.Lett.68 313.
[61]Wei Nan-xia,Xue Ju-kui.2006 Phys.Plasmas.13 052101.
[62]Varma R K,Shukla P K,Krishan V.1993 Phys.Rev.E 47 3612.
[63]Melandso F,Askalsen F T,Havnes O.1993 Plant Space Sci.41 321.
[64]Jana M R,Sen A,Kaw P K.1993 Phys.Rev.E 48 3930.
铩颷65]Khrapak S A,Morfill G.2001 Phys.Plasmas.8 2629.
[66]Gupt M R,Sarkar S,Ghosh S,Debnath M,Khan M.2001 Phys.Rev.E 63 046406-1.
[67]Xie B S.2000 Chin.Phys.9 922.
[68]Ghosh S,Sarkan S,Khan M et al.2002 Phys.Plasmas 9 1150.
[69]Xue Ju-Kui.2005 Eur.Phys.J.D,DOI:10.1140/epjd/e2005-00041-9.
[70]Allen J E.1992 Phys.Scr.45 497.
[71]Rubinstein J,Laframboise J G.1982 Phys.Fluid 25 1174.
[72]Singh S V,Rao N N.1998 J.Plasma Phys.60 541.
[73]Hartquist T W,Havnes O,Morfill G E.1992 Fundam Cosmic Phys.15 107.
[74]Bingham R,U de Angelis,Tsytovich V N,Havnes O.1991 Phys Fluids B 3 811.
[75]Chu J H,I Lin.1994 Phys.Rev.Lett.72 4009.
[76]Xie Bai-Song,He Kai-Fen,Huang Zu-Qia.1998 Phys.Lett.A 247 403.
[77]Mamun A A,Russell S M,Mendoza-Briceno C A,Alam M N,Datta T K,Das A K.2000 Planet.Space Sci.48 163.
[2]杜世刚.等离子体物理[M],原子能出版社(1998)91.
[3]Vladimirov S V,Ostrikov K.2004 Physics Reports.393 175.
[4]Lin I,Ying-Ju Lai,Wen-Tau Juan,Ming-Hua Chang,Hong-Yu Chue.2002 Vacuum66 285.
[5]Melandso F,Goree J.1995 Phys.Rev.E 52 5312.
[6]Lin I,Juan W T,Chiang C H.2002 Science 272 1626.
[7]Barkan A,D'Angelo N,Merlino R L.1994 Phys.Rev.Lett.73 3093.
[8]Rosenberg M,Mendis D A.1995 IEEE Trans.Plasmas Sci.23 177.
[9]Sickafoose A A,Colwell J E,Horanyi M,Robertson S.2000 Phys.Rev.Lett.84 6034.
[10]Sodha M S,Guha S,1971 Adv.Plasma Phys.4 219.
[11]Yakubov I T,Khrapak A G.1989 Sov.Technol.Rev.B 2 269.
[12]Feuerbacher B,Fitton B.1972 J.Appl.Phys.43 1563.
[13]Chow V W,Rosenberg M.1994 IEEE Trans.Plasma Sci.22 179.
[14]Havnes O,Goertz C K,Morrill G E,Lp W.1987 J.Geophys.Res.92 2281.
[15]Ma J X,Liu J.1997 Phys.Plasmas 4 253.
[16]Fortov V E,Nefedov A P,Petrov OF,Samarian A A,Chernyschev A V.1996 Phys.Rev.E 54 R2236.
[17]Khodataev Y K,Khrapak S A,Nefedov A P,Petrov O F.1998.Phys.Rev.(?)57 7886.
[18]Nejoh Y N.1997 Phys.Plasmas 4 2813.
[19]Geortz C K.1989 Rev.Geophys 27 271.
[20]Samarian A A,Vaulina O S,Nefedov A P,Fortov V E,James B W,Petrov O F.2001Phys.Rev.E 64 056407-1.
[21]Chang J S,Spariosu K.1993 J.Phys.Soc.Jpn.62 97.
[22]Barkan A,Merlino R L.Angelo N D.1995 Phys.Plasmas 2 3563.
[23]Barkan A,D'Angelo N,Merlino R L.1995 Planet.Space Sci.43 905.
[24]Barkan A,D'Angelo N,Merlino R L.1996 Planet.Space Sci.44 239.
[25]Merlino R L,Barkan A,Thompson C,D'Angelo N.1998 Phys.Plasmas 5 1637.
[26]Molotokov V I,Nefedov A P,Torchinskii V M etc..1999 JETP 89 477.
[27]Nakamura Y,Bailung H,Shukla P K.1999 Phys,Rev.Lett.83 1602.
[28]Pieper J B,Goree J.1996 Phys,Rev.Lett.77 3137.
[29]Prabhakara H R,Tana P L.1996 Phys.Plasmas 3 3176.
[30]Thomas E Jr,Watson M.1999 Phys.Plasmas 6 4111.
[31]Thompson C,Barkan A,D'Angelo,Merlino R L.1997 Phys.Plasmas 4 2331.
铩颷32]Heydari-Malayeri M,Rosa M R,Zinnecker H etc.1999 Astwn.Astrophys.344 848.
[33]Carlquist P,Gahm G F,Kirsten H.2003 Astron.Astrophys.403 399.
[34]Ellis R F,Marden-Marshall E.1979 Phys.Fluids 22 2137.
[35]Marden-Marshall E,Ellis R F,Walsh J E.1986 Plasma Phys.Controlled Fusion 281461.
[36]Vranjes J,Okamoto A,Yoshimura S,Poedts S,Kono M,Tanaka M Y.2002 Phys.Rev.Lett.89 265002.
[37]Zhang L.1992 Plasma Phys.Controlled Fusion 34 501.
[38]Perkins F W,Jassby D L.1971 Phys.fluids 14 102.
[39]Jassby D L.1972 Phys.fluids 15 1590.
[40]Kent G I.1969 Phys.fluids 12 2140.
[41]Rao N N,Shukla P K,Yu M Y.1990 Planet.Space Sci.38 543.
[42]Shulda P K,Silin V P.1992 Phys.Scr.45 508.
[43]D'Angelo N,Merlino R L.1996 Planet.Space Sci.44 1593.
[44]D'Angelo N.2002 Phys.Lett.A 304 102.
[45]D'Angelo N.1998 Planet.Space Sci.46 1671.
[46]D'Angelo N.2001 Phys.Lett.A 292 195.
[47]Ghosh S,Bharuthram R,Khan M et al.2004 Phys.Plasmas 11 3602.
[48]Zhang Li-ping,Xue Ju-kui.2005 Chin.Phys.14 2052.
[49]Cairns R A,Mamun A A,Bingham R,Dendy R O,Bostrom R,Shukla P K,Nai(?)OM C.1995 Geophys.Res.Lett.22 2709.
[50]Zhang Li-ping,Xue Ju-kui.2005 Chaos,Solitons and Fractals 23 543.
[51]Chu J H,Du J B,Lin I.1994 J.Phys.D 27 296.
[52]Vranjes J,Poedts S.2004 Phys.Plasmas 11 891.
[53]Vranjes J,Poedts S.2004 Phys.Plasmas 11 2178.
[54]Shukla P K,Rosenberg M.1999 Phys.Plasmas 6 1038.
[55]Shukla P K,Mamun A A.2001 J.Plasma Phys.65 97.
[56]Baines M F,Williams I P,Asebiomo R L.1965 Mon.Not.R.Astron.Soc.130 63.
[57]Melandso F,Askalsen F T,Haynes O.1993 Plant Space Sci.41 312.
[58]Winske D,Jones M E.1995 IEEE Trans.Plasmas Sci.23 188.
[59]Melandso F.1996 Phys.Plasmas 3 3890.
[60]Barnes M S.1992 Phys.Rev.Lett.68 313.
[61]Wei Nan-xia,Xue Ju-kui.2006 Phys.Plasmas.13 052101.
[62]Varma R K,Shukla P K,Krishan V.1993 Phys.Rev.E 47 3612.
[63]Melandso F,Askalsen F T,Havnes O.1993 Plant Space Sci.41 321.
[64]Jana M R,Sen A,Kaw P K.1993 Phys.Rev.E 48 3930.
铩颷65]Khrapak S A,Morfill G.2001 Phys.Plasmas.8 2629.
[66]Gupt M R,Sarkar S,Ghosh S,Debnath M,Khan M.2001 Phys.Rev.E 63 046406-1.
[67]Xie B S.2000 Chin.Phys.9 922.
[68]Ghosh S,Sarkan S,Khan M et al.2002 Phys.Plasmas 9 1150.
[69]Xue Ju-Kui.2005 Eur.Phys.J.D,DOI:10.1140/epjd/e2005-00041-9.
[70]Allen J E.1992 Phys.Scr.45 497.
[71]Rubinstein J,Laframboise J G.1982 Phys.Fluid 25 1174.
[72]Singh S V,Rao N N.1998 J.Plasma Phys.60 541.
[73]Hartquist T W,Havnes O,Morfill G E.1992 Fundam Cosmic Phys.15 107.
[74]Bingham R,U de Angelis,Tsytovich V N,Havnes O.1991 Phys Fluids B 3 811.
[75]Chu J H,I Lin.1994 Phys.Rev.Lett.72 4009.
[76]Xie Bai-Song,He Kai-Fen,Huang Zu-Qia.1998 Phys.Lett.A 247 403.
[77]Mamun A A,Russell S M,Mendoza-Briceno C A,Alam M N,Datta T K,Das A K.2000 Planet.Space Sci.48 163.