二维磁化尘埃等离子体模拟研究
|
摘要
尘埃等离子体物理是近年来快速发展起来的新兴学科,特别是上世纪90年代初尘埃等离子体晶体结构发现以来,以尘埃等离子体结构特性、尘埃等离子体波、输运过程为代表的相关研究,成为尘埃等离子体物理研究的重要组成部分。本文采用分子动力学模拟方法对二维磁化尘埃等离子体的动力学特性以及结构特征进行了研究。主要内容包括：考虑等离子体密度分布变化,得到修正屏蔽库伦势的修正解,在此基础上应用分子动力学模拟方法讨论了二维尘埃等离子体系统的动力学以及结构特性,结果发现随着磁场强度增强,等离子体动力学扩散能力依次减弱,在极限条件下,系统的扩散能力显著降低,系统内粒子的受力发生了显著变化,系统结构也发生了明显变化,系统内粒子将会呈圆球状聚合；同时我们还考虑二维模拟系统的不同初始分布、各种组成成分、带电尘埃粒子间不同相互作用势以及外均匀磁场等因素,对二维尘埃等离子体系统的基本物理过程-弛豫进行了讨论；最后采用速度定标法对二维模拟系统进行加热,我们初步研究了二维尘埃等离子体系统的过热固态结构。
此外,本文还对杂质离子对反场箍缩下的磁约束聚变温度梯度的影响进行了模拟,并给出了反场箍缩下的杂质模的回旋动理学模拟结果。在对反场箍缩(Reversed Field Pinch-RFP)等离子体的微观漂移不稳定性的研究中,我们利用回旋动理学积分本征方程方法研究了杂质对离子温度梯度(Ion Temperature Gradient-ITG)模的影响。结果表明RFP等离子体中杂质对ITG模的影响与tokamak等离子体中的相关结果类似,当杂质离子和电子的密度梯度方向相反时,杂质效应能增强ITG模的不稳定性。当杂质效应足够强的时候,会有杂质模的出现。同时还发现当电子密度分布比较平坦的时候,RFP中的杂质模比tokamak中的杂质模要稳定的多；只有当电子的密度分布非常陡峭的时候,RFP和tokamak等离子体中杂质模才是同样容易被激发的;同时,我们又把该本征方程方法应用于RFX-mod实验中,发现在等离子体边缘会有ITG模和杂质模的出现,并可能对该区域的反常输运有影响。
In the early1990s, particularly since the observation of crystal of dusty plasmas in the laboratory, the dusty plasmas have been extensively studied by the experiments, simulations and theories. Fields such as the structure of dusty plasmas, the transport of dusty plasmas and the waves of dusty plasmas turn out to be the very interested subjects for researchers. This thesis focuses on the structure and dynamical properties of the two-dimensional magnetized dusty plasmas through the molecular dynamical simulation method. It mainly contains the following studies: the modified screen Coulomb is derived with considering the plasmas gradient. Based on the modified screen Coulomb potential, the dynamical and structural properties of two-dimensional dusty plasmas is investigated. The fundamental process of relaxation is discussed by changing the initial velocity distribution, the components of dusty plasmas system and the interaction of the charged particles as well as the external magnetic field. The ordered structure above the melting point, named as super-heated solid, of the dusty plasmas is roughly studied by using the velocity scaling method in order to heat the dusty plasmas. In addition, this thesis shows the simulation results of temperature gradient mode of reversed field pinch with including the impurity ions, and the gyro-kinetic simulation of impurity mode.
On the other hand, the ion temperature gradient (ITG) driven modes in the presence of impurity ions are studied in the toroidal reversed field pinch (RFP) plasmas by solving the gyrokinetic integral eigenmode equation. The detailed numerical studies resemble the effects of impurities in tokamak plasmas. For instance, the impurities enhance the ion temperature gradient-driving if the impurity populations have density gradients which are opposite to that of the electrons. In addition, the impurity mode will appear when the impurity ion effecs are strong enough.The further study of impurity mode in a RFP using the gyrokinetic integral equation reveals that the impurity mode in RFP plasmas is relatively more difficult to be excited than that in tokamak plasmas under similar geometry when density profile is flat, whereas it turns out to be easier when density profile is rather peaked. In addition, the analysis of the typical RFX-mod experiments is performed and the results show that the ITG and impurity driven modes may be linearly unstable in the edge region of the plasmas when the observed radial profiles of the impurity ions are considered. And these modes may make a considerable contribution to the transport in this region.
此外,本文还对杂质离子对反场箍缩下的磁约束聚变温度梯度的影响进行了模拟,并给出了反场箍缩下的杂质模的回旋动理学模拟结果。在对反场箍缩(Reversed Field Pinch-RFP)等离子体的微观漂移不稳定性的研究中,我们利用回旋动理学积分本征方程方法研究了杂质对离子温度梯度(Ion Temperature Gradient-ITG)模的影响。结果表明RFP等离子体中杂质对ITG模的影响与tokamak等离子体中的相关结果类似,当杂质离子和电子的密度梯度方向相反时,杂质效应能增强ITG模的不稳定性。当杂质效应足够强的时候,会有杂质模的出现。同时还发现当电子密度分布比较平坦的时候,RFP中的杂质模比tokamak中的杂质模要稳定的多；只有当电子的密度分布非常陡峭的时候,RFP和tokamak等离子体中杂质模才是同样容易被激发的;同时,我们又把该本征方程方法应用于RFX-mod实验中,发现在等离子体边缘会有ITG模和杂质模的出现,并可能对该区域的反常输运有影响。
In the early1990s, particularly since the observation of crystal of dusty plasmas in the laboratory, the dusty plasmas have been extensively studied by the experiments, simulations and theories. Fields such as the structure of dusty plasmas, the transport of dusty plasmas and the waves of dusty plasmas turn out to be the very interested subjects for researchers. This thesis focuses on the structure and dynamical properties of the two-dimensional magnetized dusty plasmas through the molecular dynamical simulation method. It mainly contains the following studies: the modified screen Coulomb is derived with considering the plasmas gradient. Based on the modified screen Coulomb potential, the dynamical and structural properties of two-dimensional dusty plasmas is investigated. The fundamental process of relaxation is discussed by changing the initial velocity distribution, the components of dusty plasmas system and the interaction of the charged particles as well as the external magnetic field. The ordered structure above the melting point, named as super-heated solid, of the dusty plasmas is roughly studied by using the velocity scaling method in order to heat the dusty plasmas. In addition, this thesis shows the simulation results of temperature gradient mode of reversed field pinch with including the impurity ions, and the gyro-kinetic simulation of impurity mode.
On the other hand, the ion temperature gradient (ITG) driven modes in the presence of impurity ions are studied in the toroidal reversed field pinch (RFP) plasmas by solving the gyrokinetic integral eigenmode equation. The detailed numerical studies resemble the effects of impurities in tokamak plasmas. For instance, the impurities enhance the ion temperature gradient-driving if the impurity populations have density gradients which are opposite to that of the electrons. In addition, the impurity mode will appear when the impurity ion effecs are strong enough.The further study of impurity mode in a RFP using the gyrokinetic integral equation reveals that the impurity mode in RFP plasmas is relatively more difficult to be excited than that in tokamak plasmas under similar geometry when density profile is flat, whereas it turns out to be easier when density profile is rather peaked. In addition, the analysis of the typical RFX-mod experiments is performed and the results show that the ITG and impurity driven modes may be linearly unstable in the edge region of the plasmas when the observed radial profiles of the impurity ions are considered. And these modes may make a considerable contribution to the transport in this region.
引文
[1]汪诗金.等离子体与等离子体物理学[J].物理,1980,9(03)：252-259
[2]I.Langmuir.Oscillations in Ionized Gases.Proc. Nat. Acad. Sci.,1928,14(8):627-637
[3]L.Tonks, I. Langmuir.Oscillations in Ionized Gases.Phys.Rev.1929,33(2):195-210
[4]O.Heaviside.Nature.1902,67:6
[5]Chapman. S. Ferraro, V. C. A. The geomagnetic ring current.Its radial stability. Terr. Magn. Atmos. Eleetr.,1941,46,(1):15-26.
[6]L.D. Landau.Die kinetische gleichung fur den fall Coulombscher vechselwirkung Phys. Z. Sowjet.,1936,10:154-164
[7]A.A. Vlasov. On Vibration Properties of Electron Gas (in Russian). J. Exp. Theor. Phys.,1938,8 (3):291-318
[8]Alfven, H. Existence of electromagnetic-hydrodynamic waves.Nature,1942,150 (3805): 405-406.
[9]S. Chandrasekhar. Principles of Stellar Dynamics. Chicago:University of Chicago Press, 1942
[10]Landau, L. On the vibration of the electronic plasma. J. Phys. USSR.,1946,10(1): 25-34.
[11]R. Atkinson and F. Houtermans.Zur Frage der Aufbaum glichkeit der Elemente in Sternen.Zeitschrift f r Physik,1929,54(9-10):656-665
[12]J. D. Lawson. Some Criteria for a Power Producing Thermonuclear Reactor.Proceedings of the Physical Society B,1957,70(1):6-10
[13]Shafranov, V.D.. Plasma equilibrium in a magnetic field. Reviews of Plasma Physics, New York:Consultants Bureau,1966,2:103-151
[14]I. B. Bernstein,E. A. Frieman, M. D. Kruskal, R. M. KulsrudProc.An Energy Principle for Hydromagnetic StabilityProblems. R. Soc. Lond. A,1958,244(1236):17-40
[15]Pfirsch D. Mikroinstabilitaten vom Spiegeltyp in inhomogenen Plasmen. Zeitschrift Naturforschung Teil A,1962,17:861-870
[16]Galeev, A. A. Ion loss from the mirror trap due to the losscone instability development. Sov. Phys. JETP,1965,49:672-681.
[17]Van Allen, J. A., G. H. Ludwig, E. C. Ray, et al. Observations of high intensity radiation by satellites 1958 Alpha and Gamma, Jet Propul,1958,28(9):588-592
[18]James Alfred Van Allen, L. A. Frank.Survey of Radiation Around the Earth to a Radial Distance of 107,400 Kilometers.Nature,1959,183(4659):430-434
[19]Parker, E. N. Dynamics of the Interplanetary Gas and Magnetic Fields.Astrophysical Journal,1958,128:664-676.
[20]江南.我国低温等离子体研究进展(I)[J].物理,2006,(02)：130-139
[21]江南.我国低温等离子体研究进展(Ⅱ)[J].物理,2006,(03)：230-237
[22]Chu J H and I L.Direct observation of Coulomb crystals and liquids in strongly coupled rf dusty plasmas. Phys. Rev. Lett.1994,72(25):4009-4012
[23]Thomas H, Morfill G E, Demmel V. Plasma crystal:coulomb crystallization in a dusty plasma. Phys. Rev. Lett. Textbf,1994,73(5):652-655
[24]P. K. Shukla and A. A. Mamun.Introduction to Dusty Plasma Physics.Bristol and Philadelphia:Institute of Physics publishing,2002
[25]VEFortov, A G Khra Pak, AKhraPak.et al. Dusty plasmas. Physics-UsPekhi, 2004,47(5)447-492
[26]V.E.Fortov, A.V.Ivlev, S.A.KhraPak, et al. Complex (dusty) plasmas:Current status.open issues, perspectives.Physics RePorts,2005,421(1-2):1-103
[27]Alfven H. On the origin of the solar system. Clarendon Press, oxford, UK,1954
[28]SPitzerJrL. Physical Proeesses in the Interstellar Medium Wiley.New York,1978
[29]Shukla P.K. Introduction to Dusty Plasma. Physics Bristol:Institute of physics London,2002
[30]Roth R M, Spears K G, Stein G D, et al. Spatial dependence of particle light scattering in an rf silane discharge.Appl. Phys.Lett.,1985,46(3):253-255
[31]Smy P R. Role of gas breakdown in the charging and discharging of macron clouds.Proc. Inst. Electr. Eng. (UK),1973,120 (4):523-526
[32]Smith B A, Soderblom L, Beebe R et al. Encounter with Saturn:Voyager 1 Imaging Science Results.Science,1981,212(4491):163-191
[33]N.N.Rao,.PK.Shukla, M..Y Yu. Dust acoustie/avesin Dusyt Plasmas planet. SPace.Sci, 1990,38(4):543-546
[34]A. Barkan, R. L. Merlino, N. D'Angelo. Laboratory observation of the dust-acoustic wave mode. Phys.Plasmas,1995,2(10):3563-3565
[35]Harry L. F. Houpis, D. A. Mendis. The fine structure of the Saturnian ring system. TheMoon and the Planets,1983,29 (1):39-46
[36]H. Ikezi. Coulomb solid of small particles in plasmas. Physics of Fluids,1986,29 (6): 1764-1766
[37]Yu.MY, Luo H. Self-similar motion of a dusty plasma. Physics Letters A,1992,161 (6):506-509
[38]陈耀,李中元,李嘉巍等.彗星中尘埃的带电特性和平衡电势的研究.空间科学学报,2003,23(5)：329-333
[39]Chen Y H, Yu M Y. Exact ion acoustic solitary waves in an impurity-containing magnetized plasma. Physics of Plasmas,1994,1 (6):1868-1870
[40]Ma J X, Yu M Y. Langmuir wave instability in a dusty plasma. Phys. Rev. E,1994,50 (4):2431-2434
[41]Liu Y H, Liu B, Yang S Z etal. Defects related self-diffusion in a two-dimensional dusty plasma crystal. Journal of PhysicsA:Mathematical and General,2002,35 (45) 9535-9540
[42]Liu Y H, Liu B, Chen Y P et.al. Wave dispersion relations in two-dimensional Yukawa systems. Phys. Rev. E,2003,67(6) Part 2:66408
[43]Wang Y N, Hou L J, Wang X G. Self-Consistent Nonlinear Resonance and Hysteresis of a Charged Microparticle in a rf Sheath. Phys. Rev. Lett.,2002,89 (15):155001
[44]徐家莺,金尚宪.等离子体物理学.原子能出版社,北京,1981
[45]胡希伟.等离子体理论基础,北京大学出版社.2006
[46]C.K.Goertz, W.H.IP. Limitation of electrostatic charging of dust particles in a plasma. J.GeoPhys.Res,1984,11(4):349-352
[47]E.C.WhiPPle, T.GNorthrop, D.A.Mendis. The Electrostatics of a Dusty Plasma. J.GeoPhys.Res,1985,90(A8):7405-7413
[48]V.N.Tsytovich, U.de Angelis. Kinetic theory of dusty plasmas. Ⅳ. Distribution and fluctuations of dust charges. Phys.Plasmas,2002,9(6):2497-2506
[49]V.N.TsytoviehandU.deAngelis. Kinetic theory of dusty plasmas. Ⅴ. The hydrodynamic equations. Phys.Plasmas,2004,11(2):496-506
[50]I.Denysenko M.Y.Yu, K.Ostrikov, et al. A kinetic model for an argon plasma containing dust grains. Phys.of Plasmas,2004,11(11):4959-4967
[51]P.Schmidt, G.Zwieknagel, P.GReinhard, et al. Longitudinal and transversal collective modes in strongly correlated plasmas.Phys.Rev.E,1997,56(6):7310-7313
[52]H.ohta.Hamaguehi. Molecular dynamics evaluation of self-diffusion in Yukawa systems. Phys.Plasmas,2000,7(11):4506-4014
[53]Giovanni Lapenta. Simulation of charging and shielding of dust particles in drifting plasmas. Phys.Plasmas,1999,6(5):1442-1447
[54]H.Ohta, S.Hamaguehi. Wave Dispersion Relations in Yukawa Fluids. Phys.Rev.Lett., 2000,84(26):6026-6029
[55]W. Kong, X. Wang, S. F. Liu, et.al. Effect of particle's size on the structural and dynamical properties in 2D dusty plasma.Commun. Theor. Phys.2007,47(3):569-572
[56]W. Kong, S. F. Liu, Q. L. Wang, et.al. Effects of charge.and mass variations on the structure in 2D one-component and two-component dusty plasmas. J. Phys. A:Math. Theor.2007,40(5):1171-1180
[57]S. F. Liu, X. Wang, B. L. Hu, et.al. The structure of a two-dimensional magnetic dusty plasma. J. Phys. A:Math. Gen.2005,38(13):3057-3063
[58]D. R. Resendes, J. T. Mendonca, P. K. Shukla, Formation of dusty plasma molecules, Physics Letter A,1998,239(3),181-186
[59]L.Wang. Comments on Modern Phys.1999, Part C 1:117
[60]S. Hamaguchi, R. T. Rarouki. Polarization force on a charged particulate in a nonuniform plasma.Phys. Rev. E.1994,49(5):4430-4441
[61]R. T. Farouki, S. Hamaguchi. Thermodynamics of strongly-coupled Yukawa systems near the one-component-plasma limit. Ⅱ. Molecular dynamics simulations.J. Chem. Phys.,1994,101(11):9885-9893
[62]S. Hamaguchi, R. T. Farouki, D. H. E. Dubin.Triple point of Yukawa systems.Phys. Rev. E,1997,56(4):4671-4682
[63]Y. H. Liu, B. Liu, S. Z. Yang, et al. Negative Dispersion of Lattice Waves in a Two-Dimensional Yukawa System.Chin. Phys. Lett.,2002,19(8):1207-1210
[64]Y. H. Liu, B. Liu, S. Z. Yang, et al. Defects related self-diffusion in a two-dimensional dusty plasma crystal.J. Phys. A:Math. Gen,2002,35(45):9535-9540
[65]J. J. Hua, Y. H. Liu, M. F. Ye, et al. Structural and Dynamical Analysis of a Two-Dimensional Dusty Plasma Lattice.Chin. Phys. Lett.,2003,20(1):155-158
[66]Guy Dimonte, Jerome Daligault. Molecular-Dynamics Simulations of Electron-Ion Temperature Relaxation in a Classical Coulomb Plasma. Phys. Rev. Lett.,2008,101(13), 135001
[67]Wei Kong, Songfen Liu, Beilai Hu.et al. Diffusive and structural properties in a binary mixture of charged particles.Phys. Rev. E.2009,80(3),036406
[68]刘艳红.二维尘埃等离子体的结构、相变和动力学性质的数值模拟研究.博士后报告,2002
[69]B. Liu and J. Goree. Superdiffusion in two-dimensional Yukawa liquids.Phys. Rev. E 2007,75(1),016405
[70]C. C. Grimes, G. Adams. Evidence for a Liquid-to-Crystal Phase Transition in a Classical Two-Dimensional Sheet of Electrons.Phys. Rev. Lett.1979,4(12):795-798
[71]Y. N. Nejoh.The dust charging effect on electrostatic ion waves in a dusty plasma with trapped electrons. Phys. Plasmas 1997,4(8):2813-2819
[72]Y. H. Liu, Z. Y Chen, M. Y. Yu, et al. Structure of multispecies charged particles in a quadratic trap.Phys, Rev. E,2006,73(4),047402
[73]Y. H. Liu, L. Y. Chew, M. Y. Yu. Self-assembly of complex structures in a two-dimensional system with competing interaction forces.Phys. Rev. E,2008,78(6), 066405
[74]L. Zhang, Z. H. Jin, L. H. Zhang, et al. Superheating of Confined Pb Thin Films. Phys. Rev. Lett.2000,85(7):1484-1487
[75]H. J. Fecht and W. L. Johnson.Entropy and enthalpy catastrophe as a stability limit for crystalline material.Nature (London) 1988,334(6177):50-51
[76]K. Lu, Y. Li. Homogeneous Nucleation Catastrophe as a Kinetic Stability Limit for Superheated Crystal Phys. Rev. Lett.1998,80(20):4474-4477
[77]F. F. Chen,等离子体物理导论,人民教育出版社1980,93
[78]Lorenzini R. et al and RFX-mod Team and Collaborators. Selforganized helical equilibria as a new paradigm for ohmically heated fusion plasmas.Nature Phys. 2009,5(8):570-574
[79]Sarff J.S. et al. Tokamak-like confinement at high beta and low field in the reversed field pinch Plasma. Phys. Control. Fusion,2003,45 (12A):457-470
[80]Chapman B.E. et al. Generation and confinement of hot ions and electrons in a reversed-field pinch plasma. Plasma Phys. Control. Fusion 2010,52(12),124048
[81]S.C. Guo. Stability threshold of ion temperature gradient driven mode in reversed field pinch plasmas.Plasma Phys.2008,15(12),122510
[82]Songfen Liu, S.C Guo, J.Q.Dong,.Toroidal kinetic ηi-mode study in reversed-field pinch plasmas.Physics of Plasmas,2010,17(5),052505
[83]I. Predebon, C. Angioni, S. C. Guo. Gyrokinetic simulations of ion temperature gradient modes in the reversed field pinch.Phys. Plasmas,2010,17(1),012304
[84]F. Sattin, et al. Proceedings of the 11th Easter Plasma Meeting.Torino, Italy,2009
[85]Tang W.M., White R.B. Guzdar P.N. Impurity effects on ion-drift-wave eigenmodes in a sheared magnetic field. Phys. Fluids,1980,23(1):167-173
[86]Dominguez R.R., Staebler G.M. Impurity effects on drift wave stability and impurity transport. Nucl. Fusion,1993,33(1):51-62
[87]J.Q.Dong, W.Horton. Studies of impurity mode and ion temperature gradient mode in toroidal plasmas. Phys.Plasmas,1995,2(9):3412-3419
[88]J. Q. Dong, W. Horton, J.Y.Kim. Toroidal kinetic ηi-mode study in high-temperature plasmas. Phys. Fluids B,1992,4(7):1867-1876
[89]Fu X.Y., Dong J.Q., Horton W., et al. Turbulent particle transport in tokamak plasmas with impurities.Phys. Plasmas 1997,4(3):588-597
[90]Coppi B., Furth H.P., Rosenbluth M.N. et al. Drift instability due to impurity ions.Phys. Rev. Lett.1966,17(7):377-379
[91]Liu S. F., Guo S. C., Zhang C. L., et al. Impurity effects on the ion temperature gradient mode in reversed-field pinch plasmas. Nucl. Fusion,2011,51(8),083021
[92]Lorenzini R. et al and RFX-mod Team and Collaborators, Selforganized helical equilibria as a new paradigm for ohmically heated fusion plasmas. Nature Phys.2009, 5(8):570-574
[93]Chapman B.E. et al. Reduced edge instability and improved confinement in the MST reversed-field pinch.Phys. Rev. Lett.,2001,87(20),205001.
[2]I.Langmuir.Oscillations in Ionized Gases.Proc. Nat. Acad. Sci.,1928,14(8):627-637
[3]L.Tonks, I. Langmuir.Oscillations in Ionized Gases.Phys.Rev.1929,33(2):195-210
[4]O.Heaviside.Nature.1902,67:6
[5]Chapman. S. Ferraro, V. C. A. The geomagnetic ring current.Its radial stability. Terr. Magn. Atmos. Eleetr.,1941,46,(1):15-26.
[6]L.D. Landau.Die kinetische gleichung fur den fall Coulombscher vechselwirkung Phys. Z. Sowjet.,1936,10:154-164
[7]A.A. Vlasov. On Vibration Properties of Electron Gas (in Russian). J. Exp. Theor. Phys.,1938,8 (3):291-318
[8]Alfven, H. Existence of electromagnetic-hydrodynamic waves.Nature,1942,150 (3805): 405-406.
[9]S. Chandrasekhar. Principles of Stellar Dynamics. Chicago:University of Chicago Press, 1942
[10]Landau, L. On the vibration of the electronic plasma. J. Phys. USSR.,1946,10(1): 25-34.
[11]R. Atkinson and F. Houtermans.Zur Frage der Aufbaum glichkeit der Elemente in Sternen.Zeitschrift f r Physik,1929,54(9-10):656-665
[12]J. D. Lawson. Some Criteria for a Power Producing Thermonuclear Reactor.Proceedings of the Physical Society B,1957,70(1):6-10
[13]Shafranov, V.D.. Plasma equilibrium in a magnetic field. Reviews of Plasma Physics, New York:Consultants Bureau,1966,2:103-151
[14]I. B. Bernstein,E. A. Frieman, M. D. Kruskal, R. M. KulsrudProc.An Energy Principle for Hydromagnetic StabilityProblems. R. Soc. Lond. A,1958,244(1236):17-40
[15]Pfirsch D. Mikroinstabilitaten vom Spiegeltyp in inhomogenen Plasmen. Zeitschrift Naturforschung Teil A,1962,17:861-870
[16]Galeev, A. A. Ion loss from the mirror trap due to the losscone instability development. Sov. Phys. JETP,1965,49:672-681.
[17]Van Allen, J. A., G. H. Ludwig, E. C. Ray, et al. Observations of high intensity radiation by satellites 1958 Alpha and Gamma, Jet Propul,1958,28(9):588-592
[18]James Alfred Van Allen, L. A. Frank.Survey of Radiation Around the Earth to a Radial Distance of 107,400 Kilometers.Nature,1959,183(4659):430-434
[19]Parker, E. N. Dynamics of the Interplanetary Gas and Magnetic Fields.Astrophysical Journal,1958,128:664-676.
[20]江南.我国低温等离子体研究进展(I)[J].物理,2006,(02)：130-139
[21]江南.我国低温等离子体研究进展(Ⅱ)[J].物理,2006,(03)：230-237
[22]Chu J H and I L.Direct observation of Coulomb crystals and liquids in strongly coupled rf dusty plasmas. Phys. Rev. Lett.1994,72(25):4009-4012
[23]Thomas H, Morfill G E, Demmel V. Plasma crystal:coulomb crystallization in a dusty plasma. Phys. Rev. Lett. Textbf,1994,73(5):652-655
[24]P. K. Shukla and A. A. Mamun.Introduction to Dusty Plasma Physics.Bristol and Philadelphia:Institute of Physics publishing,2002
[25]VEFortov, A G Khra Pak, AKhraPak.et al. Dusty plasmas. Physics-UsPekhi, 2004,47(5)447-492
[26]V.E.Fortov, A.V.Ivlev, S.A.KhraPak, et al. Complex (dusty) plasmas:Current status.open issues, perspectives.Physics RePorts,2005,421(1-2):1-103
[27]Alfven H. On the origin of the solar system. Clarendon Press, oxford, UK,1954
[28]SPitzerJrL. Physical Proeesses in the Interstellar Medium Wiley.New York,1978
[29]Shukla P.K. Introduction to Dusty Plasma. Physics Bristol:Institute of physics London,2002
[30]Roth R M, Spears K G, Stein G D, et al. Spatial dependence of particle light scattering in an rf silane discharge.Appl. Phys.Lett.,1985,46(3):253-255
[31]Smy P R. Role of gas breakdown in the charging and discharging of macron clouds.Proc. Inst. Electr. Eng. (UK),1973,120 (4):523-526
[32]Smith B A, Soderblom L, Beebe R et al. Encounter with Saturn:Voyager 1 Imaging Science Results.Science,1981,212(4491):163-191
[33]N.N.Rao,.PK.Shukla, M..Y Yu. Dust acoustie/avesin Dusyt Plasmas planet. SPace.Sci, 1990,38(4):543-546
[34]A. Barkan, R. L. Merlino, N. D'Angelo. Laboratory observation of the dust-acoustic wave mode. Phys.Plasmas,1995,2(10):3563-3565
[35]Harry L. F. Houpis, D. A. Mendis. The fine structure of the Saturnian ring system. TheMoon and the Planets,1983,29 (1):39-46
[36]H. Ikezi. Coulomb solid of small particles in plasmas. Physics of Fluids,1986,29 (6): 1764-1766
[37]Yu.MY, Luo H. Self-similar motion of a dusty plasma. Physics Letters A,1992,161 (6):506-509
[38]陈耀,李中元,李嘉巍等.彗星中尘埃的带电特性和平衡电势的研究.空间科学学报,2003,23(5)：329-333
[39]Chen Y H, Yu M Y. Exact ion acoustic solitary waves in an impurity-containing magnetized plasma. Physics of Plasmas,1994,1 (6):1868-1870
[40]Ma J X, Yu M Y. Langmuir wave instability in a dusty plasma. Phys. Rev. E,1994,50 (4):2431-2434
[41]Liu Y H, Liu B, Yang S Z etal. Defects related self-diffusion in a two-dimensional dusty plasma crystal. Journal of PhysicsA:Mathematical and General,2002,35 (45) 9535-9540
[42]Liu Y H, Liu B, Chen Y P et.al. Wave dispersion relations in two-dimensional Yukawa systems. Phys. Rev. E,2003,67(6) Part 2:66408
[43]Wang Y N, Hou L J, Wang X G. Self-Consistent Nonlinear Resonance and Hysteresis of a Charged Microparticle in a rf Sheath. Phys. Rev. Lett.,2002,89 (15):155001
[44]徐家莺,金尚宪.等离子体物理学.原子能出版社,北京,1981
[45]胡希伟.等离子体理论基础,北京大学出版社.2006
[46]C.K.Goertz, W.H.IP. Limitation of electrostatic charging of dust particles in a plasma. J.GeoPhys.Res,1984,11(4):349-352
[47]E.C.WhiPPle, T.GNorthrop, D.A.Mendis. The Electrostatics of a Dusty Plasma. J.GeoPhys.Res,1985,90(A8):7405-7413
[48]V.N.Tsytovich, U.de Angelis. Kinetic theory of dusty plasmas. Ⅳ. Distribution and fluctuations of dust charges. Phys.Plasmas,2002,9(6):2497-2506
[49]V.N.TsytoviehandU.deAngelis. Kinetic theory of dusty plasmas. Ⅴ. The hydrodynamic equations. Phys.Plasmas,2004,11(2):496-506
[50]I.Denysenko M.Y.Yu, K.Ostrikov, et al. A kinetic model for an argon plasma containing dust grains. Phys.of Plasmas,2004,11(11):4959-4967
[51]P.Schmidt, G.Zwieknagel, P.GReinhard, et al. Longitudinal and transversal collective modes in strongly correlated plasmas.Phys.Rev.E,1997,56(6):7310-7313
[52]H.ohta.Hamaguehi. Molecular dynamics evaluation of self-diffusion in Yukawa systems. Phys.Plasmas,2000,7(11):4506-4014
[53]Giovanni Lapenta. Simulation of charging and shielding of dust particles in drifting plasmas. Phys.Plasmas,1999,6(5):1442-1447
[54]H.Ohta, S.Hamaguehi. Wave Dispersion Relations in Yukawa Fluids. Phys.Rev.Lett., 2000,84(26):6026-6029
[55]W. Kong, X. Wang, S. F. Liu, et.al. Effect of particle's size on the structural and dynamical properties in 2D dusty plasma.Commun. Theor. Phys.2007,47(3):569-572
[56]W. Kong, S. F. Liu, Q. L. Wang, et.al. Effects of charge.and mass variations on the structure in 2D one-component and two-component dusty plasmas. J. Phys. A:Math. Theor.2007,40(5):1171-1180
[57]S. F. Liu, X. Wang, B. L. Hu, et.al. The structure of a two-dimensional magnetic dusty plasma. J. Phys. A:Math. Gen.2005,38(13):3057-3063
[58]D. R. Resendes, J. T. Mendonca, P. K. Shukla, Formation of dusty plasma molecules, Physics Letter A,1998,239(3),181-186
[59]L.Wang. Comments on Modern Phys.1999, Part C 1:117
[60]S. Hamaguchi, R. T. Rarouki. Polarization force on a charged particulate in a nonuniform plasma.Phys. Rev. E.1994,49(5):4430-4441
[61]R. T. Farouki, S. Hamaguchi. Thermodynamics of strongly-coupled Yukawa systems near the one-component-plasma limit. Ⅱ. Molecular dynamics simulations.J. Chem. Phys.,1994,101(11):9885-9893
[62]S. Hamaguchi, R. T. Farouki, D. H. E. Dubin.Triple point of Yukawa systems.Phys. Rev. E,1997,56(4):4671-4682
[63]Y. H. Liu, B. Liu, S. Z. Yang, et al. Negative Dispersion of Lattice Waves in a Two-Dimensional Yukawa System.Chin. Phys. Lett.,2002,19(8):1207-1210
[64]Y. H. Liu, B. Liu, S. Z. Yang, et al. Defects related self-diffusion in a two-dimensional dusty plasma crystal.J. Phys. A:Math. Gen,2002,35(45):9535-9540
[65]J. J. Hua, Y. H. Liu, M. F. Ye, et al. Structural and Dynamical Analysis of a Two-Dimensional Dusty Plasma Lattice.Chin. Phys. Lett.,2003,20(1):155-158
[66]Guy Dimonte, Jerome Daligault. Molecular-Dynamics Simulations of Electron-Ion Temperature Relaxation in a Classical Coulomb Plasma. Phys. Rev. Lett.,2008,101(13), 135001
[67]Wei Kong, Songfen Liu, Beilai Hu.et al. Diffusive and structural properties in a binary mixture of charged particles.Phys. Rev. E.2009,80(3),036406
[68]刘艳红.二维尘埃等离子体的结构、相变和动力学性质的数值模拟研究.博士后报告,2002
[69]B. Liu and J. Goree. Superdiffusion in two-dimensional Yukawa liquids.Phys. Rev. E 2007,75(1),016405
[70]C. C. Grimes, G. Adams. Evidence for a Liquid-to-Crystal Phase Transition in a Classical Two-Dimensional Sheet of Electrons.Phys. Rev. Lett.1979,4(12):795-798
[71]Y. N. Nejoh.The dust charging effect on electrostatic ion waves in a dusty plasma with trapped electrons. Phys. Plasmas 1997,4(8):2813-2819
[72]Y. H. Liu, Z. Y Chen, M. Y. Yu, et al. Structure of multispecies charged particles in a quadratic trap.Phys, Rev. E,2006,73(4),047402
[73]Y. H. Liu, L. Y. Chew, M. Y. Yu. Self-assembly of complex structures in a two-dimensional system with competing interaction forces.Phys. Rev. E,2008,78(6), 066405
[74]L. Zhang, Z. H. Jin, L. H. Zhang, et al. Superheating of Confined Pb Thin Films. Phys. Rev. Lett.2000,85(7):1484-1487
[75]H. J. Fecht and W. L. Johnson.Entropy and enthalpy catastrophe as a stability limit for crystalline material.Nature (London) 1988,334(6177):50-51
[76]K. Lu, Y. Li. Homogeneous Nucleation Catastrophe as a Kinetic Stability Limit for Superheated Crystal Phys. Rev. Lett.1998,80(20):4474-4477
[77]F. F. Chen,等离子体物理导论,人民教育出版社1980,93
[78]Lorenzini R. et al and RFX-mod Team and Collaborators. Selforganized helical equilibria as a new paradigm for ohmically heated fusion plasmas.Nature Phys. 2009,5(8):570-574
[79]Sarff J.S. et al. Tokamak-like confinement at high beta and low field in the reversed field pinch Plasma. Phys. Control. Fusion,2003,45 (12A):457-470
[80]Chapman B.E. et al. Generation and confinement of hot ions and electrons in a reversed-field pinch plasma. Plasma Phys. Control. Fusion 2010,52(12),124048
[81]S.C. Guo. Stability threshold of ion temperature gradient driven mode in reversed field pinch plasmas.Plasma Phys.2008,15(12),122510
[82]Songfen Liu, S.C Guo, J.Q.Dong,.Toroidal kinetic ηi-mode study in reversed-field pinch plasmas.Physics of Plasmas,2010,17(5),052505
[83]I. Predebon, C. Angioni, S. C. Guo. Gyrokinetic simulations of ion temperature gradient modes in the reversed field pinch.Phys. Plasmas,2010,17(1),012304
[84]F. Sattin, et al. Proceedings of the 11th Easter Plasma Meeting.Torino, Italy,2009
[85]Tang W.M., White R.B. Guzdar P.N. Impurity effects on ion-drift-wave eigenmodes in a sheared magnetic field. Phys. Fluids,1980,23(1):167-173
[86]Dominguez R.R., Staebler G.M. Impurity effects on drift wave stability and impurity transport. Nucl. Fusion,1993,33(1):51-62
[87]J.Q.Dong, W.Horton. Studies of impurity mode and ion temperature gradient mode in toroidal plasmas. Phys.Plasmas,1995,2(9):3412-3419
[88]J. Q. Dong, W. Horton, J.Y.Kim. Toroidal kinetic ηi-mode study in high-temperature plasmas. Phys. Fluids B,1992,4(7):1867-1876
[89]Fu X.Y., Dong J.Q., Horton W., et al. Turbulent particle transport in tokamak plasmas with impurities.Phys. Plasmas 1997,4(3):588-597
[90]Coppi B., Furth H.P., Rosenbluth M.N. et al. Drift instability due to impurity ions.Phys. Rev. Lett.1966,17(7):377-379
[91]Liu S. F., Guo S. C., Zhang C. L., et al. Impurity effects on the ion temperature gradient mode in reversed-field pinch plasmas. Nucl. Fusion,2011,51(8),083021
[92]Lorenzini R. et al and RFX-mod Team and Collaborators, Selforganized helical equilibria as a new paradigm for ohmically heated fusion plasmas. Nature Phys.2009, 5(8):570-574
[93]Chapman B.E. et al. Reduced edge instability and improved confinement in the MST reversed-field pinch.Phys. Rev. Lett.,2001,87(20),205001.