Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-23T20:37:52.707Z Has data issue: false hasContentIssue false
  • English
  • Français

Linear and nonlinear behaviour of two-stream instabilities in collisionless plasmas

Published online by Cambridge University Press:  21 September 2015

Y. W. Hou ,
M. X. Chen ,
M. Y. Yu  and
B. Wu
Y. W. Hou*
Affiliation:
Key Laboratory of Neutronics and Radiation Safety, Institute of Nuclear Energy Safety Technology, Chinese Academy of Science, Hefei, Anhui 230031, China
M. X. Chen
Affiliation:
School of Electronic Science and Applied Physics, Hefei University of Technology, Hefei, Anhui 230009, China
M. Y. Yu
Affiliation:
Institute for Fusion Theory and Simulation and Department of Physics, Zhejiang University, Hangzhou 310027, China Institute for Theoretical Physics I, Ruhr University, D-44780 Bochum, Germany
B. Wu
Affiliation:
Institute of Plasma Physics, Chinese Academy of Sciences, Hefei, Anhui 230031, China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

The transient, growth and nonlinear saturation stages in the evolution of the electrostatic two-stream instabilities as described by the Vlasov–Poisson system are reconsidered by numerically following the evolution of the total wave energy of the plasma oscillations excited from (numerical) noise. Except for peculiarities related to the necessarily finite (even though very small) magnitude of the perturbations in the numerical simulation, the existence and initial growth properties of the instabilities from the numerical results are found to be consistent with those from linear normal mode analysis and the Penrose criteria. However, contradictory to the traditional point of view, the growth of instability before saturation is not always linear. The initial stage of the growth can exhibit fine structures that can be attributed to the harmonics of the excited plasma oscillations, whose wavelengths are determined by the system size and the numerical noise. As expected, saturation of the unstable oscillations is due to electron trapping when they reach sufficiently large amplitudes.

Type
Research Article
Information
Journal of Plasma Physics , Volume 81 , Issue 6 , December 2015 , 905810602
Copyright
© Cambridge University Press 2015 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Boyd, T. J. M. & Sanderson, J. J. 2003 The Physics of Plasmas. Cambridge University Press.CrossRefGoogle Scholar
Chen, F. F. 1984 Introduction to Plasma Physics. Plenum.Google Scholar
Cheng, C. Z. & Knorr, G. 1976 The integration of the Vlasov equation in configuration space. J. Comput. Phys. 22, 330–351.Google Scholar
Clemmow, P. C. & Dougherty, J. P. 1969 Electrodynamics of Particles and Plasmas. Addison-Wesley.Google Scholar
Daldorff, L. K. S., Pecseli, H. L., Trulsen, J. K., Ulriksen, M. I., Eliasson, B. & Stenflo, L. 2011 Nonlinear beam generated plasma waves as a source for enhanced plasma and ion acoustic lines. Phys. Plasmas 18, 052107.Google Scholar
Deneef, C. P., Malmberg, J. H. & O’Neil, T. M. 1973 Launched waves on a beam-plasma system. Phys. Rev. Lett. 30, 1032–1035.Google Scholar
Dieckmann, M. E., Eliasson, B., Shukla, P. K., Sircombe, N. J. & Dendy, R. O. 2006 Two-stream instability in collisionless shocks and foreshock. Plasma Phys. Control. Fusion 48, B303–B311.CrossRefGoogle Scholar
El-Labany, S. K. & Rowlands, G. 1986 The non-linear two-stream problem–a new approach. Plasma Phys. Control. Fusion 28, 1549–1558.Google Scholar
Eliasson, B. 2010 Numerical simulations of the Fourier-transformed Vlasov – Maxwell system in higher dimensions–theory and applications. Transp. Theory Stat. Phys. 39, 387–465.Google Scholar
Eliasson, B. & Shukla, P. K. 2010 Dispersion properties of electrostatic oscillations in quantum plasmas. J. Plasma Phys. 76, 7–17.CrossRefGoogle Scholar
Fijalkow, E. & Nocera, L. 2005 Superposition of phase-space hole streets in Vlasov plasmas. J. Plasma Phys. 71, 401–410.CrossRefGoogle Scholar
Gentle, K. W. & Hohr, J. 1973 Phase-space evolution of a trapped electron beam. Phys. Rev. Lett. 30, 75–77.Google Scholar
Haas, F. & Eliasson, B. 2015 A new two-stream instability mode in magnetized quantum plasma. Phys. Scr. 90, 088005.CrossRefGoogle Scholar
Hartmann, D. A., Driscoll, C. F., O’Neil, T. M. & Shapiro, V. D. 1995 Measurements of the weak warm beam instability. Phys. Plasmas 2, 654–677.Google Scholar
Hasegawa, A. 1968 Theory of longitudinal plasma instabilities. Phys. Rev. 169, 204–214.Google Scholar
Hasegawa, A. 1971 Plasma instabilities in the magnetosphere. Rev. Geophys. 9, 703–772.Google Scholar
Hou, Y. W., Ma, Z. W. & Yu, M. Y. 2011a The plasma wave echo revisited. Phys. Plasmas 18, 012108.Google Scholar
Hou, Y. W., Ma, Z. W. & Yu, M. Y. 2011b Trapped particle effects in long-time nonlinear Landau damping. Phys. Plasmas 18, 082101.Google Scholar
Infeld, E. & Skorupski, A. 1970 The two-stream instability and its classification into absolute and convective for hot plasmas. J. Plasma Phys. 4, 607–615.CrossRefGoogle Scholar
Kohn, W. 1999 Nobel lecture: electronic structure of matter–wave functions and density functionals. Rev. Mod. Phys. 71, 1253–1266.Google Scholar
Lacina, J., Krlin, L. & Korbel, S. 1976 Effect of beam density and of higher harmonics on beam–plasma interaction. Plasma Phys. 18, 471–483.CrossRefGoogle Scholar
Morey, I. J. & Boswell, R. W. 1989 Evolution of bounded beam–plasma interactions in a one-dimensional particle simulation. Phys. Fluids B 1, 1502–1510.Google Scholar
Morse, R. L. & Nielson, C. W. 1969 One-, two-, and three-dimensional numerical simulation of two-beam plasmas. Phys. Rev. Lett. 23, 1087–1090.Google Scholar
Ng, C. S., Bhattacharjee, A. & Skiff, F. 2004 Complete spectrum of kinetic eigenmodes for plasma oscillations in a weakly collisional plasma. Phys. Rev. Lett. 92, 065002.CrossRefGoogle Scholar
Penrose, O. 1960 Electrostatic instabilities of a uniform non-Maxwellian plasma. Phys. Fluids 3, 258–265.Google Scholar
Roberts, K. V. & Berk, H. L. 1967 Nonlinear evolution of a two-stream instability. Phys. Rev. Lett. 19, 297–300.CrossRefGoogle Scholar
Rostomian, E. V. 1994 The dynamics of superdense electron beam instability in plasma. Plasma Phys. Control. Fusion 36, 1737–1742.Google Scholar
Schamel, H. 1982 Stability of electron vortex structures in phase space. Phys. Rev. Lett. 48, 481–483.CrossRefGoogle Scholar
Scholl, J. A., Garcia-Etxarri, A., Koh, A. L. & Dionne, J. A. 2013 Observation of quantum tunneling between two plasmonic nanoparticles. Nano Lett. 13, 564–569.Google Scholar
Uzdensky, D. A. & Rightley, S. 2014 Plasma physics of extreme astrophysical environments. Rep. Prog. Phys. 77, 036902.Google Scholar
Van-Wakeren, J. H. A. & Hopman, H. J. 1975 Thermalization of a beam by beam-plasma interaction. J. Plasma Phys. 13, 349–360.Google Scholar
Volokitin, A. & Krafft, C. 2012 Velocity diffusion in plasma waves excited by electron beams. Plasma Phys. Control. Fusion 54, 085002.Google Scholar
Whelan, D. A. & Stenzel, R. L. 1983 Nonlinear energy flow in a beam-plasma system. Phys. Rev. Lett. 50, 1133–1136.CrossRefGoogle Scholar
Wu, Y. 2006 Conceptual design activities of FDS series fusion power plants in China. Fusion Engng Des. 81, 2713–2718.Google Scholar
Wu, Y. 2008 Conceptual design of the China fusion power plant FDS-II. Fusion Engng Des. 83, 1683–1689.Google Scholar
Wu, Y., Jiang, J., Wang, M., Jin, M.& FDS Team 2011 A fusion-driven subcritical system concept based on viable technologies. Nucl. Fusion 51, 103036.Google Scholar
Yoon, P. H. 2000 Generalized weak turbulence theory. Phys. Plasmas 7, 4858–4871.Google Scholar
Yoon, P. H. 2005a Effects of spontaneous fluctuations on the generalized weak turbulence theory. Phys. Plasmas 12, 042306.CrossRefGoogle Scholar
Yoon, P. H. 2005b Progress in the kinetic theory of electrostatic harmonics of plasma waves. Phys. Plasmas 12, 052313.Google Scholar
Zheng, C. Y., Liu, Z. J., Zhang, A. Q., Zhu, S. P. & He, X. T. 2006 Simulation of electron beam instabilities in collisionless plasmas. J. Plasma Phys. 72, 249–258.Google Scholar