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Particle-in-cell simulation of two stream instability in the non-extensive statistics

Published online by Cambridge University Press:  06 June 2014

Mohammad Ghorbanalilu ,
Elahe Abdollahzadeh  and
S.H. Ebrahimnazhad Rahbari
Mohammad Ghorbanalilu*
Affiliation:
Physics Department, Shahid Beheshti University, G. C., Tehran, Iran Physics Department of Azarbaijan Shahid Madani University, Tabriz, Iran
Elahe Abdollahzadeh
Affiliation:
Physics Department of Azarbaijan Shahid Madani University, Tabriz, Iran
S.H. Ebrahimnazhad Rahbari
Affiliation:
Physics Department of Azarbaijan Shahid Madani University, Tabriz, Iran
*
Address correspondence and reprint requests to: M. Ghorbanalilu, Physics Department, Shahid Beheshti University, G. C., Tehran, Iran; Physics Department of Azarbaijan Shahid Madani University, Tabriz, Iran. E-mail: [email protected]; [email protected]
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Abstract

We have performed extensive one dimensional particle-in-cell (PIC) simulations to explore generation of electrostatic waves driven by two-stream instability (TSI) that arises due to the interaction between two symmetric counterstreaming electron beams. The electron beams are considered to be cold, collisionless and magnetic-field-free in the presence of neutralizing background of static ions. Here, electrons are described by the non-extensive q-distributions of the Tsallis statistics. Results shows that the electron holes structures are different for various q values such that: (i) for q > 1 cavitation of electron holes are more visible and the excited waves were more strong (ii) for q < 1 the degree of cavitation decreases and for q = 0.5 the holes are not distinguishable. Furthermore, time development of the velocity root-mean-square (VRMS) of electrons for different q-values demonstrate that the maximum energy conversion is increased upon increasing the non-extensivity parameter q up to the values q > 1. The normalized total energy history for a arbitrary entropic index q = 1.5, approves the energy conserving in our PIC simulation.

Keywords

electron beamsPIC simulationTwo stream instability
Type
Research Article
Information
Laser and Particle Beams , Volume 32 , Issue 3 , September 2014 , pp. 399 - 407
Copyright
Copyright © Cambridge University Press 2014 

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References

REFERENCES

Benedetti, C., Londrillo, P., Petrillo, V., Serafini, L., Sgattoni, A., Tomassini, P. & Turchetti, G. (2009). PIC simulations of the production of high-quality electron beams via laser-plasma interaction. Nucl. Instr. Meth. Phys. Res. A 608, S94.CrossRefGoogle Scholar
Birdsall, C.K. & Langdon, A.B. (1985). Plasma Physics via Computer Simulation. New York: McGraw-Hill.Google Scholar
Buneman, O. (1959). Dissipation of currects in ionized media. Phys. Rev. 115, 503.CrossRefGoogle Scholar
Chen, F.F. (1994). Introduction to Plasma Physics and Controlled Fusion. New York: Plenum Press.Google Scholar
Chen, X. & Li, X. (2012). Comment on Plasma oscillations and nonextensive statistics. Phys. Rev. E 86, 068401.CrossRefGoogle ScholarPubMed
Dai, J., Chen, X. & Li, X. (2013). Dust ion acoustic with q-distribution in non-extensive statistics. Astrophys. Space Sci. 346, 183.CrossRefGoogle Scholar
Dawson, J.M. (1962). One-dimensional plasma model. Phys. Fluids 5, 445.CrossRefGoogle Scholar
Dieckmann, M.E., Drury, L. & Shukla, P.K. (2006). On the ultra-relativistic two-stream instability, electrostatic turbulence and Brownian motion. New J. Phys. 8, 40.CrossRefGoogle Scholar
Fehske, H.Schneider, R. & Wei Be, A. (2008). Computational Many-Particle Physics. Heidelberg: Springer-Verlag.CrossRefGoogle Scholar
Feng, Z. & Liu, L. (2010). Energy fluctuation and correlation in Tsallis statistics. Physica A 389, 237.CrossRefGoogle Scholar
Haas, F., Bret, A. & Shukla, P.K. (2009). Physical interpretation of the quantum two-stream instability. Phys. Rev. E 80, 066407.CrossRefGoogle ScholarPubMed
Startsev, E.A. & Davidson, R.C. (2006). Two-stream instability for a longitudinally compressing charged particle beam. Phys. Plasmas 13, 062108.CrossRefGoogle Scholar
Startsev, E.A., Kaganovich, I.D. & Davidson, R.C. (2014). Effects of beam-plasma instabilities on neutralized propagation of intense ion beams in background plasma. Nucl. Instr. Meth. Phys. A 733, 80.CrossRefGoogle Scholar
Tautz, R.C., Schlickeiser, R. & Lerche, I. (2007). Non-resonant kinetic instabilities of a relativistic plasma in a uniform maganetic field: Longitudinal and transverse mode coupling effects. J. Math. Phys. 48, 013302.CrossRefGoogle Scholar
Thode, L.E. & Sudan, R.N. (1973). Two-stream instability heating of plasmas by relativistic electron beams. Phys. Rev. Lett. 30, 732.CrossRefGoogle Scholar
Tsallis, C. (1988). Possible generalization of Boltzmann-Gibbs statistics. Stat. Phys. 52, 479.CrossRefGoogle Scholar
Tsallis, C. (2002). Entropic non-extensivity: A possible measure of complexity. Chaos, Solitons and Fractals. 13, 371.CrossRefGoogle Scholar
Valentini, F. (2005). Nonlinear Landau damping in non-extensive statistics. Phys. Plasmas 12, 072106.CrossRefGoogle Scholar
Weibel, E.S. (1959). Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Phys. Rev. Lett. 2, 83.CrossRefGoogle Scholar
Yoo, J., Rhee, T. & Ryu, C. (2007). 1D PIC simulation study of non linear beam plasma interaction. Comp. Phys. Comm. 177, 93.CrossRefGoogle Scholar
Zeba, I., Yahia, M.E., Shukla, P.K. & Moslem, W.M. (2012). Electron-hole two-stream instability in a quantum semiconductor plasma with exchange-correlation effects. Phys. Lett. A 376, 2309.CrossRefGoogle Scholar
Haeff, A.V. (1949). The electron-wave tube: A novel method of generation and amplification of microwave energy. Proc. I. R. E 37, 4.Google Scholar
Hasegawa, A. (1968). Theory of longitudinal plasma instability. Phys. Rev. 169, 204.CrossRefGoogle Scholar
Hockney, R.W. & Eastwood, J.W. (1988). Computer Simulation using Particles. London: Arrowsmith.CrossRefGoogle Scholar
Jackson, E.A. (1960). Drift instabilities in a Maxwellian plasma. Phys. Fluids 3, 786.CrossRefGoogle Scholar
Krall, N.A. & Trivelpiece, A.W. (1973). Principles of Plasma Physics. New York: McGraw-HillCrossRefGoogle Scholar
Lapenta, G., Markidis, S., Marocchino, A. & Kaniadakis, G. (2007). Relaxation of relativistic plasmas under the effect of wave-particle interaction. Astrophys. 666, 949.CrossRefGoogle Scholar
Liu, S. & Chen, X. (2011). Dispersion relation of longitudinal oscillation in relativistic plasmas with non-extensive distribution. Physica A 390, 1704.CrossRefGoogle Scholar
Liu, S., Qiu, H. & Li, X. (2012). Landau damping of dust acoustic waves in the plasma with non-extensive distribution. Physica A 391, 5795.CrossRefGoogle Scholar
Liu, Y., Liu, S.Q. & Dai, B. (2011). Arbitrary amplitude kinetic Alfven solitons in a plasma with a q-non-extensive electron velocity distribution. Phys. Plasmas 18, 092309.CrossRefGoogle Scholar
Liyan, L. & Jiulin, D. (2008). Energy fluctuations and the ensemble equivalence in Tsallis statistics. Physica A 387, 5417.Google Scholar
Pierce, J.R. (1948). Possible fluctuations in electron streams due to ions. Appl. Phys. 19, 231.CrossRefGoogle Scholar
Renyi, A. (1955). On a new axiomatic theory of probability. Acta Math. Acad. Sci. Hung. 6, 285.CrossRefGoogle Scholar
Silin, I., Sydora, R. & Sauer, K. (2007). Electron beam-plasma inter-action: Linear theory and Vlasov-Poisson simulation. Phys. Plasmas 14, 012106.CrossRefGoogle Scholar

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