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Extension of temperature anisotropy Weibel instability to non-Maxwellian plasmas by 2D PIC simulation

Published online by Cambridge University Press:  29 December 2017

Mohammad Ghorbanalilu  and
Elahe Abdollahazadeh
Mohammad Ghorbanalilu*
Affiliation:
Physics Department, Shahid Beheshti University, G. C., Tehran, Iran
Elahe Abdollahazadeh
Affiliation:
Physics Department of Azarbaijan Shahid Madani University, Tabriz, Iran
*
Author for correspondence: Mohammad Ghorbanalilu, Physics Department, Shahid Beheshti University, G. C., Tehran, Iran. E-mail: m_alilu@sbu.ac.ir, mh_alilo@yahoo.com
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Abstract

The Weibel instability driven by temperature anisotropy is investigated in a two-dimensional (2D) particle-in-cell simulation in non-extensive statistics in the relativistic regime. In order to begin the simulation, we introduced a new 2D anisotropic distribution function in the context of non-extensive statistics. The heavy ions considered to be immobile and form the neutralizing background. The numerical results show that non-extensive parameter q plays an important role on the magnetic field saturation time, the time of reduction temperature anisotropy, evolution time to the quasi-stationary state, and the peak energy density of magnetic field. We observe that the instability saturation time increases by increasing the non-extensive parameter q. It is shown that structures with superthermal electrons (q < 1) could generate strong magnetic fields during plasma thermalization. The simulation results agree with the previous simulations for an anisotropic Maxwellian plasma (q = 1).

Keywords

PIC simulationWeibel instabilitynon-extensive statistics
Type
Research Article
Information
Laser and Particle Beams , Volume 36 , Issue 1 , March 2018 , pp. 1 - 7
Copyright
Copyright © Cambridge University Press 2017 

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References

Basu, B (2002) Moment equation description of Weibel instability. Physics of Plasmas 9, 5131.Google Scholar
Bendib, A, Bendib, K and Sid, A (1997) Weibel instability due to inverse bremsstrahlung absorption. Physical Review E 55, 7522.CrossRefGoogle Scholar
Bendib, K, Bendib, A, Bendib, K, Bendib, A, Sid, A and Bendib, K (1998) Weibel instability analysis in laser-produced plasmas. Laser and Particle Beams 16, 473.Google Scholar
Benedetti, C, Londrillo, P, Petrillo, V, Serafini, L, Sgattoni, A, Tomassini, P and Turchetti, G (2009) PIC simulations of the production of high-quality electron beams via laser–plasma interaction. Nuclear Instruments and Methods in Physics Research A 608, S94.Google Scholar
Birdsall, CK and Langdon, AB (1985) Plasma Physics via Computer Simulation. New York: McGraw-Hill.Google Scholar
Bret, A (2006) A simple analytical model for the Weibel instability in the non-relativistic regime. Physics Letters A 359, 52.CrossRefGoogle Scholar
Buneman, O (1959) Dissipation of currents in ionized media. Physical Review 115, 503.CrossRefGoogle Scholar
Burger, P (1965) Theory of large-amplitude oscillations in the one-dimensional low-pressure Cesium thermionic converter. Journal of Applied Physics 36, 1938.Google Scholar
Caruso, F, Pluchino, A, Latora, V, Vinciguerra, S and Rapisarda, A (2007) Analysis of self-organized criticality in the Olami–Feder–Christensen model and in real earthquakes. Physical Review E 75, 055101.Google Scholar
Dai, J, Chen, X and Li, X (2013) Dust ion acoustic instability with q-distribution in nonextensive statistics. Astrophysics and Space Science 346, 183.CrossRefGoogle Scholar
Dawson, J (1962) One-dimensional plasma model. Physics of Fluids 5, 445.Google Scholar
Drouin, M, Gremillet, L, Adam, J-C and Heron, A (2010) Particle-in-cell modeling of relativistic laser–plasma interaction with the adjustable-daming, direct implicit method. The Journal of Computational Physics 229, 4781.Google Scholar
Ghorbanalilu, M (2013) Resonance and non-resonance Weibel-like modes generation in optical breakdown of a dilute neutral gas by an intense laser field. Plasma Physics and Controlled Fusion 55, 045002.Google Scholar
Ghorbanalilu, M, Abdollahzadeh, E and Ebrahimnazhad Rahbari, SH (2014 a) Particle-in-cell simulation of two stream instability in the non-extensive statistics. Laser and Particle Beams 32, 399.Google Scholar
Ghorbanalilu, M and Sadegzadeh, S (2017) Estimate of the maximum induced magnetic field in relativistic shocks. Monthly Notices of the Royal Astronomical Society 464, 1202.Google Scholar
Ghorbanalilu, M, Sadeghzadeh, S, Ghaderi, Z and Niknam, AR (2014 b) Weibel instability for a streaming electron, counterstreaming e–e, and e–p plasmas with intrinsic temperature anisotropy. Physics of Plasmas 21, 052102.CrossRefGoogle Scholar
Hockney, RW and Eastwood, JW (1988) Computer Simulation using Particles. London: Arrowsmith.Google Scholar
Kuri, DK, Das, N and Patel, K (2017) Formation of periodic magnetic field structures in overdense plasmas. Laser and Particle Beams 35, 467.Google Scholar
Lemons, DS, Winske, D and Gary, SP (1979) Nonlinear theory of the Weibel instability. Journal of Plasma Physics 21, 287.CrossRefGoogle Scholar
Mishchenko, A, Hatzky, R and Konies, A (2008) Global particle-in-cell simulations of Alfvenic modes. Physics of Plasmas 15, 112106.CrossRefGoogle Scholar
Moreira, DA, Albuquerque, EL, da Silva, LR and Galvao, DS (2008) Low temperature specific heat spectra considering nonextensive long-range correlated quasiperiodic DNA molecules. Physica A 387, 5477.Google Scholar
Morse, RL and Nielson, CW (1971) Numerical simulation of the Weibel instability in one and two dimensions. Physics of Fluids 14, 830.CrossRefGoogle Scholar
Moslem, WM, Sabry, R, El-Labany, SK and Shukla, PK (2011) Dust acoustic rogue waves in a nonextensive plasma. Physical Review E 84, 066402.CrossRefGoogle Scholar
Okada, T, Sajiki, I and Satou, K (1999) Weibel instability by ultraintense laser pulses. Laser and Particle Beams 17, 515.Google Scholar
Plastino, AR and Plastino, A (1995) Non-extensive statistical mechanics and generalized Fokker–Planck equation. Physica A 222, 347.Google Scholar
Pommier, L and Lefebvre, E (2004) Simulations of energetic proton emission in laser-plasma interaction. Laser and Particle Beams 21, 573.CrossRefGoogle Scholar
Pukhov, A and Meyer-ter-vehn, J (1999) Physics of short pulse laser plasma interaction by multi-dimensional particle-in-cell simulation. Laser and Particle Beams 17, 571.Google Scholar
Qi, X, Xu, Y, Duan, W, Zhang, L and Yang, L (2014) Particle-in-cell simulation of the head on collision between two ion acoustic solitary waves in plasmas. Physics of Plasmas 21, 082118.Google Scholar
Qiu, H-B and Liu, S-B (2013) Weibel instability with nonextensive distribution. Physics of Plasmas 20, 102119.CrossRefGoogle Scholar
Rajawat, RS and Sengupta, S (2016) One dimensional PIC simulation of relativistic Buneman instability. Physics of Plasmas 23, 102110.CrossRefGoogle Scholar
Renyi, A (1955) On a new aximatic theory of probability. Acta Mathematica Academiae Scientiarum Hungaricae 6, 285.CrossRefGoogle Scholar
Schaefer-Rolffs, U, Lerche, I and Schlickeiser, R (2006) The relativistic kinetic Weibel instability: general arguments and specific illustrations. Physics of Plasmas 13, 012107.Google Scholar
Seough, J, Yoon, PH and Hwang, J (2015 a) Simulation and quasilinear theory of proton firehose instability. Physics of Plasmas 22, 012303.Google Scholar
Seough, J, Yoon, PH, Hwang, J and Nariyuki, Y (2015 b) Simulation and quasilinear theory of a periodic ordinary mode intability. Physics of Plasmas 22, 082122.CrossRefGoogle Scholar
Shokri, B and Ghorbanalilu, M (2004) Weibel instability of microwave gas discharge in strong linear and circular pulsed fields. Physics of Plasmas 11, 2989.CrossRefGoogle Scholar
Siemon, C, Khudik, V and Shvets, G (2011) Analytic model of electron beam thermalization during the resistive Weibel instability. Physics of Plasmas 18, 103109.Google Scholar
Silva, R Jr., Plastino, AR and Lima, JAS (1998) A maxwellian path to the q-nonextensive velocity distribution function. Physics Letters A 249, 401.CrossRefGoogle Scholar
Stockem, A, Dieckmann, ME and Schlickeiser, R (2010) PIC simulations of the temperature anisotropy-driven Weibel instability: analysing the perpendicular mode. Plasma Physics and Controlled Fusion 52, 085009.Google Scholar
Tribeche, M, Amour, R and Shukla, PK (2012) Ion acoustic solitary waves in a plasma with nonthermal electrons featuring Tsallis distribution. Physical Review E 85, 037401.CrossRefGoogle Scholar
Tsallis, C (1988) Possible generalization of Boltzmann–Gibbs statistics. Journal of Statistical Physics 52, 479.Google Scholar
Tsallis, C (2002) Entropic non-extensivity: a possible measure of complexity. Chaos, Solitons and Fractals 13, 371.CrossRefGoogle Scholar
Weibel, ES (1959) Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Physical Review Letters 2, 83.Google Scholar
Wu, SZ, Zhou, CT, He, XT and Zhu, S-P (2009) Generation of strong magnetic fields from laser interaction with two-layer targets. Laser and Particle Beams 27, 471.Google Scholar

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