Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-06-01T09:30:37.783Z Has data issue: false hasContentIssue false
  • English
  • Français

A pressure tensor description for the time-resonant Weibel instability

Part of: PLA The Vlasov Equation

Published online by Cambridge University Press:  17 January 2017

M. Sarrat ,
D. Del Sarto  and
A. Ghizzo
M. Sarrat*
Affiliation:
Institut Jean Lamour, UMR 7198 CNRS – Université de Lorraine, F-54506 Vandoeuvre-lès-Nancy, France
D. Del Sarto
Affiliation:
Institut Jean Lamour, UMR 7198 CNRS – Université de Lorraine, F-54506 Vandoeuvre-lès-Nancy, France
A. Ghizzo
Affiliation:
Institut Jean Lamour, UMR 7198 CNRS – Université de Lorraine, F-54506 Vandoeuvre-lès-Nancy, France
*
†Email address for correspondence: mathieu.sarrat@univ-lorraine.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

We discuss a fluid model with inclusion of the complete pressure tensor dynamics for the description of Weibel-type instabilities in a counterstreaming beam configuration. Differently from the case recently studied in Sarrat et al. (Europhys. Lett., vol. 115, 2016, 45001), where perturbations perpendicular to the beams were considered, here we focus only on modes propagating along the beams. Such a configuration is responsible for the growth of two kinds of instabilities, the two-stream instability and the Weibel instability, which in this geometry becomes ‘time resonant’, i.e. propagating. This fluid description agrees with the kinetic one and makes it possible e.g. to identify the transition between non-propagating and propagating Weibel modes, already evidenced by Lazar et al. (J. Plasma Phys., vol. 76 (1), 2010, p. 49) as a ‘slope breaking’ of the growth rate, in terms of a merger of two non-propagating Weibel modes.

Keywords

astrophysical plasmasplasma instabilitiesspace plasma physics
Type
Research Article
Information
Journal of Plasma Physics , Volume 83 , Issue 1 , February 2017 , 705830103
Copyright
© Cambridge University Press 2017 

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

Abramovitz, M. 1965 Elementary analytical methods. In Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables (ed. Abramovitz, M. & Stegun, I. A.), pp. 113–138. National Bureau of Standards.Google Scholar
Albrecht-Marc, M., Ghizzo, A., Johnston, T. W., Réveillé, T., Del Sarto, D. & Bertrand, P. 2007 Saturation processes induced by vortex-merging in numerical Vlasov–Maxwell experiments of stimulated Raman backscattering. Phys. Plasmas 14, 072704.CrossRefGoogle Scholar
Basu, B. 2002 Moment equation description of Weibel instability. Phys. Plasmas 9, 5131–5134.CrossRefGoogle Scholar
Bret, A., Firpo, M. C. & Deutsch, C. 2005 Electromagnetic instabilities for relativistic beam–plasma interaction in whole $k$ space: nonrelativistic beam and plasma temperature effects. Phys. Rev. E 72 (1), 016403.Google ScholarPubMed
Bret, A., Gremillet, L. & Bellido, J. C. 2007 How really transverse is the filamentation instability? Phys. Plasmas 14 (3), 032103.Google Scholar
Bret, A., Gremillet, L. & Dieckmann, M. E. 2010 Multidimensional electron beam–plasma instabilities in the relativistic regime. Phys. Plasmas 17 (12), 120501.CrossRefGoogle Scholar
Bret, A., Stockem, A., Narayan, R. & Silva, L. O. 2014 Collisionless Weibel shocks: full formation mechanism and timing. Phys. Plasmas 21 (7), 072301.Google Scholar
Califano, F., Attico, N., Pegoraro, F., Bertin, G. & Bulanov, S. V. 2001 Fast formation of magnetic islands in a plasma in the presence of counterstreaming electrons. Phys. Rev. Lett. 86 (23), 5293–5296.CrossRefGoogle Scholar
Califano, F., Del Sarto, D. & Pegoraro, F. 2006 Three-dimensional magnetic structures generated by the development of the filamentation (Weibel) instability in the relativistic regime. Phys. Rev. Lett. 96 (10), 105008.Google Scholar
Califano, F., Pegoraro, F. & Bulanov, S. V. 1997 Spatial structure and time evolution of the Weibel instability in collisionless inhomogeneous plasmas. Phys. Rev. E 56 (1), 963–969.Google Scholar
Califano, F., Prandi, R., Pegoraro, F. & Bulanov, S. V. 1998 Nonlinear filamentation instability driven by an inhomogeneous current in a collisionless plasma. Phys. Rev. E 58 (6), 7837–7845.Google Scholar
Del Sarto, D., Pegoraro, F. & Califano, F. 2016 Pressure anisotropy and small spatial scales induced by velocity shear. Phys. Rev. E 93 (5), 053203.Google Scholar
Del Sarto, D., Pegoraro, F. & Tenerani, A.2017 ‘Magneto-elastic’ waves in an anisotropic magnetised plasma. Plasma Phys. Contoll. Fusion, to appear, http://dx.doi.org/10.1088/1361-6587/aa56bd.CrossRefGoogle Scholar
Denavit, J. 1992 Absorption of high-intensity subpicosecond lasers on solid density targets. Phys. Rev. Lett. 69 (21), 3052–3055.CrossRefGoogle ScholarPubMed
Franci, L., Hellinger, P., Matteini, L., Verdini, A. & Landi, S. 2016 Two-dimensional hybrid simulations of kinetic plasma turbulence: current and vorticity vs proton temperature. AIP Conf. Proc. 1720 (1), 040003.CrossRefGoogle Scholar
Fried, B. D. 1959 Mechanism for instability of transverse plasma waves. Phys. Fluids 2 (3), 337.Google Scholar
Fried, B. D. & Conte, S. D. 1961 The Plasma Dispersion Function. Academic Press.Google Scholar
Ghizzo, A. & Bertrand, P. 2013 On the multi-stream approach of relativistic Weibel instability. I, II and III. Phys. Plasmas 20 (8), 082109, 082110 and 082111.Google Scholar
Ghizzo, A., Del Sarto, D. & Réveillé, T. 2009 Hamiltonian stochastic processes induced by successive wave-particle interactions in stimulated Raman scattering. Phys. Plasmas 79 (4), 046404.Google Scholar
Ghizzo, A., Del Sarto, D., Réveillé, T., Besse, N. & Klein, R. 2007 Self-induced transparency scenario revisited via beat-wave heating induced by Doppler shift in overdense plasma layer. Phys. Plasmas 14 (6), 062702.Google Scholar
Ghizzo, A., Huot, F. & Bertrand, P. 2003 A non-periodic 2D semi-Lagrangian Vlasov code for laser–plasma interaction on parallel computer. J. Comput. Phys. 186 (1), 47–69.Google Scholar
Ghizzo, A., Johnston, T. W., Réveillé, T., Bertrand, P. & Albrecht-Marc, M. 2006 Stimulated-Raman-scatter behavior in a relativistically hot plasma slab and an electromagnetic low-order pseudocavity. Phys. Rev. E 74 (4), 046407.Google Scholar
Ghizzo, A., Sarrat, M. & Del Sarto, D. 2016 Vlasov models for kinetic Weibel-type instabilities. J. Plasma Phys. 83 (1), doi:10.1017/S0022377816001215.Google Scholar
Ghorbanalilu, M., Sadegzadeh, S., Ghaderi, Z. & Niknam, A. R. 2014 Weibel instability for a streaming electron, counterstreaming e-e, and e-p plasmas with intrinsic temperature anisotropy. Phys. Plasmas 21 (5), 052102.Google Scholar
Guérin, S., Mora, P., Adam, J. C., Hron, A. & Laval, G. 1996 Propagation of ultraintense laser pulses through overdense plasma layers. Phys. Plasmas 3 (7), 2693–2701.Google Scholar
Inglebert, A., Ghizzo, A., Réveillé, T., Bertrand, P. & Califano, F. 2012 Electron temperature anisotropy instabilities represented by superposition of streams. Phys. Plasmas 19 (12), 122109.CrossRefGoogle Scholar
Inglebert, A., Ghizzo, A., Réveillé, T., Del Sarto, D., Bertrand, P. & Califano, F. 2011 A multi-stream Vlasov modeling unifying relativistic Weibel-type instabilities. Europhys. Lett. 95 (4), 45002.CrossRefGoogle Scholar
Lazar, M. 2008 Fast magnetization in countestreaming plasmas with temperature anisotropies. Phys. Lett. A 372 (14), 2446–2449.Google Scholar
Lazar, M., Dieckmann, M. E. & Poedts, S. 2010 Resonant Weibel instability in counterstreaming plasmas with temperature anisotropies. J. Plasma Phys. 76 (1), 49–56.Google Scholar
Lazar, M., Schlickeiser, R. & Shukla, P. K. 2006 Cumulative effect of the filamentation and Weibel instabilities in countestreaming thermal plasmas. Phys. Plasmas 13 (10), 102107.Google Scholar
Lazar, M., Schlickeiser, R., Wielebinski, R. & Poedts, S. 2009 Cosmological effects of Weibel-type instabilities. Astrophys. J. 693, 1133–1141.Google Scholar
Masson-Laborde, P. E., Rozmus, W., Peng, Z., Pesme, D., Hller, S., Casanova, M., Bychenkov, V. Yu., Chapman, T. & Loiseau, P. 2010 Evolution of the stimulated Raman scattering instability in two-dimensional particle-in-cell simulations. Phys. Plasmas 17 (9), 092704.Google Scholar
Matteini, L., Hellinger, P., Landi, S., Trávnícek, P. M. & Velli, M. 2011 Ion kinetics in the solar wind: coupling global expansion to local microphysics. Space Sci. Rev. 172 (1–4), 373.CrossRefGoogle Scholar
Medvedev, M. V. & Loeb, A. 1999 Generation of magnetic fields in the relativistic shock of gamma-ray burst sources. Astrophys. J. 526 (2), 697.Google Scholar
Parashar, T. N. & Matthaeus, W. H. 2016 Propinquity of current and vortex structures: effects on collisionless plasma heating. Astrophys. J. 832, 1, 57.Google Scholar
Pegoraro, F., Bulanov, S. V., Califano, F. & Lontano, M. 1996 Nonlinear development of the Weibel instability and magnetic field generation in collisionless plasmas. Phys. Scripta T63, 262.Google Scholar
Sarrat, M., Del Sarto, D. & Ghizzo, A. 2016 Fluid description of Weibel-type instabilities via full pressure tensor dynamics. Europhys. Lett. 115 (4), 45001.Google Scholar
Schlickeiser, R. & Shukla, P. K. 2003 Cosmological magnetic field generation by the Weibel instability. Astrophys. J. 599, L57–L60.CrossRefGoogle Scholar
Scudder, J. D. 2016 Collisionless reconnection and electron demagnetization. In Magnetic Reconnection, pp. 33–100. Springer.Google Scholar
Scudder, J. D. & Daughton, W. S. 2008 Illuminating electron diffusion regions of collisionless magnetic reconnection using electron agyrotropy. J. Geophys. Res. 113, A6, 2156–2202.Google Scholar
Scudder, J. D., Holdaway, R. D., Daughton, W. S., Karimabadi, H., Roytershteyn, V., Russell, C. T. & Lopez, J. Y. 2012 First resolved observations of the demagnetized electron-diffusion region of an astrophysical magnetic-reconnection site. Phys. Rev. Lett. 108 (22), 225005.Google Scholar
Sentoku, Y., Mima, K., Kaw, P. & Nishikawa, K. 2003 Anomalous resistivity resulting from MeV-electron transport in overdense plasma. Phys. Rev. Lett. 90 (15), 155001.CrossRefGoogle ScholarPubMed
Servidio, S., Valentini, F., Califano, F. & Veltri, P. 2012 Local kinetic effects in two-dimensional plasma turbulence. Phys. Rev. Lett. 108 (4), 045001.Google Scholar
Servidio, S., Valentini, F., Perrone, D., Greco, A., Califano, F., Matthaeus, W. H. & Veltri, P. 2015 A kinetic model of plasma turbulence. J. Plasma Phys. 81 (1), 325810107.Google Scholar
Stockem, A. & Lazar, M. 2008 Revision of ‘cumulative effect of the filamentation and Weibel instabilities in countestreaming thermal plasmas’. Phys. Plasmas 15 (1), 014501.Google Scholar
Stockem, A., Lazar, M., Shukla, P. K. & Smolyakov, A. 2008 A comparative study of the filamentation and Weibel instabilities and their cumulative effect. II. Weakly relativistic beams. J. Plasma Phys. 75 (4), 529–543.CrossRefGoogle Scholar
Tzoufras, M., Ren, C., Tsung, F. S., Tonge, J. W., Mori, W. B., Fiore, M., Fonseca, R. A. & Silva, L. O. 2006 Space-charge effects in the current-filamentation or Weibel instability. Phys. Rev. Lett. 96 (10), 105002.Google Scholar
Weibel, E. S. 1959 Spontaneously growing transverse waves in a plasma due to an anisotropic velocity distribution. Phys. Rev. Lett. 2 (3), 83–84.CrossRefGoogle Scholar
Zheng, C. Y., He, X. T. & Zhu, S. P. 2005 Magnetic field generation and relativistic electron dynamics in circularly polarized intense laser interaction with dense plasma. Phys. Plasmas 12 (4), 044505.CrossRefGoogle Scholar