J. D. Scudder, H. Karimabadi, W. Daughton, and V. Roytershteyn, Frozen flux violation, electron demagnetization and magnetic reconnection, Physics of Plasmas, vol.30, issue.10, p.101204, 2015.
DOI : 10.1007/BF00751338

URL : http://aip.scitation.org/doi/pdf/10.1063/1.4932332

S. Servidio, F. Valentini, D. Perrone, A. Greco, F. Califano et al., A kinetic model of plasma turbulence, Journal of Plasma Physics, vol.68, issue.01, p.2015
DOI : 10.1017/S0022112091001957

D. , D. Sarto, F. Pegoraro, and F. Califano, Pressure anisotropy and small spatial scales induced by velocity shear, Phys. Rev. E, vol.93, issue.9, p.53203, 2016.

Y. Yang, W. H. Matthaeus, T. N. Parashar, P. Wu, M. Wan et al., Energy transfer channels and turbulence cascade in Vlasov-Maxwell turbulence, Physical Review E, vol.1, issue.6, p.61201, 2017.
DOI : 10.1016/0021-9991(76)90053-X

J. A. Araneda, E. Marsch, and A. F. Viñas, Proton Core Heating and Beam Formation via Parametrically Unstable Alfv??n-Cyclotron Waves, Physical Review Letters, vol.316, issue.12, p.125003, 2008.
DOI : 10.1029/2006JA011979

C. F. Kennel and H. E. Petschek, Limit on stably trapped particle fluxes, Journal of Geophysical Research, vol.67, issue.1, pp.1-28, 1966.
DOI : 10.1029/JZ067i010p03717

URL : http://hdl.handle.net/2060/19660001589

S. P. Gary and J. Wang, Whistler instability: Electron anisotropy upper bound, Journal of Geophysical Research: Space Physics, vol.87, issue.19, pp.10749-10754, 1996.
DOI : 10.1016/0010-4655(94)00167-Z

B. Basu, Moment equation description of Weibel instability, Physics of Plasmas, vol.45, issue.12, pp.5131-513410, 2002.
DOI : 10.1063/1.1705933

P. H. Yoon and R. C. Davidson, Exact analytical model of the classical Weibel instability in a relativistic anisotropic plasma, Physical Review A, vol.27, issue.6, pp.2718-2721, 1987.
DOI : 10.1063/1.864542

A. Inglebert, A. Ghizzo, T. Réveillé, D. D. Sarto, P. Bertrand et al., Multi-stream Vlasov model for the study of relativistic Weibel-type instabilities, Plasma Physics and Controlled Fusion, vol.54, issue.8, p.54085004, 2012.
DOI : 10.1088/0741-3335/54/8/085004

A. Inglebert, A. Ghizzo, T. Réveillé, P. Bertrand, and F. Califano, Electron temperature anisotropy instabilities represented by superposition of streams, Physics of Plasmas, vol.19, issue.12, pp.12210910-10634772770, 2012.
DOI : 10.1063/1.1758231

A. Ghizzo and P. Bertrand, On the multistream approach of relativistic Weibel instability. I. Linear analysis and specific illustrations, Physics of Plasmas, vol.20, issue.8, pp.8210910-1063, 2013.
DOI : 10.1103/PhysRevLett.96.105002

URL : https://hal.archives-ouvertes.fr/hal-01287078

A. Ghizzo, On the multistream approach of relativistic weibel instability. ii. bernsteingreene-kruskal-type waves in magnetic trapping, Physics of Plasmas, vol.20, issue.8, pp.8211010-1063, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01287078

A. Ghizzo, On the multistream approach of relativistic Weibel instability. III. Comparison with full-kinetic Vlasov simulations, Physics of Plasmas, vol.20, issue.8, pp.8211110-1063, 2013.
DOI : 10.1103/PhysRevE.53.6460

URL : https://hal.archives-ouvertes.fr/hal-01287078

B. D. Fried, Mechanism for instability of transverse plasma waves. The Physics of Fluids, pp.337-33710, 1959.

A. Inglebert, A. Ghizzo, T. Réveillé, D. D. Sarto, P. Bertrand et al., A multi-stream Vlasov modeling unifying relativistic Weibel-type instabilities, EPL (Europhysics Letters), vol.95, issue.4, pp.45002-45017, 2011.
DOI : 10.1209/0295-5075/95/45002

K. A. Taggart, B. B. Godrey, C. E. Rhoades, and H. C. Ives, Second-Order Effects in the Weibel Instability, Physical Review Letters, vol.17, issue.26, pp.1729-1731, 1972.
DOI : 10.1063/1.1693518

G. Kalman, C. Montes, and D. Quemada, Anisotropic temperature plasma instabilities. The Physics of Fluids, pp.1797-180810, 1968.
DOI : 10.1063/1.1692198

A. Bret, L. Gremillet, D. Bénisti, and E. Lefebvre, Exact Relativistic Kinetic Theory of an Electron-Beam???Plasma System: Hierarchy of the Competing Modes in the System-Parameter Space, Physical Review Letters, vol.23, issue.20, pp.205008-205024, 2008.
DOI : 10.1086/308038

C. 1. Les, W. A. De-type, L. Bret, D. Gremillet, and . Bénisti, Exact relativistic kinetic theory of the full unstable spectrum of an electron-beam?plasma system with maxwell-jüttner distribution functions, Phys. Rev. E, vol.81, pp.36402-36418, 2010.

S. P. Gary and H. Karimabadi, Linear theory of electron temperature anisotropy instabilities: Whistler, mirror, and Weibel, Journal of Geophysical Research, vol.1, issue.A10, p.18436, 2006.
DOI : 10.1029/JZ071i001p00001

S. P. Gary, W. C. Feldman, D. W. Forslund, and M. D. Montgomery, Electron heat flux instabilities in the solar wind, Geophysical Research Letters, vol.2, issue.3, pp.79-82, 1975.
DOI : 10.1086/151902

S. P. Gary, E. E. Scime, J. L. Phillips, and W. C. Feldman, The whistler heat flux instability: Threshold conditions in the solar wind, Journal of Geophysical Research, vol.99, issue.A12, pp.9923391-23399, 1994.
DOI : 10.1029/94JA02068

S. Saeed, M. Sarfraz, P. H. Yoon, M. Lazar, and M. N. Qureshi, Electron heat flux instability, Monthly Notices of the Royal Astronomical Society, vol.113, issue.2, pp.1672-168110, 2017.
DOI : 10.1029/2007JA012979

R. L. Morse and C. W. Nielson, Numerical simulation of the weibel instability in one and two dimensions. The Physics of Fluids, pp.830-84010, 1971.

R. A. Fonseca, L. O. Silva, J. W. Tonge, W. B. Mori, and J. M. Dawson, Three-dimensional Weibel instability in astrophysical scenarios, Physics of Plasmas, vol.4, issue.5, pp.1979-198410, 2003.
DOI : 10.1086/340094

T. N. Kato, Saturation mechanism of the Weibel instability in weakly magnetized plasmas, Physics of Plasmas, vol.12, issue.8, pp.8070510-1063, 2005.
DOI : 10.1063/1.1694123

A. Bret, L. Gremillet, and M. E. Dieckmann, Multidimensional electron beam-plasma instabilities in the relativistic regime, Physics of Plasmas, vol.17, issue.12, pp.12050110-1063, 2010.
DOI : 10.1063/1.3514586.4

L. Palodhi, F. Califano, and F. Pegoraro, Nonlinear kinetic development of the Weibel instability and the generation of electrostatic coherent structures, Plasma Physics and Controlled Fusion, vol.51, issue.12, pp.51125006-51125023, 2009.
DOI : 10.1088/0741-3335/51/12/125006

F. Califano, F. Pegoraro, S. V. Bulanov, and A. Mangeney, Kinetic saturation of the Weibel instability in a collisionless plasma, Physical Review E, vol.15, issue.6, pp.7048-7059, 1998.
DOI : 10.1063/1.1693910

R. C. Davidson, D. A. Hammer, I. Haber, and C. E. Wagner, Nonlinear development of electromagnetic instabilities in anisotropic plasmas. The Physics of Fluids, pp.317-33310, 1972.

M. E. Innocenti, M. Lazar, S. Markidis, G. Lapenta, and S. Poedts, Electron streams formation and secondary two stream instability onset in the post-saturation regime of the classical Weibel instability, Physics of Plasmas, vol.1, issue.5, pp.5210410-10633587089, 2011.
DOI : 10.1016/j.matcom.2009.08.038

A. Stockem, M. E. Dieckmann, and R. Schlickeiser, PIC simulations of the thermal anisotropy-driven Weibel instability: field growth and phase space evolution upon saturation, Plasma Physics and Controlled Fusion, vol.51, issue.7, pp.75014-75031, 2009.
DOI : 10.1088/0741-3335/51/7/075014

M. E. Dieckmann, The filamentation instability driven by warm electron beams: statistics and electric field generation, Plasma Physics and Controlled Fusion, vol.51, issue.12, pp.124042-124059, 2009.
DOI : 10.1088/0741-3335/51/12/124042

URL : http://arxiv.org/pdf/0910.0228

F. Califano, R. Prandi, F. Pegoraro, and S. V. Bulanov, Magnetic-field generation and wave-breaking in collisionless plasmas, Journal of Plasma Physics, vol.60, issue.2, pp.331-339, 1998.
DOI : 10.1017/S0022377898006862

M. V. Medvedev, M. Fiore, R. A. Fonseca, L. O. Silva, and W. B. Mori, Long-Time Evolution of Magnetic Fields in Relativistic Gamma-Ray Burst Shocks, The Astrophysical Journal, vol.618, issue.2, pp.618-75, 2005.
DOI : 10.1086/427921

O. Polomarov, I. Kaganovich, and G. Shvets, Merging of Super-Alfv??nic Current Filaments during Collisionless Weibel Instability of Relativistic Electron Beams, Physical Review Letters, vol.101, issue.17, pp.175001-175019, 2008.
DOI : 10.1103/PhysRevLett.94.115002

A. Grassi, M. Grech, F. Amiranoff, F. Pegoraro, A. Macchi et al., Electron Weibel instability in relativistic counterstreaming plasmas with flow-aligned external magnetic fields, Physical Review E, vol.95, issue.2, pp.23203-23222, 2017.
DOI : 10.1007/978-1-4612-2780-9

URL : https://hal.archives-ouvertes.fr/hal-01494375

D. P. Stern, A brief history of magnetospheric physics before the spaceflight era, Reviews of Geophysics, vol.79, issue.1, pp.103-114, 1989.
DOI : 10.1029/JZ068i024p06361

L. A. Frank, Plasma in the Earth's polar magnetosphere, Journal of Geophysical Research, vol.76, issue.22, pp.5202-5219, 1971.
DOI : 10.1029/JA073i009p02839

J. W. Dungey, Interplanetary Magnetic Field and the Auroral Zones, Physical Review Letters, vol.65, issue.2, pp.47-48, 1961.
DOI : 10.1029/JZ065i010p03497

URL : http://www.dtic.mil/cgi-bin/GetTRDoc?AD=AD0274336&Location=U2&doc=GetTRDoc.pdf

G. Paschmann, B. U. Sonnerup, I. Papamastorakis, N. Sckopke, G. Haerendel et al., Plasma acceleration at the Earth's magnetopause: evidence for reconnection, Nature, vol.83, issue.5736, pp.282243-246, 1979.
DOI : 10.1016/0032-0633(73)90044-5

T. D. Phan, L. M. Kistler, B. Klecker, G. Haerendel, G. Paschmann et al., Extended magnetic reconnection at the Earth's magnetopause from detection of bi-directional jets, Nature, vol.71, issue.6780, pp.404848-850, 2000.
DOI : 10.1029/JZ071i001p00155

C. Lacombe, O. Alexandrova, L. Matteini, O. Santolík, N. Cornilleau-wehrlin et al., OBSERVATIONS, The Astrophysical Journal, vol.796, issue.1, pp.5-19, 2014.
DOI : 10.1088/0004-637X/796/1/5

URL : https://hal.archives-ouvertes.fr/insu-01145708

D. Stansby, T. S. Horbury, C. H. Chen, and L. Matteini, EXPERIMENTAL DETERMINATION OF WHISTLER WAVE DISPERSION RELATION IN THE SOLAR WIND, The Astrophysical Journal, vol.829, issue.1, pp.16-19, 2016.
DOI : 10.3847/2041-8205/829/1/L16

V. Pierrard and M. Lazar, Kappa Distributions: Theory and Applications in Space Plasmas, Solar Physics, vol.626, issue.1, pp.153-174, 2010.
DOI : 10.1029/2007JA012979

URL : http://arxiv.org/pdf/1003.3532

M. Lazar, V. Pierrard, S. M. Shaaban, H. Fichtner, and S. Poedts, Dual Maxwellian-Kappa modeling of the solar wind electrons: new clues on the temperature of Kappa populations, Astronomy & Astrophysics, vol.156, pp.44-63, 2017.
DOI : 10.1007/s11214-010-9692-5

S. P. Gary, Electromagnetic electron beam instabilities: Hot, isotropic beams, Journal of Geophysical Research, vol.89, issue.A11, pp.10815-10822, 1985.
DOI : 10.1029/JA089iA10p08857

E. E. Scime, S. J. Bame, W. C. Feldman, S. P. Gary, J. L. Phillips et al., Regulation of the solar wind electron heat flux from 1 to 5 AU: Ulysses observations, Journal of Geophysical Research, vol.10, issue.A12, pp.9923401-23410, 1994.
DOI : 10.1103/PhysRev.89.977

G. P. Serbu, Explorer 35 observations of solar-wind electron density, temperature, and anisotropy, Journal of Geophysical Research, vol.74, issue.10, pp.1703-1712, 1972.
DOI : 10.1029/JA074i011p02962

J. D. Scudder, D. L. Lind, and K. W. Ogilvie, Electron observations in the solar wind and magnetosheath, Journal of Geophysical Research, vol.48, issue.28, pp.6535-6548, 1973.
DOI : 10.1016/0032-0633(68)90012-3

J. C. Kasper, A. J. Lazarus, S. P. Gary, and A. Szabo, Solar Wind Temperature Anisotropies, AIP Conference Proceedings, pp.538-54110, 2003.
DOI : 10.1063/1.1618653

P. Hellinger, P. Trávní?ek, J. C. Kasper, A. J. Lazarus, S. Stverák et al., Solar wind proton temperature anisotropy : Linear theory and wind/swe observations Electron temperature anisotropy constraints in the solar wind, Geophysical Research Letters Journal of Geophysical Research : Space Physics, vol.33, issue.9A3, pp.113-19103, 2006.

M. Lazar, S. M. Shaaban, V. Pierrard, H. Fichtner, and S. Poedts, Instability constraints for the electron temperature anisotropy in the slow solar wind. thermal core vs. suprathermal halo. pre-print, 1972.

J. F. Wardle, D. C. Homan, R. Ojha, and D. H. Roberts, Electron???positron jets associated with the quasar 3C279, Nature, vol.106, issue.6701, pp.395457-461, 1998.
DOI : 10.1086/116723

R. Z. Sagdeev, Cooperative phenomena and shock waves in collisionless plasmas, Rev. Plasma Phys, vol.4, p.23, 1921.

D. Biskamp, Collisionless shock waves in plasmas, Nuclear Fusion, vol.13, issue.5, p.719, 1921.
DOI : 10.1088/0029-5515/13/5/010

M. Lemoine, G. Pelletier, and B. Revenu, On the Efficiency of Fermi Acceleration at Relativistic Shocks, The Astrophysical Journal, vol.645, issue.2, p.129, 2006.
DOI : 10.1086/506322

URL : https://hal.archives-ouvertes.fr/in2p3-00121552

L. O. Silva, R. A. Fonseca, J. W. Tonge, J. M. Dawson, W. B. Mori et al., Interpenetrating Plasma Shells: Near-Equipartition Magnetic Field Generation and Nonthermal Particle Acceleration, The Astrophysical Journal, vol.596, issue.1, p.121, 2003.
DOI : 10.1086/379156

URL : http://cds.cern.ch/record/630883/files/0307500.pdf

A. Bret, A. Stockem, R. Narayan, and L. O. Silva, Collisionless Weibel shocks: Full formation mechanism and timing, Physics of Plasmas, vol.4, issue.7, pp.7230110-1063, 2014.
DOI : 10.1088/0004-637X/744/2/182

URL : http://arxiv.org/pdf/1406.4144

H. Park, C. M. Huntington, F. Fiuza, R. P. Drake, D. H. Froula et al., Collisionless shock experiments with lasers and observation of weibel instabilities, Physics of Plasmas, vol.22, issue.5, pp.5631110-1063, 2015.

M. Tabak, J. Hammer, M. E. Glinsky, W. L. Kruer, S. C. Wilks et al., Ignition and high gain with ultrapowerful lasers*, Physics of Plasmas, vol.2, issue.5, pp.1626-163410, 1994.
DOI : 10.1016/0030-4018(85)90120-8

J. M. Hill, M. H. Key, S. P. Hatchett, and R. R. Freeman, Beam-Weibel filamentation instability in near-term and fast-ignition experiments, Physics of Plasmas, vol.12, issue.8, pp.8230410-1063, 2005.
DOI : 10.1063/1.866305

A. Karmakar, N. Kumar, A. Pukhov, O. Polomarov, and G. Shvets, Three-dimensional filamentary structures of a relativistic electron beam in fast ignition plasmas, Physics of Plasmas, vol.30, issue.12, pp.12070210-1063, 2008.
DOI : 10.1051/0004-6361:20065366

A. Karmakar, N. Kumar, A. Pukhov, O. Polomarov, and G. Shvets, Detailed particle-in-cell simulations on the transport of a relativistic electron beam in plasmas, Physical Review E, vol.30, issue.1, p.16401, 1923.
DOI : 10.1088/0032-1028/17/6/009

T. Helgaker, P. Jorgensen, and J. Olsen, The electronic hamiltonian in an electromagnetic field

A. Inglebert, A. Ghizzo, T. Réveillé, D. D. Sarto, P. Bertrand et al., A multi-stream Vlasov modeling unifying relativistic Weibel-type instabilities, EPL (Europhysics Letters), vol.95, issue.4, pp.45002-45047, 2011.
DOI : 10.1209/0295-5075/95/45002

A. Ghizzo and P. Bertrand, On the multistream approach of relativistic Weibel instability. I. Linear analysis and specific illustrations, Physics of Plasmas, vol.20, issue.8, pp.8210910-1063, 2013.
DOI : 10.1103/PhysRevLett.96.105002

URL : https://hal.archives-ouvertes.fr/hal-01287078

A. Ghizzo, On the multistream approach of relativistic weibel instability. ii. bernsteingreene-kruskal-type waves in magnetic trapping, Physics of Plasmas, vol.20, issue.8, pp.8211010-1063, 2013.
URL : https://hal.archives-ouvertes.fr/hal-01287078

A. Ghizzo, On the multistream approach of relativistic Weibel instability. III. Comparison with full-kinetic Vlasov simulations, Physics of Plasmas, vol.20, issue.8, pp.8211110-1063, 2013.
DOI : 10.1103/PhysRevE.53.6460

URL : https://hal.archives-ouvertes.fr/hal-01287078

D. C. Depackh, The Behaviour of a Large Number of Electrons Oscillating between the Plates of a Condenser???, Journal of Electronics and Control, vol.32, issue.6, pp.521-5301000207216308937605, 1080.
DOI : 10.1080/00207216308937605

P. Bertrand and M. R. Feix, Non linear electron plasma oscillation: the ???water bag model???, Physics Letters A, vol.28, issue.1, pp.68-69, 1968.
DOI : 10.1016/0375-9601(68)90606-3

P. Bertrand and M. R. Feix, Un modèle dans l'espace des phases pour l'´ etude des plasmas non collisionnels : le " water bag, J. Phys. France, pp.31-36, 1970.
DOI : 10.1051/jphys:01970003105-6045100

K. V. Roberts and H. L. Berk, Nonlinear Evolution of a Two-Stream Instability, Physical Review Letters, vol.1, issue.6, pp.297-300, 1967.
DOI : 10.1088/0029-5515/1/2/003

M. Navet and P. Bertrand, Multiple ???water-bag??? model and Landau damping, Physics Letters A, vol.34, issue.2, pp.117-118, 1971.
DOI : 10.1016/0375-9601(71)90232-5

A. Bret, A simple analytical model for the Weibel instability in the non-relativistic regime, Physics Letters A, vol.359, issue.1, pp.52-55, 2006.
DOI : 10.1016/j.physleta.2006.05.081

P. H. Yoon and R. C. Davidson, Exact analytical model of the classical Weibel instability in a relativistic anisotropic plasma, Physical Review A, vol.27, issue.6, pp.2718-2721, 1987.
DOI : 10.1063/1.864542

A. Inglebert, A. Ghizzo, T. Réveillé, P. Bertrand, and F. Califano, Electron temperature anisotropy instabilities represented by superposition of streams, Physics of Plasmas, vol.19, issue.12, pp.12210910-10634772770, 2012.
DOI : 10.1063/1.1758231

N. Besse, P. Bertrand, P. Morel, and E. Gravier, Weak turbulence theory and simulation of the gyro-water-bag model, Physical Review E, vol.8, issue.5, pp.56410-50, 2008.
DOI : 10.1093/acprof:oso/9780198528692.001.0001

URL : https://hal.archives-ouvertes.fr/hal-00594870

S. I. Braginskii, Transport processes in a plasma, Reviews of Plasma Physics, vol.1, pp.205-54, 1965.

G. F. Chew, M. L. Goldberger, and F. E. Low, The Boltzmann Equation and the One-Fluid Hydromagnetic Equations in the Absence of Particle Collisions, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol.236, issue.1204, pp.112-118, 1204.
DOI : 10.1098/rspa.1956.0116

D. , D. Sarto, F. Pegoraro, and A. Tenerani, 'magneto-elastic' waves in an anisotropic magnetised plasma, Plasma Physics and Controlled Fusion, vol.59, issue.4, pp.45002-54, 2017.
DOI : 10.1088/1361-6587/aa56bd

URL : http://arxiv.org/pdf/1509.04938

J. J. Ramos, Dynamic evolution of the heat fluxes in a collisionless magnetized plasma, Physics of Plasmas, vol.567, issue.9, pp.3601-360710, 2003.
DOI : 10.1063/1.1724387

T. Chust and G. Belmont, Closure of fluid equations in collisionless magnetoplasmas, Physics of Plasmas, vol.109, issue.1, pp.1250610-1063, 2006.
DOI : 10.1063/1.2096582

URL : https://hal.archives-ouvertes.fr/hal-00154675

B. D. Fried, Mechanism for instability of transverse plasma waves. The Physics of Fluids, pp.337-33710, 1959.

F. Pegoraro, S. V. Bulanov, F. Califano, and M. Lontano, Nonlinear development of the weibel instability and magnetic field generation in collisionless plasmas, Physica Scripta, vol.63, issue.T63, pp.262-55, 1996.
DOI : 10.1088/0031-8949/1996/T63/046

F. Califano, F. Pegoraro, and S. V. Bulanov, Spatial structure and time evolution of the Weibel instability in collisionless inhomogeneous plasmas, Physical Review E, vol.99, issue.1, pp.963-969, 1997.
DOI : 10.1016/S0010-4655(96)00117-8

F. Califano, R. Prandi, F. Pegoraro, and S. V. Bulanov, Nonlinear filamentation instability driven by an inhomogeneous current in a collisionless plasma, Physical Review E, vol.99, issue.6, pp.7837-7845, 1998.
DOI : 10.1016/S0010-4655(96)00117-8

F. Califano, D. D. Sarto, and F. Pegoraro, Three-Dimensional Magnetic Structures Generated by the Development of the Filamentation (Weibel) Instability in the Relativistic Regime, Physical Review Letters, vol.60, issue.10, pp.105008-55, 2006.
DOI : 10.1016/0021-9991(92)90324-R

URL : https://hal.archives-ouvertes.fr/hal-00524423

A. Ghizzo, M. Sarrat, and D. D. Sarto, Vlasov models for kinetic Weibel-type instabilities, Journal of Plasma Physics, vol.81, issue.01, pp.2017-57
DOI : 10.1063/1.1705933

URL : https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B69CA9E834A957C5F84CCC68495D8D69/S0022377816001215a.pdf/div-class-title-vlasov-models-for-kinetic-weibel-type-instabilities-div.pdf

?. Pourquoi-introduire-le-tenseur-de-pression, 63 3.1.1 Premier exemplè a travers l'instabilité Weibel pure, p.63

B. Basu, Moment equation description of Weibel instability, Physics of Plasmas, vol.45, issue.12, pp.5131-513410, 2002.
DOI : 10.1063/1.1705933

M. Lazar, M. E. Dieckmann, and S. Poedts, Resonant Weibel instability in counterstreaming plasmas with temperature anisotropies, Journal of Plasma Physics, vol.57, issue.01, pp.49-56, 2010.
DOI : 10.1063/1.2357047

M. Lazar, R. Schlickeiser, R. Wielebinski, and S. Poedts, COSMOLOGICAL EFFECTS OF WEIBEL-TYPE INSTABILITIES, The Astrophysical Journal, vol.693, issue.2, pp.1133-73, 2009.
DOI : 10.1088/0004-637X/693/2/1133

B. D. Fried and S. D. Conte, The Plasma Dispersion Function, p.64, 1961.

M. Tzoufras, C. Ren, F. S. Tsung, J. W. Tonge, W. B. Mori et al., Space-Charge Effects in the Current-Filamentation or Weibel Instability, Physical Review Letters, vol.46, issue.10, pp.105002-69, 2006.
DOI : 10.1063/1.1476004

M. Sarrat, D. D. Sarto, and A. Ghizzo, Fluid description of Weibel-type instabilities via full pressure tensor dynamics, EPL (Europhysics Letters), vol.115, issue.4, pp.45001-75, 2016.
DOI : 10.1209/0295-5075/115/45001

A. Bret, L. Gremillet, and J. C. Bellido, How really transverse is the filamentation instability?, Physics of Plasmas, vol.24, issue.3, pp.3210310-10632710810, 2007.
DOI : 10.1103/PhysRevLett.88.121101

A. Ghizzo, T. W. Johnston, T. Réveillé, P. Bertrand, and M. Albrecht-marc, Stimulated-Raman-scatter behavior in a relativistically hot plasma slab and an electromagnetic low-order pseudocavity, Physical Review E, vol.8, issue.4, pp.46407-73, 2006.
DOI : 10.1063/1.873126

M. Albrecht-marc, A. Ghizzo, T. W. Johnston, T. Réveillé, D. D. Sarto et al., Saturation process induced by vortex-merging in numerical Vlasov-Maxwell experiments of stimulated Raman backscattering, Physics of Plasmas, vol.14, issue.7, pp.7270410-10632749715, 2007.
DOI : 10.1063/1.1693039

URL : https://hal.archives-ouvertes.fr/hal-00524427

A. Ghizzo, D. D. Sarto, and T. Reveille, Hamiltonian stochastic processes induced by successive wave-particle interactions in stimulated Raman scattering, Physical Review E, vol.79, issue.4, pp.46404-73, 2009.
DOI : 10.1103/PhysRevLett.99.185005

P. E. Masson-laborde, W. Rozmus, Z. Peng, D. Pesme, S. Hüller et al., Evolution of the stimulated Raman scattering instability in two-dimensional particle-in-cell simulations, Physics of Plasmas, vol.17, issue.9, pp.9270410-10633474619, 2010.
DOI : 10.1140/epjd/e2007-00181-x

A. Ghizzo, F. Huot, and P. Bertrand, A non-periodic 2D semi-Lagrangian Vlasov code for laser???plasma interaction on parallel computer, Journal of Computational Physics, vol.186, issue.1, pp.47-69, 2003.
DOI : 10.1016/S0021-9991(03)00010-X

A. Ghizzo, D. Delsarto, T. Réveillé, N. Besse, and R. Klein, Self-induced transparency scenario revisited via beat-wave heating induced by Doppler shift in overdense plasma layer, Physics of Plasmas, vol.34, issue.6, pp.6270210-10632735123, 2007.
DOI : 10.1063/1.2431161

URL : https://hal.archives-ouvertes.fr/hal-00594860

M. Lazar, R. Schlickeiser, and P. K. Shukla, Cumulative effect of the Weibel-type instabilities in symmetric counterstreaming plasmas with kappa anisotropies, Physics of Plasmas, vol.324, issue.4, pp.4210310-1063, 2008.
DOI : 10.1103/PhysRevE.70.046401

M. Lazar, Fast magnetization in counterstreaming plasmas with temperature anisotropies, Physics Letters A, vol.372, issue.14, pp.2446-2449, 2008.
DOI : 10.1016/j.physleta.2007.11.063

A. Stockem and M. Lazar, Revision of " cumulative effect of the filamentation and weibel instabilities in counterstreaming thermal plasmas " [phys, Physics of Plasmas, vol.13, issue.151, pp.10210701450110-1063, 2006.

M. Lazar, A. Smolyakov, R. Schlickeiser, and P. K. Shukla, A comparative study of the filamentation and Weibel instabilities and their cumulative effect. I. Non-relativistic theory, Journal of Plasma Physics, vol.31, issue.01, pp.19-33, 2009.
DOI : 10.1086/379309

A. Stockem, M. Lazar, P. K. Shukla, and A. Smolyakov, A comparative study of the filamentation and Weibel instabilities and their cumulative effect. II. Weakly relativistic beams, Journal of Plasma Physics, vol.70, issue.04, pp.529-543, 2009.
DOI : 10.1051/0004-6361:20065365

A. Ghizzo, M. Sarrat, and D. D. Sarto, Vlasov models for kinetic Weibel-type instabilities, Journal of Plasma Physics, vol.81, issue.01, pp.2017-83
DOI : 10.1063/1.1705933

URL : https://www.cambridge.org/core/services/aop-cambridge-core/content/view/B69CA9E834A957C5F84CCC68495D8D69/S0022377816001215a.pdf/div-class-title-vlasov-models-for-kinetic-weibel-type-instabilities-div.pdf

M. Sarrat, D. D. Sarto, and A. Ghizzo, A pressure tensor description for the time-resonant Weibel instability, Journal of Plasma Physics, vol.72, issue.01, pp.2017-90
DOI : 10.1103/PhysRevLett.96.105002

M. Abramovitz and I. A. Stegun, Handbook of mathematical functions with formulas, graphs, and mathematical tables, p.94, 1964.

V. Présentation-générale-du-code, 109 4.2.1 La méthode semi-lagrangienne, p.111

.. Leprobì-eme-de-la-conservation-de-la-charge and .. La-méthode-de-yee, 122 4.4.1 Conservation de la charge pour le solveur de, p.124

G. Lapenta, Particle simulations of space weather, Journal of Computational Physics, vol.231, issue.3, pp.795-821, 2012.
DOI : 10.1016/j.jcp.2011.03.035

R. Courant, K. Friedrichs, and H. Lewy, ??ber die partiellen Differenzengleichungen der mathematischen Physik, Mathematische Annalen, vol.100, pp.32-74, 1928.
DOI : 10.1007/978-1-4612-5385-3_7

A. Staniforth and J. Côté, Semi-Lagrangian Integration Schemes for Atmospheric Models???A Review, Monthly Weather Review, vol.119, issue.9, pp.2206-2223, 1991.
DOI : 10.1175/1520-0493(1991)119<2206:SLISFA>2.0.CO;2

M. Gutnic, M. Haefele, I. Paun, and E. Sonnendrücker, Vlasov simulations on an adaptive phase-space grid, Proceedings of the 18th International Conferene on the Numerical Simulation of Plasmas, pp.214-219, 2004.
DOI : 10.1016/j.cpc.2004.06.073

URL : https://hal.archives-ouvertes.fr/hal-00129681

E. Sonnendrücker, F. Filbet, A. Friedman, E. Oudet, and J. Vay, Vlasov simulations of beams with a moving grid, Proceedings of the 18th International Conferene on the Numerical Simulation of Plasmas, pp.390-395, 2004.
DOI : 10.1016/j.cpc.2004.06.077

N. Besse, E. Deriaz, and . Madaule, Adaptive multiresolution semi-Lagrangian discontinuous Galerkin methods for the Vlasov equations, Journal of Computational Physics, vol.332, pp.376-417, 2017.
DOI : 10.1016/j.jcp.2016.12.003

URL : https://hal.archives-ouvertes.fr/hal-01366726

C. Z. Cheng and G. Knorr, The integration of the vlasov equation in configuration space, Journal of Computational Physics, vol.22, issue.3, pp.330-351, 1976.
DOI : 10.1016/0021-9991(76)90053-X

M. M. Shoucri and R. R. Gagné, Splitting schemes for the numerical solution of a two-dimensional Vlasov equation, Journal of Computational Physics, vol.27, issue.3, pp.315-322, 1978.
DOI : 10.1016/0021-9991(78)90013-X

E. Sonnendrücker, J. Roche, P. Bertrand, and A. Ghizzo, The Semi-Lagrangian Method for the Numerical Resolution of the Vlasov Equation, Journal of Computational Physics, vol.149, issue.2, pp.201-220, 1999.
DOI : 10.1006/jcph.1998.6148

O. Coulaud, E. Sonnendrücker, E. Dillon, P. Bertrand, and A. Ghizzo, Parallelization of semi-Lagrangian Vlasov codes, Journal of Plasma Physics, vol.61, issue.3, pp.435-448, 1999.
DOI : 10.1017/S0022377899007527

URL : https://hal.archives-ouvertes.fr/inria-00110770

N. Crouseilles, G. Latu, and E. Sonnendrücker, Hermite Spline Interpolation on Patches for Parallelly Solving the Vlasov-Poisson Equation, International Journal of Applied Mathematics and Computer Science, vol.119, issue.3, pp.335-349, 2007.
DOI : 10.1109/27.510001

URL : https://hal.archives-ouvertes.fr/hal-00688671

K. S. Yee, Numerical solution of initial boundary value problems involving maxwell's equations in isotropic media, IEEE Trans. Antennas and Propagation, pp.302-307, 1966.

T. Zh and . Esirkepov, Exact charge conservation scheme for particle-in-cell simulation with an arbitrary form-factor, Computer Physics Communications, vol.135, issue.2, pp.144-153, 2001.

R. Barthelmé, Leprobì eme de conservation de la charge dans le couplage deséquationsdeséquations de Vlasov et de Maxwell, Thèse de doctorat dirigée par Sonnendrücker, p.124, 2005.

A. Inglebert, A. Ghizzo, T. Réveillé, D. D. Sarto, P. Bertrand et al., Multi-stream Vlasov model for the study of relativistic Weibel-type instabilities, Plasma Physics and Controlled Fusion, vol.54, issue.8, pp.85004-135, 2012.
DOI : 10.1088/0741-3335/54/8/085004

L. Palodhi, F. Califano, and F. Pegoraro, Nonlinear kinetic development of the Weibel instability and the generation of electrostatic coherent structures, Plasma Physics and Controlled Fusion, vol.51, issue.12, pp.51125006-135, 2009.
DOI : 10.1088/0741-3335/51/12/125006

M. E. Dieckmann, The filamentation instability driven by warm electron beams: statistics and electric field generation, Plasma Physics and Controlled Fusion, vol.51, issue.12, pp.124042-135, 2009.
DOI : 10.1088/0741-3335/51/12/124042

URL : http://arxiv.org/pdf/0910.0228

A. Bret, L. Gremillet, and M. E. Dieckmann, Multidimensional electron beam-plasma instabilities in the relativistic regime, Physics of Plasmas, vol.17, issue.12, pp.12050110-1063, 2010.
DOI : 10.1063/1.3514586.4

A. Ghizzo, B. Izrar, P. Bertrand, M. R. Feix, E. Fijalkow et al., BGK structures as quasi-particles, Physics Letters A, vol.120, issue.4, pp.191-195, 1987.
DOI : 10.1016/0375-9601(87)90334-3

A. Ghizzo, B. Izrar, P. Bertrand, E. Fijalkow, M. R. Feix et al., Stability of bernstein?greene?kruskal plasma equilibria. numerical experiments over a long time. The Physics of Fluids, pp.72-8210, 1988.

K. M. Schoeffler, N. F. Loureiro, R. A. Fonseca, and L. O. Silva, The generation of magnetic fields by the Biermann battery and the interplay with the Weibel instability, Physics of Plasmas, vol.5, issue.5, pp.5630410-1063, 2016.
DOI : 10.1063/1.4946017.1

F. Califano, R. Prandi, F. Pegoraro, and S. V. Bulanov, Nonlinear filamentation instability driven by an inhomogeneous current in a collisionless plasma, Physical Review E, vol.99, issue.6, pp.7837-7845, 1998.
DOI : 10.1016/S0010-4655(96)00117-8

F. Califano, F. Pegoraro, and D. D. Sarto, Resonant evolution of the current filamentation (Weibel) instability in the relativistic regime, AIP Conference Proceedings, pp.44-4910, 2006.
DOI : 10.1063/1.2195196