. La-comparaison-avec-le-modèle and . Complet, 1D-2V est rapidement faite avec la figure 3.13, où l'on peut voir un parfait accord pour l'énergie électrostatique. La densité suit ce mouvement oscillant, en accord avec l

B. D. Fried, Mechanism for Instability of Transverse Plasma Waves, Physics of Fluids, vol.4, issue.3, p.337, 1959.
DOI : 10.1063/1.1705933

A. Bret, L. Gremillet, and M. E. Dieckmann, Multidimensional electron beam-plasma instabilities in the relativistic regime, Physics of Plasmas, vol.17, issue.12, p.120501, 2010.
DOI : 10.1063/1.3514586.4

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

Y. Fujita and T. N. Kato, The generation of magnetic fields by the Weibel instability, Astronomische Nachrichten, vol.1, issue.5-6, p.443, 2006.
DOI : 10.1063/1.870498

M. V. Medvedev, L. O. Silva, and M. Kamionkowski, Cluster Magnetic Fields from Large-Scale Structure and Galaxy Cluster Shocks, The Astrophysical Journal, vol.642, issue.1, p.1, 2006.
DOI : 10.1086/504470

R. Schlickeiser and P. K. Schukla, Cosmological Magnetic Field Generation by the Weibel Instability, The Astrophysical Journal, vol.599, issue.2, p.57, 2003.
DOI : 10.1086/381246

M. Lazar, R. Schlickeiser, and P. K. Schukla, Cumulative effect of the filamentation and Weibel instabilities in counterstreaming thermal plasmas, Physics of Plasmas, vol.13, issue.10, p.102107, 2006.
DOI : 10.1016/B978-1-4832-2929-4.50004-6

T. Piran, Gamma-ray bursts and the fireball model, Physics Reports, vol.314, issue.6, p.575, 1999.
DOI : 10.1016/S0370-1573(98)00127-6

M. V. Medvedev and A. Loeb, Generation of Magnetic Fields in the Relativistic Shock of Gamma???Ray Burst Sources, The Astrophysical Journal, vol.526, issue.2, p.697, 1999.
DOI : 10.1086/308038

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

K. Nishikawa, J. Niemec, P. E. Hardee, M. V. Medvedev, H. Sol et al., WEIBEL INSTABILITY AND ASSOCIATED STRONG FIELDS IN A FULLY THREE-DIMENSIONAL SIMULATION OF A RELATIVISTIC SHOCK, The Astrophysical Journal, vol.698, issue.1, p.13, 2009.
DOI : 10.1088/0004-637X/698/1/L10

C. H. Jaroschek, H. Lesch, and R. A. Treumann, Self???consistent Diffusive Lifetimes of Weibel Magnetic Fields in Gamma???Ray Bursts, The Astrophysical Journal, vol.616, issue.2, p.1065, 2004.
DOI : 10.1086/424923

M. E. Dieckmann, P. K. Shukla, and L. O. Drury, The Formation of a Relativistic Partially Electromagnetic Planar Plasma Shock, The Astrophysical Journal, vol.675, issue.1, p.586, 2008.
DOI : 10.1086/525516

M. V. Medvedev and O. Zakutnyanya, MAGNETIC FIELDS AND COSMIC RAYS IN GRBs: A SELF-SIMILAR COLLISIONLESS FORESHOCK, The Astrophysical Journal, vol.696, issue.2, p.2269, 2009.
DOI : 10.1088/0004-637X/696/2/2269

F. Califano, N. Attico, F. Pegoraro, G. Bertin, and S. V. Bulanov, Fast Formation of Magnetic Islands in a Plasma in the Presence of Counterstreaming Electrons, Physical Review Letters, vol.39, issue.23, p.5293, 2001.
DOI : 10.1088/0741-3335/39/12B/020

S. Zenitani and M. Hesse, The role of the Weibel instability at the reconnection jet front in relativistic pair plasma reconnection, Physics of Plasmas, vol.15, issue.2, p.22101, 2008.
DOI : 10.1038/371495a0

S. Lu, Q. Lu, X. Shao, P. H. Yoon, and S. Wang, Weibel instability and structures of magnetic island in anti-parallel collisionless magnetic reconnection, Physics of Plasmas, vol.18, issue.7, p.72105, 2011.
DOI : 10.5194/angeo-28-789-2010

A. Benuzzi-mounaix, La fusion nucléaire : Un espoir pour une énergie propre et inépuisable, Belin, 2008.

J. Bobin, La fusion thermonucléaire contrôlée, EDP Sciences, 2011.

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, p.1626, 1994.
DOI : 10.1016/0030-4018(85)90120-8

S. Baton, Étude expérimentale du transport électronique dans le cadre de l'allumeur rapide. Mém. d'Habilitation à Diriger des Recherches, Laboratoire pour l'Utilisation des Lasers Intenses, 2008.

A. Pukhov and J. Meyer-ter-vehn, Laser Hole Boring into Overdense Plasma and Relativistic Electron Currents for Fast Ignition of ICF Targets, Physical Review Letters, vol.59, issue.14, p.2686, 1997.
DOI : 10.1103/PhysRevLett.59.52

Y. Sentoku, K. Mima, S. Kojima, and H. , Magnetic instability by the relativistic laser pulses in overdense plasmas, Physics of Plasmas, vol.60, issue.2, p.689, 2000.
DOI : 10.1103/PhysRevLett.59.52

Y. Sentoku, K. Mima, Z. M. Sheng, P. Kaw, K. Nishihara et al., Threedimensional particle-in-cell simulations of energetic electron generation and transport with relativistic laser pulses in overdense plasmas, Phys. Rev. E, pp.65-046408, 2002.

L. O. Silva, R. A. Fonseca, J. W. Tonge, W. B. Mori, and J. M. Dawson, On the role of the purely transverse Weibel instability in fast ignitor scenarios, Physics of Plasmas, vol.1, issue.6, p.2458, 2002.
DOI : 10.1103/PhysRevLett.35.1504

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, p.82304, 2005.
DOI : 10.1063/1.866305

A. Karmakar, N. Kumar, A. Pukhov, and O. Polomarov, Three-dimensional filamentary structures of a relativistic electron beam in fast ignition plasmas, Physics of Plasmas, vol.30, issue.12, p.120702, 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, 2009.
DOI : 10.1088/0032-1028/17/6/009

M. Tatarakis, F. N. Beg, E. L. Clark, A. E. Dangor, R. D. Edwards et al., Propagation Instabilities of High-Intensity Laser-Produced Electron Beams, Physical Review Letters, vol.264, issue.17, p.175001, 2003.
DOI : 10.1103/PhysRevLett.88.125001

R. Jung, J. Osterholz, K. Löwenbrück, S. Kiselev, G. Pretzler et al., Study of Electron-Beam Propagation through Preionized Dense Foam Plasmas, Physical Review Letters, vol.65, issue.19, 2005.
DOI : 10.1017/S0022377899007515

T. V. Liseikina, F. Califano, V. A. Vshivkov, F. Pegoraro, and S. V. Bulanov, Small-scale electron density and magnetic-field structures in the wake of an ultraintense laser pulse, Physical Review E, vol.27, issue.5, p.5991, 1999.
DOI : 10.1063/1.864820

C. M. Huntington, A. G. Thomas, C. Mcguffey, T. Matsuoka, V. Chvykov et al., Current Filamentation Instability in Laser Wakefield Accelerators, Physical Review Letters, vol.106, issue.10, 2011.
DOI : 10.1038/nphys1789

A. Debayle, J. J. Honrubia, E. Humières, and V. T. Tikhonchuk, Divergence of laser-driven relativistic electron beams, Physical Review E, vol.82, issue.3, p.36405, 2010.
DOI : 10.1119/1.15378

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, p.92704, 2010.
DOI : 10.1140/epjd/e2007-00181-x

N. Rostoker and M. N. Rosenbluth, Test Particles in a Completely Ionized Plasma, Physics of Fluids, vol.21, issue.1, 1960.
DOI : 10.1063/1.1705998

C. K. Birdsall and A. B. Langdon, Plasma physics via computer simulation, Institute of Physics, 1991.
DOI : 10.1887/0750301171

R. Barthelmé, Le problème de la conservation de la charge dans le couplage des équation de Vlasov et de Maxwell, Thèse de doctorat, 2005.

R. Courant, K. Freidrichs, and H. Lewy, On the Partial Difference Equations of Mathematical Physics, IBM Journal of Research and Development, vol.11, issue.2, p.215, 1967.
DOI : 10.1147/rd.112.0215

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

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, p.201, 1999.
DOI : 10.1006/jcph.1998.6148

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

M. R. Feix, P. Bertrand, and A. Ghizzo, Eulerian codes for the Vlasov equation, dans Advances kinetic theory and computing, pp.45-81, 1994.

G. Manfredi, Long-Time Behavior of Nonlinear Landau Damping, Physical Review Letters, vol.22, issue.15, p.2815, 1997.
DOI : 10.1063/1.862470

E. Fijalkow, A numerical solution to the Vlasov equation, Computer Physics Communications, vol.116, issue.2-3, p.319, 1999.
DOI : 10.1016/S0010-4655(98)00146-5

F. Filbet, E. Sonnendrücker, and P. Bertrand, Conservative Numerical Schemes for the Vlasov Equation, Journal of Computational Physics, vol.172, issue.1, p.166, 2001.
DOI : 10.1006/jcph.2001.6818

F. Filbet, Contribution à l'analyse et la simulation numérique de l'équation de Vlasov, Thèse de doctorat, 2001.

F. Filbet and E. Sonnendrücker, Comparison of Eulerian Vlasov solvers, Computer Physics Communications, vol.150, issue.3, p.247, 2003.
DOI : 10.1016/S0010-4655(02)00694-X

URL : https://hal.archives-ouvertes.fr/hal-00129663

A. Aissi, La modélisation des tubes à onde progressive à hélice en domaine temporel, Thèse de doctorat, 2008.

A. Mangeney, F. Califano, C. Cavazzoni, and P. Travnicek, A Numerical Scheme for the Integration of the Vlasov???Maxwell System of Equations, Journal of Computational Physics, vol.179, issue.2, p.495, 2002.
DOI : 10.1006/jcph.2002.7071

F. Huot, A. Ghizzo, P. Bertrand, E. Sonnendrücker, and O. Coulaud, Instability of the time splitting scheme for the one-dimensional and relativistic Vlasov???Maxwell system, Journal of Computational Physics, vol.185, issue.2, p.512, 2003.
DOI : 10.1016/S0021-9991(02)00079-7

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, 1996.
DOI : 10.1088/0031-8949/1996/T63/046

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, p.331, 1998.
DOI : 10.1017/S0022377898006862

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, p.7048, 1998.
DOI : 10.1063/1.1693910

F. Califano, T. Cecchi, and C. Chiuderi, Nonlinear kinetic regime of the Weibel instability in an electron???ion plasma, Physics of Plasmas, vol.7, issue.2, p.451, 2002.
DOI : 10.1103/PhysRev.109.10

A. Bret, L. Gremillet, and J. C. Bellido, How really transverse is the filamentation instability?, Physics of Plasmas, vol.24, issue.3, p.32103, 2007.
DOI : 10.1103/PhysRevLett.88.121101

A. Bret, L. Gremillet, D. Benisti, 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, 2008.
DOI : 10.1086/308038

P. S. Verma, S. Sengupta, and P. K. Kaw, Nonlinear evolution of an arbitrary density perturbation in a cold homogeneous unmagnetized plasma, Physics of Plasmas, vol.29, issue.1, 2011.
DOI : 10.1017/CBO9781139171281

T. Drouot, Modèle cinétique pour l'instabilité de filamentation de courant, Mém. Master, 2011.

G. Kalman, Nonlinear oscillations and nonstationary flow in a zero temperature plasma : Part I. Initial and boundary value problems, Ann. Phys, vol.10, issue.1, 1960.

G. Kalman, Nonlinear oscillations and nonstationary flow in a zero temperature plasma, Annals of Physics, vol.10, issue.1, p.29, 1960.
DOI : 10.1016/0003-4916(60)90015-4

R. C. Davidson, D. A. Hammer, I. Haber, and C. E. Wagner, Nonlinear Development of Electromagnetic Instabilities in Anisotropic Plasmas, Physics of Fluids, vol.15, issue.2, p.317, 1972.
DOI : 10.1063/1.1693910

H. J. De and . Blank, Kinetic model of electrons in drift-Alfven current-vortices, Phys. Plasmas, vol.8, p.3927, 2001.

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, p.45002, 2011.
DOI : 10.1209/0295-5075/95/45002

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.85004, 2012.
DOI : 10.1088/0741-3335/54/8/085004

H. H. Kaang, C. Ryu, and P. H. Yoon, Nonlinear saturation of relativistic Weibel instability driven by thermal anisotropy, Physics of Plasmas, vol.16, issue.8, 2009.
DOI : 10.1063/1.2646285

A. Ghizzo, T. W. Johnston, T. Réveillé, P. Bertrand, and M. Albrecht-marc, Stimulated-Ramanscatter behavior in a relativistically hot plasma slab and an electromagnetic low-order pseudocavity, Phys. Rev. E, pp.74-046407, 2006.

A. Ghizzo, D. D. Sarto, 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, p.62702, 2007.
DOI : 10.1063/1.2431161

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

R. Tautz, A??new distribution function for relativistic counterstreaming plasmas, Astrophysics and Space Science, vol.14, issue.1, p.69, 2010.
DOI : 10.1063/1.2921788

D. C. De-packh, The Water-bag Model of a Sheet Electron Beamy, Journal of Electronics and Control, vol.10, issue.5, p.417, 1962.
DOI : 10.1063/1.1728437

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

L. Palodhi, F. Califano, and F. Pegoraro, Non-linear kinetic development of the Weibel instability and the generation of electrostatic coherent structures, Plasma Phys, Control. Fusion, pp.51-125006, 2009.

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, p.52104, 2011.
DOI : 10.1016/j.matcom.2009.08.038