D. Amdahl, Validity of the single processor approach to achieving large scale computing capabilities, Proceedings of the April 18-20, 1967, spring joint computer conference on, AFIPS '67 (Spring), pp.483-485, 1967.
DOI : 10.1145/1465482.1465560

T. D. Arber and R. G. Vann, A Critical Comparison of Eulerian-Grid-Based Vlasov Solvers, Journal of Computational Physics, vol.180, issue.1, pp.339-357, 2002.
DOI : 10.1006/jcph.2002.7098

G. Arfken, Spherical harmonics Mathematics Method for Physicists, pp.680-685, 1985.

P. T. Armstrong, Numerical Studies of the Nonlinear Vlasov Equation, Phys. of Fluids, pp.1269-1280, 1967.

P. T. Armstrong and M. , Asymptotic state of the two-stream instability, Journal of Plasma Physics, vol.10, issue.04, pp.425-433, 1967.
DOI : 10.1063/1.1762272

P. T. Armstrong, R. Harding, G. Knorr, and D. Montgomery, Solution of the Vlasov's equation by transform methods, Advances in Computational Physics, vol.9, p.29, 1976.

F. Assous, P. Degond, E. Heintze, P. A. Raviart, and J. Segré, On a Finite-Element Method for Solving the Three-Dimensional Maxwell Equations, Journal of Computational Physics, vol.109, issue.2, pp.222-237, 1993.
DOI : 10.1006/jcph.1993.1214

R. Barthelmé, Leprobì eme de conservation de la charge dans le couplage deséquations deséquations de Vlasov et de Maxwell, Thèse de l'université Louis Pasteur, 2005.

C. Bernardi and Y. Maday, Spectral methods, Handbook of Numerical Analysis, vol.5, 1997.
DOI : 10.1016/S1570-8659(97)80003-8

I. B. Bernstein, J. M. Greene, and M. D. Kruskal, Exact Nonlinear Plasma Oscillations, Physical Review, vol.108, issue.3, pp.546-550, 1957.
DOI : 10.1103/PhysRev.108.546

N. Besse, Etude mathématique et numérique de l'´ equation de Vlasov non linéaire sur des maillages non structurés de l'espace des phases, Thèse de l'université Louis Pasteur, 2003.

N. Besse, F. Filbet, M. Gutnic, I. Paun, and E. Sonnendrücker, An adaptative numerical method for the Vlasov equation based on a multiresolution analysis, Numerical Mathematics and advanced applications ENUMATH, pp.437-446, 2001.

N. Besse and E. Sonnendrücker, Semi-Lagrangian schemes for the Vlasov equation on an unstructured mesh of phase space, Journal of Computational Physics, vol.191, issue.2, pp.341-376, 2003.
DOI : 10.1016/S0021-9991(03)00318-8
URL : https://hal.archives-ouvertes.fr/hal-00594781

N. Besse and M. Mehrenberger, Convergence of classes of high-order semi-Lagrangian schemes for the Vlasov--Poisson system, Mathematics of Computation, vol.77, issue.261, 2004.
DOI : 10.1090/S0025-5718-07-01912-6
URL : https://hal.archives-ouvertes.fr/hal-00594785

N. Besse, J. Segré, and E. Sonnendrücker, Semi-Lagrangian schemes for the two-dimensional Vlasov-Poisson system on unstructured meshes, Transport Theory Statist, Phys, vol.34, pp.311-332, 2005.

C. K. Birdsall and A. B. Langdon, Plasma Physics Via Computer Simulation, Inst. of Physics, 1991.
DOI : 10.1887/0750301171

J. P. Boris and D. L. Book, Solution of Continuity Equations by the Method of Flux-Corrected Transport, J. Comput. Phys, vol.20, pp.397-431, 1976.
DOI : 10.1016/B978-0-12-460816-0.50008-7

S. Bourdarie, R. H. Friedel, J. Fennel, S. Kanekal, and T. E. Cayton, Radiation belt representation of the energetic electron environment : Model and data synthesis using the Salammbô radiation belt transport code and Los Alamos geosynschonous and GPS energetic particle data, Space Weather, 2005.

M. Bostan, Convergence des solutions faibles du syst??me de Vlasov???Maxwell stationnaire vers des solutions faibles du syst??me de Vlasov???Poisson stationnaire quand la vitesse de la lumi??re tend vers l'infini, Comptes Rendus Mathematique, vol.340, issue.11, pp.803-808, 2005.
DOI : 10.1016/j.crma.2005.04.009

M. Bostan, Solutions p??riodiques en temps des ??quations de Vlasov???Maxwell, Comptes Rendus Mathematique, vol.339, issue.6, pp.451-456, 2004.
DOI : 10.1016/j.crma.2004.07.008

J. P. Boyd, Asymptotic coefficients of hermite function series, Journal of Computational Physics, vol.54, issue.3, pp.382-410, 1984.
DOI : 10.1016/0021-9991(84)90124-4

J. P. Boyd, Chebychev and Fourier Spectral Methods, Dover publications, 2001.
DOI : 10.1007/978-3-642-83876-7

A. Bret, L. Gremillet, and J. C. Bellido, How really transverse is the filamentation instability?, Physics of Plasmas, vol.14, issue.3, 2007.
DOI : 10.1063/1.2710810

F. Califano, F. Pegoraro, S. V. Bulanov, and A. Mangeney, Kinetic saturation of the Weibel instability in a collisionless plasma, Physical Review E, vol.57, issue.6, pp.7048-7059, 1998.
DOI : 10.1103/PhysRevE.57.7048

N. Canouet, L. Fezoui, and S. Piperno, 3D Maxwell's equations and orthogonal non-conforming meshes : a hp-type Discontinuous Galerkin method, 2003.

C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods -Fundamentals in Single Domains, 2006.

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

R. Ciurea-borcia, G. Matthieussent, J. Solomon, L. Bel, E. Simonet et al., Pitch-angle diffusion of relativistic electrons due to resonant interactions with whistler waves, Physics of Plasmas, vol.6, issue.12, pp.4597-4606, 1999.
DOI : 10.1063/1.873747

R. Ciurea-borcia, G. Matthieussent, L. Bel, E. Simonet, F. Solomon et al., Oblique whistler waves generated in cold plasma by relativistic electron beams, Physics of Plasmas, vol.7, issue.1, pp.359-370, 2000.
DOI : 10.1063/1.873804

G. Cohen and P. Monk, Mur-n??d??lec finite element schemes for Maxwell's equations, Computer Methods in Applied Mechanics and Engineering, vol.169, issue.3-4, pp.197-217, 1999.
DOI : 10.1016/S0045-7825(98)00154-6

G. Cohen, X. Ferrì-eres, and S. Pernet, A spatial high-order hexahedral discontinuous Galerkin method to solve Maxwell???s equations in time domain, Journal of Computational Physics, vol.217, issue.2, pp.340-363, 2006.
DOI : 10.1016/j.jcp.2006.01.004

R. Dautray and J. L. Lions, Analyse mathématique et calcul scientifique pour les sciences et les techniques, 1985.

R. C. Davidson, Kinetic waves and instabilities in a uniform plasma, Handbook of Plasma Physics, vol.1, issue.554, 1983.

R. E. Denton, . Kotschenreuther, and . ?f-algorithm, ??f Algorithm, Journal of Computational Physics, vol.119, issue.2, p.283, 1995.
DOI : 10.1006/jcph.1995.1136

R. J. Diperna and J. L. Lions, Global weak solutions of Vlasov-Maxwell systems, Communications on Pure and Applied Mathematics, vol.2, issue.6, pp.729-757, 1989.
DOI : 10.1002/cpa.3160420603

G. Dipeso, E. C. Morse, and R. W. Ziolkowski, ??f and particle simulations of parametric instabilities, Journal of Computational Physics, vol.96, issue.2, p.325, 1991.
DOI : 10.1016/0021-9991(91)90239-H

B. Eliasson, Outflow Boundary Conditions for the Fourier Transformed One- Dimensional Vlasov-Poisson System, Journal of Scientific Computing, vol.16, issue.1, pp.1-28, 2001.
DOI : 10.1023/A:1011132312956

B. Eliasson, Domain Decomposition of the Padé Scheme and Pseudo-Spectral Method, Used in Vlasov Simulations, 2002.

B. Eliasson, Outflow Boundary Conditions for the Fourier Transformed Two-Dimensional Vlasov Equation, Journal of Computational Physics, vol.181, issue.1, pp.98-125, 2002.
DOI : 10.1006/jcph.2002.7121

B. Eliasson, Numerical modelling of the two-dimensional Fourier transformed Vlasov???Maxwell system, Journal of Computational Physics, vol.190, issue.2, pp.501-522, 2003.
DOI : 10.1016/S0021-9991(03)00295-X

B. Eliasson, The parallel implementation of the one-dimensional Fourier transformed Vlasov???Poisson system, Computer Physics Communications, vol.170, issue.2, pp.205-230, 2005.
DOI : 10.1016/j.cpc.2005.03.107

N. V. Elkina and J. Büchner, A new conservative unsplit method for the solution of the Vlasov equation, Journal of Computational Physics, vol.213, issue.2, pp.862-875, 2006.
DOI : 10.1016/j.jcp.2005.09.023

Z. Y. Ezzuddin, Numerical solutions of nonlinear plasma equations by the finite element method, 1975.

H. Figua, F. Bouchut, M. R. Feix, and E. Fijalkow, Instability of the Filtering Method for Vlasov's Equation, Journal of Computational Physics, vol.159, issue.2, pp.440-447, 2000.
DOI : 10.1006/jcph.2000.6423

E. Fijalkow, A numerical solution to the Vlasov equation, Computer Physics Communications, vol.116, issue.2-3, pp.319-328, 1999.
DOI : 10.1016/S0010-4655(98)00146-5

E. Fijalkow, Numerical solution to the Vlasov equation: The 1D code, Computer Physics Communications, vol.116, issue.2-3, pp.329-335, 1999.
DOI : 10.1016/S0010-4655(98)00147-7

F. Filbet, E. Sonnendrücker, and P. Bertrand, Conservative Numerical Schemes for the Vlasov Equation, Journal of Computational Physics, vol.172, issue.1, pp.166-187, 2001.
DOI : 10.1006/jcph.2001.6818

F. Filbet and E. Sonnendrücker, Comparison of Eulerian Vlasov solvers, Computer Physics Communications, vol.150, issue.3, pp.247-266, 2003.
DOI : 10.1016/S0010-4655(02)00694-X
URL : https://hal.archives-ouvertes.fr/hal-00129663

C. Fochesato and D. Bouche, Evaluation de différents solveurs de Maxwell pour la résolution de Maxwell-Vlasov par une méthode PIC, Rapport CEA-R-6140, 2007.

B. Fornberg, A practical guide to Pseudospectral Methods, Cambridge Monographs on Applied and Computational Mathematics, 1998.
DOI : 10.1017/CBO9780511626357

D. Funaro and O. Kavian, Approximation of some diffusion evolution equations in unbounded domains by Hermite functions, Mathematics of Computation, vol.57, issue.196, pp.597-619, 1991.
DOI : 10.1090/S0025-5718-1991-1094949-X

R. Gagne and M. Shoucri, A splitting scheme for the numerical solution of a one-dimensional Vlasov equation, Journal of Computational Physics, vol.24, issue.4, p.445, 1977.
DOI : 10.1016/0021-9991(77)90032-8

R. Glassey and J. Schaeffer, On the ???one and one-half dimensional??? relativistic Vlasov-Maxwell system, Mathematical Methods in the Applied Sciences, vol.33, issue.2, pp.169-179, 1990.
DOI : 10.1002/mma.1670130207

R. Glassey and J. Schaeffer, The "Two and One-Half Dimensional" Relativistic Vlasov Maxwell System, Communications in Mathematical Physics, vol.185, issue.2, pp.257-284, 1997.
DOI : 10.1007/s002200050090

R. Glassey and J. Schaeffer, The Relativistic Vlasov-Maxwell System in Two Space Dimensions: Part II, Archive for Rational Mechanics and Analysis, vol.141, issue.4, pp.56-90, 1986.
DOI : 10.1007/s002050050080

R. Glassey and W. Strauss, Singularity formation in a collisionless plasma could occur only at high velocities, Archive for Rational Mechanics and Analysis, vol.92, issue.1, pp.56-90, 1986.
DOI : 10.1007/BF00250732

D. Gottlieb and S. A. Orszag, Numerical analysis of spectral methods : Theory and applications, Soc. Ind. and Appl. Math, 1977.
DOI : 10.1137/1.9781611970425

F. C. Grant and M. R. Feix, Fourier-Hermite Solutions of the Vlasov Equations in the Linearized Limit, Physics of Fluids, vol.10, issue.4, p.696, 1967.
DOI : 10.1063/1.1762177

B. Y. Guo, Error estimation of Hermite spectral method for nonlinear partial differential equations, Mathematics of Computation, vol.68, issue.227, pp.1067-1078, 1999.
DOI : 10.1090/S0025-5718-99-01059-5

Y. Guo, Global weak solutions of the Vlasov-Maxwell system with boundary conditions, Communications in Mathematical Physics, vol.42, issue.2, pp.245-263, 1993.
DOI : 10.1007/BF02096997

B. Y. Guo and C. L. Xu, Hermite pseudospectral method for nonlinear partial differential equations, ESAIM: Mathematical Modelling and Numerical Analysis, vol.34, issue.4, pp.859-872, 2000.
DOI : 10.1051/m2an:2000100

M. Gutnic, M. Haefele, I. Paun, and E. Sonnendrücker, Vlasov simulations on an adaptive phase-space grid, Computer Physics Communications, vol.164, issue.1-3, pp.214-219, 2004.
DOI : 10.1016/j.cpc.2004.06.073
URL : https://hal.archives-ouvertes.fr/hal-00129681

M. Gutnic, M. Haefele, and E. Sonnendrücker, Moments conservation in adaptive Vlasov solver, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.558, issue.1, pp.159-162, 2006.
DOI : 10.1016/j.nima.2005.11.225
URL : https://hal.archives-ouvertes.fr/inria-00110757

F. Hermeline, Two Coupled Particle-Finite Volume Methods Using Delaunay-Vorono???? Meshes for the Approximation of Vlasov-Poisson and Vlasov-Maxwell Equations, Journal of Computational Physics, vol.106, issue.1, pp.1-18, 1993.
DOI : 10.1006/jcph.1993.1086

R. W. Hockney and J. W. Eastwood, Computer Simulation Using Particles, 1981.
DOI : 10.1201/9781439822050

J. P. Holloway, Spectral velocity discretizations for the Vlasov-Maxwell equations, Transport theory and statistical physics, pp.1-32, 1996.

J. P. Holloway, On Numerical Methods for Hamiltonian PDEs and a Collocation Method for the Vlasov???Maxwell Equations, Journal of Computational Physics, vol.129, issue.1, p.121, 1996.
DOI : 10.1006/jcph.1996.0238

R. E. Holzer, R. K. Burton, and K. W. Chan, Comparison of magnetospheric hiss with plasma parameters during weak diffusion, Rapport technique, Pub n ? 1550, Institute of Geophysics and Planetary physics, 1976.

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, pp.512-531, 2003.
DOI : 10.1016/S0021-9991(02)00079-7

B. Izrar, A. Ghizzo, P. Bertrand, E. Fijalkow, and M. R. Feix, Integration of Vlasov equation by a fast Fourier Eulerian code, Computer Physics Communications, vol.52, issue.3, pp.375-382, 1989.
DOI : 10.1016/0010-4655(89)90112-4

P. Jogalekar and M. Woodside, Evaluating the scalability of distributed systems, IEEE Transactions on Parallel and Distributed Systems, vol.11, issue.6, pp.589-603, 2000.
DOI : 10.1109/71.862209

G. Joyce, G. Knorr, and H. Meier, Numerical integration methods of the Vlasov equation, Journal of Computational Physics, vol.8, issue.1, pp.53-63, 1971.
DOI : 10.1016/0021-9991(71)90034-9

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/JZ071i001p00001

A. J. Klimas, A method for overcoming the velocity space filamentation problem in collisionless plasma model solutions, Journal of Computational Physics, vol.68, issue.1, p.202, 1987.
DOI : 10.1016/0021-9991(87)90052-0

A. J. Klimas and W. M. Farrell, A Splitting Algorithm for Vlasov Simulation with Filamentation Filtration, Journal of Computational Physics, vol.110, issue.1, pp.150-163, 1994.
DOI : 10.1006/jcph.1994.1011

L. Bel and E. , Etude physique et numérique de la saturation des ceintures de Van Allen, Thèse de l'université Paris XI, 2002.

L. Bourdiec, S. De-vuyst, F. Jacquet, and L. , Numerical solution of the Vlasov???Poisson system using generalized Hermite functions, Computer Physics Communications, vol.175, issue.8, pp.528-544, 2006.
DOI : 10.1016/j.cpc.2006.07.004

E. Lefebvre, N. Cochet, S. Fritzler, V. Malka, M. Aléonard et al., Electron and photon production from relativistic laser???plasma interactions, Nuclear Fusion, vol.43, issue.7, pp.629-633, 2003.
DOI : 10.1088/0029-5515/43/7/317
URL : https://hal.archives-ouvertes.fr/hal-00570540

H. Ma, W. Sun, and T. Tang, Hermite Spectral Methods with a Time-Dependent Scaling for Parabolic Equations in Unbounded Domains, SIAM Journal on Numerical Analysis, vol.43, issue.1, pp.58-75, 2005.
DOI : 10.1137/S0036142903421278

G. Manfredi, Long-Time Behavior of Nonlinear Landau Damping, Physical Review Letters, vol.79, issue.15, pp.2815-2818, 1997.
DOI : 10.1103/PhysRevLett.79.2815

G. Manfredi and P. Bertrand, Stability of Bernstein???Greene???Kruskal modes, Physics of Plasmas, vol.7, issue.6, pp.2425-2431, 2000.
DOI : 10.1063/1.874081

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, pp.495-538, 2002.
DOI : 10.1006/jcph.2002.7071

M. Mehrenberger, E. Violard, O. Hoenen, C. Pinto, M. Sonnendrücker et al., A parallel adaptive Vlasov solver based on hierarchical finite element interpolation, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol.558, issue.1, pp.188-191, 2006.
DOI : 10.1016/j.nima.2005.11.094
URL : https://hal.archives-ouvertes.fr/inria-00111165

T. Nakamura and T. Yabe, Cubic interpolated propagation scheme for solving the hyper-dimensional Vlasov???Poisson equation in phase space, Computer Physics Communications, vol.120, issue.2-3, pp.122-154, 1999.
DOI : 10.1016/S0010-4655(99)00247-7

Y. Omura and D. Summers, Computer simulations of relativistic whistler-mode wave???particle interactions, Physics of Plasmas, vol.11, issue.7, p.3530, 2004.
DOI : 10.1063/1.1757457

O. Neil and T. M. , Collisionless Damping of Nonlinear Plasma Oscillations, Physics of Fluids, vol.8, issue.12, p.2255, 1965.
DOI : 10.1063/1.1761193

S. A. Orszag, Comparison of Pseudospectral and Spectral Approximation, Studies in Applied Mathematics, vol.49, issue.3, pp.253-259, 1972.
DOI : 10.1002/sapm1972513253

S. L. Ossakow, E. Ott, and I. Haber, Nonlinear Evolution of Whistler Instabilities, Physics of Fluids, vol.15, issue.12, pp.2314-2326, 1972.
DOI : 10.1063/1.1693875

S. Piperno, M. Remaki, and L. Fezoui, A Nondiffusive Finite Volume Scheme for the Three-Dimensional Maxwell's Equations on Unstructured Meshes, SIAM Journal on Numerical Analysis, vol.39, issue.6, pp.2089-2108, 2002.
DOI : 10.1137/S0036142901387683

S. Piperno and L. Fezoui, A discontinous Galerkin FVTD method for 3D Maxwell equations, 2003.

S. Piperno, Schémas enélémentsenéléments finis discontinus localement raffinés en espace et en temps pour leséquationsleséquations de Maxwell 1D, 2003.

F. Poupaud, Boundary value problems for the stationary Vlasov-Maxwell system, Forum Mathematicum, vol.4, issue.4, pp.499-527, 1992.
DOI : 10.1515/form.1992.4.499

E. Pohn, M. Shoucri, and G. Kamelander, Eulerian Vlasov codes, Computer Physics Communications, vol.166, issue.2, pp.81-93, 2005.
DOI : 10.1016/j.cpc.2004.10.009

G. Rein, Global Weak Solutions to the Relativistic Vlasov-Maxwell System Revisited, Communications in Mathematical Sciences, vol.2, issue.2, pp.145-158, 2004.
DOI : 10.4310/CMS.2004.v2.n2.a1

M. Remaki, A new finite volume scheme for solving Maxwell's system, COMPEL, pp.913-931, 2000.

T. Réveillé, P. Bertrand, A. Ghizzo, F. Simonet, and N. Baussard, Dynamic evolution of relativistic electrons in the radiation belts, Journal of Geophysical Research: Space Physics, vol.2, issue.A9, pp.18883-18894, 2001.
DOI : 10.1029/2000JA900177

P. Ricci, G. Lapenda, and J. U. Brackbill, A Simplified Implicit Maxwell Solver, Journal of Computational Physics, vol.183, issue.1, p.117, 2002.
DOI : 10.1006/jcph.2002.7170

P. A. Robinson and P. Coakley, Spacecraft charging-progress in the study of dielectrics and plasmas, IEEE Transactions on Electrical Insulation, vol.27, issue.5, p.994, 1992.
DOI : 10.1109/14.256471

A. Roux and J. Solomon, Mécanismes non linéaires associés aux interactions ondes-particules dans la magnétosphère, Ann. Géophys, vol.26, issue.2, pp.279-297, 1970.

H. Schmitz and R. Grauer, Darwin???Vlasov simulations of magnetised plasmas, Journal of Computational Physics, vol.214, issue.2, pp.738-756, 2006.
DOI : 10.1016/j.jcp.2005.10.013

J. W. Schumer and J. P. Holloway, Vlasov Simulations Using Velocity-Scaled Hermite Representations, Journal of Computational Physics, vol.144, issue.2, pp.626-661, 1998.
DOI : 10.1006/jcph.1998.5925

J. V. Shebalin, A spectral algorithm for solving the relativistic Vlasov???Maxwell equations, Computer Physics Communications, vol.156, issue.1, pp.86-94, 2003.
DOI : 10.1016/S0010-4655(03)00438-7

M. Shoucri and G. Knorr, Numerical integration of the vlasov equation, Journal of Computational Physics, vol.14, issue.1, p.84, 1974.
DOI : 10.1016/0021-9991(74)90006-0

M. Shoucri, Numerical simulation of plasma edge turbulence due to E×B flow velocity shear, Czechoslovak Journal of Physics, vol.51, issue.10, pp.1139-1151, 2001.
DOI : 10.1023/A:1012862604854

M. Shoucri, H. Gerhauser, and K. Finken, Integration of the Vlasov equation along characteristics in one and two dimensions, Computer Physics Communications, vol.154, issue.1, pp.65-75, 2003.
DOI : 10.1016/S0010-4655(03)00281-9

I. Silin and J. Büchner, Three-dimensional Vlasov-code simulations of magnetopause-like current sheets, Advances in Space Research, vol.37, issue.7, pp.1354-1362, 2006.
DOI : 10.1016/j.asr.2005.05.025

J. Solomon, Injection de particulesénergétiquesparticulesénergétiques dans la magnétosphère. Conséquence sur les déformations des fonctions de distribution et sur les interactions de gyrorésonance, Thèse de l'université, 1977.

J. Solomon and N. Cornilleau-wehrlin, An experimental study of ELF/VLF hiss generation in the Earth's magnetosphere, Journal of Geophysical Research, vol.84, issue.5, p.1839, 1988.
DOI : 10.1029/JA093iA03p01839

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, 1998.
DOI : 10.1006/jcph.1998.6148

E. Sonnendrücker, F. Filbet, A. Friedman, E. Oudet, and J. L. Vay, Vlasov simulations of beams with a moving grid, Computer Physics Communications, vol.164, issue.1-3, p.390, 2004.
DOI : 10.1016/j.cpc.2004.06.077

E. Sonnendrücker and P. Navaro, Développement du code Maxwell-Vlasov PICparalì ele Brennus : Mise en oeuvre d'un solveur 2D par la méthode de Galerkin discontinu, 2006.

G. Strang, On the Construction and Comparison of Difference Schemes, SIAM Journal on Numerical Analysis, vol.5, issue.3, pp.506-517, 1968.
DOI : 10.1137/0705041

R. D. Sydora, Low-noise electromagnetic and relativistic particle-in-cell plasma simulation models, Journal of Computational and Applied Mathematics, vol.109, issue.1-2, pp.243-259, 1999.
DOI : 10.1016/S0377-0427(99)00161-2

A. Taflove and S. C. Hagness, Computational Electrodynamics : The Finite Difference Time-Domain method, 2000.

T. Tang, The Hermite Spectral Method for Gaussian-Type Functions, SIAM Journal on Scientific Computing, vol.14, issue.3, pp.594-606, 1993.
DOI : 10.1137/0914038

T. Tang, S. Mckee, and M. W. Reeks, A spectral method for the numerical solutions of a kinetic equation describing the dispersion of small particles in a turbulent flow, Journal of Computational Physics, vol.103, issue.2, pp.222-230, 1992.
DOI : 10.1016/0021-9991(92)90397-H

F. Valentini, P. Veltri, and A. Mangeney, A numerical scheme for the integration of the Vlasov???Poisson system of equations, in the magnetized case, Journal of Computational Physics, vol.210, issue.2, pp.730-751, 2005.
DOI : 10.1016/j.jcp.2005.05.014

J. A. Van-allen, C. E. Mcilwain, and G. H. Ludwig, Radiation observations with satellite 1958 ??, Journal of Geophysical Research, vol.152, issue.3, p.271, 1959.
DOI : 10.1029/JZ064i003p00271

J. A. Van-allen and L. A. Frank, Radiation around the Earth to a radial distance of 107, Nature, vol.400, issue.184, p.219, 1959.

J. A. Van-allen, The first public lecture on the discovery of the geomagnetically trapped radiation, 1960.

R. C. Webb, L. Palkuti, L. Cohn, and K. Lt, The commercial and military survivability crisis, Defense Electronics, Col. G. and Costantine A, vol.21, 1995.

J. A. Weideman, The eigenvalues of Hermite and rational spectral differentiation matrices, Numerische Mathematik, vol.21, issue.1, pp.409-431, 1992.
DOI : 10.1007/BF01385518

S. Wollman, An existence and uniqueness theorem for the Vlasov-Maxwell system, Communications on Pure and Applied Mathematics, vol.2, issue.4, pp.457-462, 1984.
DOI : 10.1002/cpa.3160370404

S. Wollman and E. Ozizmir, Numerical Approximation of the One-Dimensional Vlasov???Poisson System with Periodic Boundary Conditions, SIAM Journal on Numerical Analysis, vol.33, issue.4, pp.1377-1409, 1996.
DOI : 10.1137/S0036142993233585

F. Xiao, R. M. Thorne, and D. Summers, Instability of electromagnetic R-mode waves in a relativistic plasma, Physics of Plasmas, vol.5, issue.7, pp.2489-2497, 1998.
DOI : 10.1063/1.872932

T. Y. Yang, J. Arons, and A. B. Langdon, Evolution of the Weibel instability in relativistically hot electron???positron plasmas, Physics of Plasmas, vol.1, issue.9, pp.3059-3077, 1994.
DOI : 10.1063/1.870498

K. S. Yee, Numerical solution of initial boundary value problems involving Maxwell's equations in isotropic media, IEEE Trans. Antennas and Propagation, vol.14, issue.3, pp.302-307, 1966.

K. S. Yee and J. S. Chen, The finite-difference time-domain (FDTD) and the finite-volume time-domain (FVTD) methods in solving Maxwell's equations, IEEE Transactions on Antennas and Propagation, vol.45, issue.3, pp.354-363, 1997.
DOI : 10.1109/8.558651

W. Yu, R. Mittra, T. Su, Y. Liu, and X. Yang, Parallel Finite-Difference Time-Domain Method, 2006.

S. I. Zaki, L. R. Gardner, and T. J. Boyd, A finite element code for the simulation of one-dimensional vlasov plasmas. I. Theory, Journal of Computational Physics, vol.79, issue.1, pp.184-199, 1988.
DOI : 10.1016/0021-9991(88)90010-1

C. Zenger and S. Grids, Parallel Algorithms for Partial Differential Equations, Proceedinds of the Sixth GAMM-Seminar, Notes on Num. Fluid Mech, vol.31, 1990.

G. Zumbusch, P. Grid, and . Solver, A Sparse Grid PDE Solver; Discretization, Adaptivity, Software Design and Parallelization, Advances in Software Tools for Scientific Computing (Proceedings SciTools '98, pp.133-178, 2000.
DOI : 10.1007/978-3-642-57172-5_4

Y. Omura and D. Summers, Computer simulations of the relativistic whistlermode wave-particle interactions, Phys. Plasmas, vol.11, issue.3530, 2004.

P. T. Armstrong, Numerical Studies of the Nonlinear Vlasov Equation, Physics of Fluids, vol.10, issue.6, pp.1269-1280, 1967.
DOI : 10.1063/1.1762272

G. Joyce, G. Knorr, and H. Meier, Numerical integration methods of the Vlasov equation, Journal of Computational Physics, vol.8, issue.1, pp.53-63, 1971.
DOI : 10.1016/0021-9991(71)90034-9

T. Tang, The Hermite Spectral Method for Gaussian-Type Functions, SIAM Journal on Scientific Computing, vol.14, issue.3, pp.594-606, 1993.
DOI : 10.1137/0914038

T. Tang, S. Mckee, and M. W. , A spectral method for the numerical solutions of a kinetic equation describing the dispersion of small particles in a turbulent flow, Journal of Computational Physics, vol.103, issue.2, pp.222-230, 1992.
DOI : 10.1016/0021-9991(92)90397-H

J. P. Holloway, Spectral velocity discretizations for the Vlasov?Maxwell equations, Transport Theory Statist, Phys, vol.25, issue.1, pp.1-32, 1996.

J. W. Schumer and J. P. Holloway, Vlasov Simulations Using Velocity-Scaled Hermite Representations, Journal of Computational Physics, vol.144, issue.2, pp.626-661, 1998.
DOI : 10.1006/jcph.1998.5925

F. C. Grant and M. R. Feix, Fourier-Hermite Solutions of the Vlasov Equations in the Linearized Limit, Physics of Fluids, vol.10, issue.4, 1967.
DOI : 10.1063/1.1762177

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

G. Manfredi, Long-Time Behavior of Nonlinear Landau Damping, Physical Review Letters, vol.79, issue.15, pp.2815-2818, 1997.
DOI : 10.1103/PhysRevLett.79.2815

J. P. Boyd15-]-a, W. M. Klimas, and . Farrell, Chebychev and Fourier Spectral Methods A splitting algorithm for Vlasov simulation with filamentation filtration, J. Comput. Phys, pp.110-150, 1994.

B. Elliasson, Numerical modelling of the two-dimensional Fourier transformed Vlasov???Maxwell system, Journal of Computational Physics, vol.190, issue.2, pp.501-522, 2003.
DOI : 10.1016/S0021-9991(03)00295-X

M. Shoucri and G. Knorr, Numerical integration of Vlasov equation, J. Comput . Phys, vol.14, issue.84, 1974.

R. Dautray and J. L. Lions, Analyse mathématique et calcul scientifique pour les sciences et les techniques, 1985.

G. Strang, On the Construction and Comparison of Difference Schemes, SIAM Journal on Numerical Analysis, vol.5, issue.3, pp.506-517, 1968.
DOI : 10.1137/0705041

T. Tang, The Hermite Spectral Method for Gaussian-Type Functions, SIAM Journal on Scientific Computing, vol.14, issue.3, pp.594-606, 1993.
DOI : 10.1137/0914038

B. Fornberg, A Practical Guide to Pseudospectral Methods, Cambridge Monographs on Applied and Computational Mathematics, 1998.
DOI : 10.1017/CBO9780511626357

C. Bernardi and Y. Maday, Spectral methods, Handbook of Numerical Analysis, pp.209-486, 1997.
DOI : 10.1016/S1570-8659(97)80003-8

C. Canuto, M. Y. Hussaini, A. Quarteroni, and T. A. Zang, Spectral Methods? Fundamentals in Single Domains, 2006.

S. A. Orszag, Comparison of Pseudospectral and Spectral Approximation, Studies in Applied Mathematics, vol.49, issue.3, pp.253-259, 1972.
DOI : 10.1002/sapm1972513253

G. Rein, Global Weak Solutions to the Relativistic Vlasov-Maxwell System Revisited, Communications in Mathematical Sciences, vol.2, issue.2, pp.145-158, 2004.
DOI : 10.4310/CMS.2004.v2.n2.a1

R. Gagne and M. Shoucri, A splitting scheme for the numerical solution of a one-dimensional Vlasov equation, Journal of Computational Physics, vol.24, issue.4, pp.24-445, 1977.
DOI : 10.1016/0021-9991(77)90032-8

E. Pohn, M. Shoucri, and G. Kamelander, Eulerian Vlasov codes, Computer Physics Communications, vol.166, issue.2, pp.81-93, 2005.
DOI : 10.1016/j.cpc.2004.10.009