Mathematical models for strongly magnetized plasmas with mass disparate particles
Pages: 513 - 544,
Volume 15,
Issue 3,
May 2011
doi:10.3934/dcdsb.2011.15.513 Abstract
References
Full text (371.7K)
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Mihai Bostan - Laboratoire de Mathématiques de Besançon, Université de Franche-Comté, 16 route de Gray, Besançon, 25030 Cedex, France (email)
Claudia Negulescu - CMI/LATP (UMR 6632), Université de Provence, 39, rue Joliot Curie, 13453 Marseille Cedex 13, France (email)
| 1 |
H. D. I. Abarbanel, Hamiltonian description of almost geostrophic flow, Geophysical and Astrophysical Fluid Dynamics, 33 (1985), 145-171. |
|
| 2 |
J. S. Allen and D. Holm, Extended-geostrophic Hamiltonian models for rotating shallow water motion, Physica D, 98 (1996), 229-248. |
|
| 3 |
N. N. Bogoliubov and Y. A. Mitropolsky, "Asymptotic Methods in the Theory of Nonlinear Oscillations," Gordon and Breach Sciences Publishers, New York, 1961. |
|
| 4 |
M. Bostan, The Vlasov-Poisson system with strong external magnetic field. Finite Larmor radius regime, Asymptot. Anal., 61 (2009), 91-123. |
|
| 5 |
M. Bostan, Transport equations with singular coefficients. Application to the gyrokinetic models in plasma physics, Research Report INRIA, hal:inria-00232800, submitted 2009. |
|
| 6 |
M. Bostan, Gyrokinetic Vlasov equation in three dimensional setting. Second order approximation, hal-00431289, submitted 2009. |
|
| 7 |
Y. Brenier, Convergence of the Vlasov-Poisson system to the incompressible Euler equations, Comm. Partial Differential Equations, 25 (2000), 737-754. |
|
| 8 |
A. H. Boozer, Physics of magnetically confined plasmas, Rev. Modern Phys., 76 (2004), 1071-1141. |
|
| 9 |
A. J. Brizard and T. S. Hahm, Foundations of nonlinear gyrokinetic theory, Rev. Modern Phys., 79 (2007), 421-468. |
|
| 10 |
F. Charles and L. Desvillettes, Small mass ratio limit of Boltzmann equations in the context of the study of evolution of dust particles in a rarefied atmosphere, J. Stat. Phys., 137 (2009), 539-567. |
|
| 11 |
J.-Y. Chemin, B. Desjardins, I. Gallagher, E. Grenier, "Mathematical Geophysics: An Introduction to Rotating Fluids and the Navier-Stokes Equations," Oxford Lecture Series in Mathematics and Its Applications 32, The Clarendon Press, Oxford University Press, 2006. |
|
| 12 |
P. Degond and B. Lucquin-Desreux, Transport coefficients of plasmas and disparate mass binary gases, Transport Theory Statist. Phys, 25 (1996), 595-633. |
|
| 13 |
E. Frénod and E. Sonnendrücker, Homogenization of the Vlasov equation and of the Vlasov-Poisson system with strong external magnetic field, Asymptotic Anal., 18 (1998), 193-213. |
|
| 14 |
E. Frénod and E. Sonnendrücker, The finite Larmor radius approximation, SIAM J. Math. Anal., 32 (2001), 1227-1247. |
|
| 15 |
F. Golse and L. Saint-Raymond, The Vlasov-Poisson system with strong magnetic field, J. Math. Pures Appl., 78 (1999), 791-817. |
|
| 16 |
T. Goudon, P.-E. Jabin and A. Vasseur, Hydrodynamic limit for the Vlasov-Navier-Stokes equations. I. Light particles regime, Indiana Univ. Math. J., 53 (2004), 1495-1515. |
|
| 17 |
V. Grandgirard, M. Brunetti, P. Bertrand, N. Besse, X. Garbet, P. Ghendrih, G. Manfredi, Y. Sarazin, O. Sauter, E. Sonnendrücker, J. Vaclavik and L. Villard, A drift-kinetic semi-Lagrangian 4D code for ion turbulence simulation, J. Comput. Phys., 217 (2006), 395-423. |
|
| 18 |
R. D. Hazeltine and J. D. Meiss, "Plasma Confinement," Dover Publications, Inc. Mineola, New York, 2003. |
|
| 19 |
R. G. Littlejohn, A guiding center Hamiltonian : A new approach, J. Math. Phys. 20 (1979) 2445-2458. |
|
| 20 |
R. G. Littlejohn, Hamiltonian formulation of guiding center motion, Phys. Fluids, 24 (1981), 1730-1749. |
|
| 21 |
J.-M. Rax, "Physique des plasmas, Cours et applications," Dunod, 2007. |
|
| 22 |
M. Reed and B. Simon, "Methods of Modern Mathematical Physics," Vol. I, Functional Analysis, Academic Press, 1980. |
|
| 23 |
R. Salmon, New equations for nearly geostrophic flow, J. Fluid Mechanics, 153 (1985), 461-477. |
|
| 24 |
J. Vanneste and O. Bokhove, Dirac-bracket approach to nearly geostrophic Hamiltonian balanced models, Physica D Nonlinear Phenomena, 164 (2002), 152-167. |
|
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