Instability of the ionospheric plasma: Modeling and analysis

SIAM Journal on Applied Mathematics

Volumn 65, Issue 6, 2005, Pages 2178-2198

  Besse, Christophe ^a   Claudel, Jean ^b   Degond, Pierre ^a   Deluzet, Fabrice ^a   Gallice, Gérard ^b   Tessieras, Christian ^b  

^a INSTITUT DE MATHÉMATIQUES DE TOULOUSE   (France)

^b CEA CESTA   (France)

Author keywords

Dynamo model; Euler maxwell system; Ionospheric plasma; Linearized stability analysis; Statistical approach; Striation model; Striations; Turbulence

Indexed keywords

ELECTROMAGNETIC WAVE PROPAGATION IN PLASMA; IONOSPHERE; MATHEMATICAL MODELS; PERTURBATION TECHNIQUES; PLASMA APPLICATIONS; PLASMA STABILITY; TURBULENCE;

DYNAMO MODELS; EULER-MAXWELL SYSTEM; IONOSPHERIC PLASMAS; LINEARIZED STABILITY ANALYSIS; STATISTICAL APPROACH; STRIATION MODELS; STRIATIONS;

PLASMA THEORY;

EID: 29144518703     PISSN: 00361399     EISSN: None     Source Type: Journal    
DOI: 10.1137/040606582     Document Type: Article

References (44)

1. W. G. BAKER AND D. F. MARTYN, Electric currents in the ionosphere, I. The conductivity, Phil. Trans. Roy. Soc. London, A246 (1953), pp. 295-305.
2. J. J. BERTHELIER, L'ionosphère, in Environnement spatial: Prévention des risques liés aux phénomènes de charge, J. P. Catani and M. Romero, eds., Cépaduès éditions, Toulouse, 1996.
3. C. BESSE, J. CLAUDEL, P. DEGOND, F. DELUZET, G. GALLICE, AND C. TESSIERAS, A model hierarchy for ionospheric plasma modeling, Math. Models Methods Appl. Sci., 14 (2004), pp. 393-415.
4. C. BESSE, J. CLAUDEL, P. DEGOND, F. DELUZET, G. GALLICE, AND C. TESSIERAS, Numerical simulations of the ionospheric dynamo model in a nonuniform magnetic field, J. Comput. Phys., submitted.
5. C. BESSE, J. CLAUDEL, P. DEGOND, F. DELUZET, G. GALLICE, AND C. TESSIERAS, Ionospheric plasmas: Model derivation, stability analysis, and numerical simulations, in Numerical Method for Hyperbolic and Kinetic Problems, Th. Goudon and E. Sonnendrücker, eds., de Gruyter, New York, Berlin, to appear.
6. C. BESSE, P. DEGOND, H-J. HWANG, AND R. PONCET, Nonlinear instability of the two-dimensional striation model about smooth steady states, Comm. Partial Differential Equations, to appear.
7. D. BILITZA, International reference ionosphere 2000, Radio Science, 36 (2001), pp. 261-275.
8. E. BLANC, B. MERCANDELLI, AND E. HOUNGNINOU, Kilometric irregularities in E and F regions of the daytime equatorial ionosphere observed by a high resolution HF radar, Geophys. Res. Lett., 23 (1996), pp. 645-648.
9. J. W. CHAMBERLAIN AND D. W. HUNTER, Theory of Planetary Atmospheres, Academic Press, New York, 1987.
10. S. CHANDRASEKHAR, Hydrodynamic and Hydromagnetic Stability, Dover, New York, 1981.
11. B. DESJARDINS AND E. GRENIER, Linear instability implies nonlinear instability for various types of viscous boundary layers, Ann. Inst. H. Poincaré Anal. Non Linéaire, 20 (2003), pp. 87-106.
12. J. H. DOLES, III, N. J. ZABUSKI, AND F. W. PERKINS, Deformation and striation of plasma clouds in the ionosphere. 3. Numerical simulations of a multilevel model with recombination chemistry, J. Geophys. Res., 81 (1976), pp. 5987-6004.
13. D. T. FARLEY, Theory of equatorial eletrojet plasma waves, new developments and current status, J. Atmospheric Terrestrial Phys., 47 (1985), pp. 729-744.
14. B. G. FEJER AND M. C. KELLEY, Ionospheric irregularities, Rev. Geophys. Space Phys., 18 (1980), pp. 401-454.
15. X. GARBET, Instabilités, Turbulence et Transport dans un Plasma Magnétisé, Habilitation dissertation, University of Marseille, France, 2001.
16. V. GIRAULT AND P.-A. RAVIART, Finite Element Methods for Navier Stokes Equations, Theory and Algorithms, Springer, New York, 1986.
17. E. GODLEWSKI AND P. A. RAVIART, Numerical Approximation of Hyperbolic Systems of Conservation Laws, Springer, New York, 1996.
18. E. GRENIER, On the nonlinear instability of Euler and Prandtl equations, Comm. Pure Appl. Math., 53 (2000), pp. 1067-1091.
19. C. GRIMAULT, Caractérisation des canaux de propagation satellite-Terre SHF et EHF en présence de plasma post-nucléaire, Ph.D. dissertation, University of Rennes, France, 1995.
20. Y. Guo AND W. STRAUSS, Nonlinear instability of double-humped equilibria, Ann. Inst. H. Poincaré Anal. Non Linéaire, 12 (1995), pp. 339-352.
21. J. K. HARGREAVES, The Solar-Terrestrial Environment, Cambridge University Press, Cambridge, UK, 1992.
22. A. M. HAMZA AND J. P. ST. MAURICE, A fully self-consistent fluid theory of anomalous transport in Farley-Buneman turbulence, J. Geophys. Res., 100 (1995), pp. 9653-9668.
23. A. M. HAMZA AND J. P. ST. MAURICE, A turbulent theoretical framework for the study of current-driven E region irregularities at high latitudes: Basic derivation and application to gradient-free situations, J. Geophys. Res., 98 (1993), pp. 11587-11599.
24. H. J. HWANG AND Y. GUO, On the dynamical Rayleigh-Taylor instability, Arch. Ration. Mech. Anal., 167 (2003), pp. 235-253.
25. M. J. KESKINEN, Nonlinear theory of the E × B instability with an inhomogeneous electric field, J. Geophys. Res., 89 (1984), pp. 3913-3920.
26. M. J. KESKINEN, S. L. OSSAKOW, AND B. G. FEJER, Three-dimensional nonlinear evolution of equatorial ionospheric spread-F bubbles, Geophys. Res. Lett., 30 (2003), pp. 1855-1858.
27. H. KESTEN AND G. C. PAPANICOLAOU, A limit theorem for stochastic acceleration, Comm. Math. Phys., 78 (1980), pp. 19-63.
28. F. KRAUSE AND K. H. RÄDLER, Mean-field magnetohydrodynamics and dynamo theory, Pergamon Press, Elmsford, NY, 1980.
29. M. LESIEUR, Turbulence in Fluids: Stochastic and Numerical Modeling, Kluwer Academic Publishers, Dordrecht, The Netherlands, 1990.
30. R. J. LEVEQUE, Numerical Methods for Conservation Laws, Birkhaüser-Verlag, Basel, Switzerland, 1992.
31. S. MATSUSHITA, On artificial geomagnetic and ionospheric storms associated with high-altitude explosions, J. Geophys. Res., 64 (1959), pp. 1149-1161.
32. B. MOHAMMADI AND O. PIRONNEAU, Analysis of the K-Epsilon Turbulence Model, Wiley, New York, 1994.
33. M. OPPENHEIM, N. OTANI, AND C. RONCHI, Saturation of the Farley-Buneman instability via nonlinear E × B drifts, J. Geophys. Res., 101 (1996), pp. 17273-17286.
34. S. L. OSSAKOW AND P. K. CHATUVERDI, Morphological studies of rising equatorial spread F bubbles, J. Geophys. Res., 83 (1978), pp. 2085-2090.
35. F. POUPAUD AND A. VASSEUR, Classical and quantum transport in random media, J. Math. Pures Appl., 82 (2003), pp. 711-748
36. G. C. REID, The formation of small-scale irregularities in the ionosphere, J. Geophys. Res., 73 (1968), pp.1627-1640.
37. H. RISHBETH AND O. K. GARRIOTT, Introduction to Ionospheric Physics, Academic Press, New York, 1969.
38. C. RONCHI, R. N. SUDAN, AND D. T. FARLEY, Numerical simulations of large-scale plasma turbulence in the daytime equatorial electrojet, J. Geophys. Res., 96 (1991), pp. 21263-21279.
39. C. RONCHI, R. N. SUDAN, AND P. L. SIMILON, Effect of short-scale turbulence on kilometer wavelength irregularities in the equatorial electrojet, J. Geophys. Res., 95 (1990), pp. 189-200.
40. Y. SAAD, SPARSKIT: A Basic Tool Kit for Sparse Matrix Computations - Version 2, Technical Report, Computer Science Department, University of Minnesota, Minneapolis, MN, 1994.
41. R. N. SUDAN, J. AKINRIMISI, AND D. T. FARLEY, Generation of small scale irregularities in the equatorial electrojet, J. Geophys. Res., 78 (1973), pp. 240-248.
42. E. F. TORO, Riemann Solvers and Numerical Methods for Fluid Dynamics, Springer, New York, 1999.
43. W. WHITE, An overview of high-altitude nuclear weapons phenomena, Heart conference short course, preprint, 1998.
44. S. T. ZALESAK AND S. L. OSSAKOW, Nonlinear equatorial spread F: The effect of neutral winds and background Pedersen conductivity, J. Geophys. Res., 87 (1982), pp. 151-166.