Tsallis distributions of the large-scale magnetic field strength fluctuations in the solar wind from 7 to 87 AU

Journal of Geophysical Research: Space Physics

Volumn 110, Issue A7, 2005, Pages

  Burlaga, L F ^a   Vinas A F ^a  

^a NASA GODDARD SPACE FLIGHT CENTER   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33746371352     PISSN: None     EISSN: 21699402     Source Type: Journal    
DOI: 10.1029/2005JA011132     Document Type: Article

References (39)

1. Alemany, P. A., and D. H. Zanette (1994), Fractal random walks from a variational formalism for Tsallis entropies, Phys. Rev. E., 49, R956.
2. Bard, Y. (1974), Nonlinear Parameter Estimation, chaps. 4-7, pp. 54-216, Elsevier, New York.
3. Beck, C. (2001), On the small-scale statistics of Lagrangian turbulence, Phys. Lett. A, 287, 240-244.
4. Beck, C. (2002a), Non-additivity of Tsallis entropies and fluctuations of temperature, Europhys. Lett., 57(3), 329-333.
5. Beck, C. (2002b), Generalized statistical mechanics and fully developed turbulence, Physica A, 306(1-4), 189-198.
6. Beck, C. (2004), Superstatistics: Theory and applications, Continuum Mech. Thermodyn., 16(3), 293-304.
7. Beck, C., and E. G. D. Cohen (2003), Superstatistics, Physica A, 322(1-4), 267-275.
8. Budde, C., D. Prato, and M. Re' (2001), Superdiffusion in decoupled continuous time random walks, Phys. Lett. A, 283, 309-312.
9. Burlaga, L. F. (1995), Interplanetary Magnetohydrodynamics, Oxford Univ. Press, New York.
10. Burlaga, L. F. (2001), Lognormal and multifractal distributions of the heliospheric magnetic field, J. Geophys. Res., 106(A8), 15,917-15,927.
11. Burlaga, L. F. (2004), Multifractal structure of the large-scale heliospheric magnetic field strength fluctuations near 85 AU, Nonlinear Processes Geophys., 11(4), 441-445.
12. Burlaga, L. F., and A. F.-Viñas (2004a), Multiscale structure of the magnetic field and speed at 1 AU during the declining phase of solar cycle 23 described by a generalized Tsallis probability distribution function, J. Geophys. Res., 109, A12107, doi:10.1029/2004JA010763.
13. Burlaga, L. F., and A. F.-Viñas (2004b), Multi-scale probability distributions of solar wind speed fluctuations at 1 AU described by a generalized Tsallis distribution, Geophys. Res. Lett., 31, L16807, doi:10.1029/2004GL020715.
14. Burlaga, L. F., C. Wang, J. D. Richardson, and N. F. Ness (2003), Evolution of magnetic fields in corotating interaction regions from 1 to 95 AU: Order to chaos, Astrophys. J., 590(1), 554-566.
15. Chavanis, P. H. (2003), Generalized thermodynamics and Fokker-Planck equations: Applications to stellar dynamics and two-dimensional turbulence, Phys. Rev. E, 68(3).
16. Chavanis, P. H., and M. Rieutord (2003), Statistical mechanics and phase diagrams of rotating self-gravitating fermions, Astron. Astrophys., 412(1), 1-17.
17. Daroczy, Z. (1970), Generalized information functions, Inf. Control, 16(1), 36.
18. Gnedenko, B. V., and A. N. Kolmogorov (1954), Limit Distributions for Sums of Independent Random Variables, Addison-Wesley, Boston, Mass.
19. Gorenflo, R., F. Mainardi, D. Moretti, G. Pagnini, and P. Paradisi (2002), Fractional diffusion: Probability distributions and random walk models, Physica A, 305, 106-202.
20. Hasegawa, A., K. Mima, and M. Duong-van (1985), Plasma distribution function in a superthermal radiation field, Phys. Rev. Lett., 54, 2608.
21. Hundhausen, A. J. (1972), Coronal Expansion and Solar Wind. Springer, New York.
22. Kaniadakis, G. (2001), Non-linear kinetics underlying generalized statistics, Physica A, 296(3-4), 405-425.
23. Leubner, M. P. (2004), Core-halo distribution functions: A natural equilibrium state in generalized thermostatistics, Astrophys. J., 604, 469.
24. Leubner, M. P., and Z. Vörös (2005), A nonextensive entropy approach to solar wind intermittency, Astrophys. J., 618, 547-555.
25. Levenberg, K. (1944), A method for the solution of certain problems in least squares, Q. Appl. Math., 2, 164-168.
26. Maksimovic, M., V. Pierrard, and P. Riley (1997), Ulysses electron distributions fitted with kappa functions, Geophys. Res. Lett., 24, 1151.
27. Marquardt, D. (1963), An algorithm for least-squares estimation of non-linear parameters, SIAM J. Appl. Math., 11, 431-441.
28. Olbert, S. (1968), Summary of experimental results from M. I. T. detector on IMP-1, in Physics of the Magnetosphere, edited by R. L. Carovillano, J. F. McClay, and H. R. Radoski, pp. 641-659, Springer, New York.
29. Prato, D., and C. Tsallis (1999), Nonextensive foundation of Levy distributions, Phys. Rev. E, 60, 2398.
30. Renyi, A. (1970), Probability Theory, Elsevier, New York.
31. Samorodnitsky, G., and M. S. Taqqu (1994), Stable Non-Gaussian Random Processes, CRC Press, Boca Raton, Fla.
32. Scudder, J. D., and S. Olbert (1979), A theory of local and global processes which affect solar wind electrons: 1. The origin of typical 1 AU velocity distribution functions - Steady state theory, J. Geophys. Res., 84, 2755.
33. Tsallis, G. (1988), Possible generalization of Boltzmann-Gibbs statistics, J. Stat. Phys., 52, 479.
34. Tsallis, C. (2004), Nonextensive statistical mechanics: Construction and physical interpretation, in Nonextensive Entropy-Interdisciplinary Applications, edited by M. Gell-Mann and C. Tsallis, pp. 1-54, Oxford Univ. Press, New York.
35. Tsallis, C., and E. Brigatti (2004), Nonextensive statistical mechanics: A brief introduction, Continuum Mech. Thermodyn., 16, 223.
36. Tsallis, C., and M. C. Souza (2003), Constructing a statistical mechanics for Beck-Cohen superstatistics, Phys. Rev. E, 67, 026106, 1-5.
37. Tsallis, C., S. V. F. Levy, A. Souza, and R. Maynard (1995), Statistical-mechanical foundation on the ubiquity of Levy distributions in nature, Phys. Rev. Lett., 75, 3589.
38. Tsallis, C., S. V. F. Levy, A. Souza, and R. Maynard (1996), Erratum, Phys. Rev. Lett., 27, 5442.
39. Vasyliunas, V. M. (1968), A survey of low-energy electrons in the evening sector of the magnetosphere with OGO 1 and OGO 3, J. Geophys. Res., 73, 2839.