Abstract
One can assume that energetic particles follow magnetic field lines while they propagate through a magnetized plasma. The latter scenario is usually described by the so-called field line random walk limit. This limit, however, is only valid if parallel diffusion is suppressed. As soon as the latter effect is taken into account, perpendicular transport becomes subdiffusive. This physical scenario is usually called compound diffusion or compound subdiffusion and can be described by a Chapman-Kolmogorov equation. In the latter equation the parallel distribution function is an essential ingredient. In the present paper we replace the standard Gaussian model by a Kappa distribution to compute distribution functions and mean square displacements across the field.
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References
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1974)
Alexandrova, O., Carbone, V., Veltri, P., Sorriso-Valvo, L.: Astrophys. J. 674, 1153 (2008)
Burlaga, L.F., Vinas, A.F.: Geophys. Res. Lett. 31, 16 (2004) L16807
Chollet, E.E., Giacalone, J.: Astrophys. J. 728, 64 (2011)
Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Academic Press, New York (2000)
Hellberg, M.A., Mace, R.L., Baluku, T.K., Kourakis, I., Saini, N.S.: Phys. Plasmas 16, 094701 (2009)
Jokipii, J.R.: Astrophys. J. 146, 480 (1966)
Kóta, J., Jokipii, J.R.: Astrophys. J. 531, 1067 (2000)
Lazar, M., Schlickeiser, R., Poedts, S., Tautz, R.C.: Mon. Not. R. Astron. Soc. 390, 168 (2008)
Lazar, M., Tautz, R.C., Schlickeiser, R., Poedts, S.: Mon. Not. R. Astron. Soc. 401, 362 (2010)
Leamon, R.J., Smith, C.W., Ness, N.F., Matthaeus, W.H., Wong, H.K.: J. Geophys. Res. 103, 4775 (1998)
Leubner, M.P., Vörös, Z.: Nonlinear Process. Geophys. 12(2), 171 (2005)
Liu, B., Goree, J.: Phys. Rev. Lett. 100, 055003 (2008)
Liu, B., Goree, J., Feng, Y.: Phys. Rev. E 78, 046403 (2008)
Livadiotis, G., McComas, D.J.: J. Geophys. Res. 114, A11105 (2009)
Saini, N.S., Kourakis, I., Hellberg, M.A.: Phys. Plasmas 16, 062903 (2009)
Schlickeiser, R.: Cosmic Ray Astrophysics. Springer, Berlin (2002)
Shalchi, A.: Plasma Phys. Control. Fusion 50, 055001 (2008)
Shalchi, A.: Nonlinear Cosmic Ray Diffusion Theories. Astrophysics and Space Science Library, vol. 362. Springer, New York (2009)
Shalchi, A., Kourakis, I.: Astron. Astrophys. 470, 405 (2007a)
Shalchi, A., Kourakis, I.: Phys. Plasmas 14, 092903 (2007b)
Shalchi, A., Kourakis, I.: Phys. Plasmas 14, 112901 (2007c)
Shalchi, A., Weinhorst, B.: Adv. Space Res. 43, 1429 (2009)
Shalchi, A., Kourakis, I., Dosch, A.: J. Phys. A, Math. Theor. 40, 36 (2007a)
Shalchi, A., Tautz, R.C., Schlickeiser, R.: Astron. Astrophys. 475, 415 (2007b)
Shalchi, A., le Roux, J.A., Webb, G.M., Zank, G.P.: J. Phys. A, Math. Theor. 42, 34 (2009)
Sharma, A., Kourakis, I.: Laser Part. Beams 28, 479 (2010)
Sorriso-Valvo, L., Carbone, V., Veltri, P., Consolini, G., Bruno, R.: Geophys. Res. Lett. 26, 1804 (1999)
Vasyliunas, V.M.: J. Geophys. Res. 73, 2839 (1968)
Webb, G.M., Zank, G.P., Kaghashvili, E.Kh., le Roux, J.A.: Astrophys. J. 651, 211 (2006)
Zimbardo, G.: Plasma Phys. Control. Fusion 47, B755 (2005)
Zimbardo, G., Veltri, P., Basile, G., Principato, S.: Phys. Plasmas 2, 2653 (1995)
Acknowledgements
Andreas Shalchi acknowledges support by the Natural Sciences and Engineering Research Council (NSERC) of Canada.
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Buffie, K., Shalchi, A. Compound diffusion of energetic particles: a Kappa model for the parallel distribution function. Astrophys Space Sci 340, 351–358 (2012). https://doi.org/10.1007/s10509-012-1057-y
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DOI: https://doi.org/10.1007/s10509-012-1057-y