Abstract
We investigate cosmic ray scattering in the direction perpendicular to a mean magnetic field. Unlike in previous articles we employ a general form of the turbulence wave spectrum with arbitrary behavior in the energy range. By employing an improved version of the nonlinear guiding center theory we compute analytically the perpendicular mean free path. As shown, the energy range spectral index, has a strong influence on the perpendicular diffusion coefficient. If this parameter is larger than one we find for some cases a perpendicular diffusion coefficient that is independent of the parallel mean free path and particle energy. Two applications are considered, namely transport of Galactic protons in the solar system and diffusive particle acceleration at highly perpendicular interplanetary shock waves.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Abramowitz, M., Stegun, I.A.: Handbook of Mathematical Functions. Dover, New York (1974)
Axford, W.I., Leer, E., Skadron, G.: Proc. Int. Conf. Cosmic Rays 15th, vol. 11, p. 132 (1977)
Belcher, J.W., Davis, L.: J. Geophys. Res. 76, 3534 (1971)
Bell, A.R.: Mon. Not. R. Astron. Soc. Lett. 182, 147 (1978a)
Bell, A.R.: Mon. Not. R. Astron. Soc. Lett. 182, 443 (1978b)
Berezhko, E.G., Völk, H.J.: Astrophys. J. 661, L175 (2007)
Bieber, J.W., Matthaeus, W.H., Smith, C.W., Wanner, W., Kallenrode, M.-B., Wibberenz, G.: Astrophys. J. 420, 294 (1994)
Bieber, J.W., Wanner, W., Matthaeus, W.H.: J. Geophys. Res. 101, 2511 (1996)
Blandford, R.D., Ostriker, J.P.: Astrophys. J. 221, 269 (1978)
Burger, R.A., Potgieter, M.S., Heber, B.: J. Geophys. Res. 105, 27447 (2000)
Dosch, A., Shalchi, A., Weinhorst, B.: Adv. Space Res. 44, 1326 (2009)
Dröge, W.: Space Sci. Rev. 93, 121 (2000)
Gradshteyn, I.S., Ryzhik, I.M.: Table of Integrals, Series, and Products. Academic Press, New York (2000)
Kolmogorov, A.N.: Dokl. Akad. Nauk SSSR 30, 301 (1941)
Kraichnan, R.: Phys. Fluids 8, 1835 (1965)
Krymsky, G.F.: Dokl. Akad. Nauk SSSR 234, 1306 (1977)
Li, G., Zank, G.P., Rice, W.K.M.: J. Geophys. Res. 108, 1082 (2003)
Li, G., Zank, G.P., Rice, W.K.M.: J. Geophys. Res. 110, A06104 (2005)
Li, G., Webb, G.M., Shalchi, A., Zank, G.P.: Non-linear Guiding Center Theory and acceleration of cosmic rays at supernova remnant shocks. In: Shock Waves in Space and Astrophysical Environments, 8th Annual International Astrophysics Conference (2009)
Matthaeus, W.H., Goldstein, M.L., Roberts, D.A.: J. Geophys. Res. 95, 20.673 (1990)
Matthaeus, W.H., Qin, G., Bieber, J.W., Zank, G.P.: Astrophys. J. 590, L53 (2003)
Matthaeus, W.H., Bieber, J.W., Ruffolo, D., Chuychai, P., Minnie, J.: Astrophys. J. 667, 956 (2007)
Palmer, I.D.: Rev. Geophys. Space Phys. 20, 335 (1982)
Parker, E.N.: Astrophys. J. 123, 664 (1958)
Qin, G., Matthaeus, W.H., Bieber, J.W.: Geophys. Res. Lett. 29, 7 (2002a)
Qin, G., Matthaeus, W.H., Bieber, J.W.: Astrophys. J. 578, L117 (2002b)
Qin, G., Matthaeus, W.H., Bieber, J.W.: Astrophys. J. 640, L103 (2006)
Reville, B., O’Sullivan, S., Duffy, P., Kirk, J.G.: Mon. Not. R. Astron. Soc. 386, 509 (2008)
Shadmehri, M.: Mon. Not. R. Astron. Soc. 397, 1521 (2009)
Shalchi, A.: Astron. Astrophys. 453, L43 (2006)
Shalchi, A., Dosch, A.: Astrophys. J. 685, 971 (2008)
Shalchi, A., Kourakis, I.: Phys. Plasmas 14, 092903 (2007)
Shalchi, A., Schlickeiser, R.: Astrophys. J. 626, L97 (2005)
Shalchi, A., Bieber, J.W., Matthaeus, W.H.: Astrophys. J. 604, 675 (2004a)
Shalchi, A., Bieber, J.W., Matthaeus, W.H., Qin, G.: Astrophys. J. 616, 617 (2004b)
Shalchi, A., Bieber, J.W., Matthaeus, W.H.: Astrophys. J. 615, 805 (2004c)
Shalchi, A., Bieber, J.W., Matthaeus, W.H., Schlickeiser, R.: Astrophys. J. 642, 230 (2006)
Teufel, A., Schlickeiser, R.: Astron. Astrophys. 393, 703 (2002)
Webb, G.M., Zank, G.P., Ko, C.M., Donohue, D.J.: Astrophys. J. 453, 178 (1995)
Webb, G.M., Zank, G.P., Kaghashvili, E.Kh., le Roux, J.A.: Astrophys. J. 651, 211 (2006)
Webb, G.M., Le Roux, J.A., Zank, G.P., Kaghashvili, E.Kh., Li, G.: Am. Inst. Phys. 1039, 246 (2008)
Weinhorst, B., Shalchi, A., Fichtner, H.: Astrophys. J. 677, 671 (2008)
Yan, H., Lazarian, A.: Phys. Rev. Lett. 89, 281102 (2002)
Zank, G.P., Rice, W.K.M., Wu, C.C.: J. Geophys. Res. 105, 25079 (2000)
Zank, G.P., Li, G., Florinski, V., Matthaeus, W.H., Webb, G.M., le Roux, J.A.: J. Geophys. Res. 109, A04107 (2004)
Zank, G.P., Li, G., Florinski, V., Hu, Q., Lario, D., Smith, C.W.: J. Geophys. Res. 111, A06108 (2006)
Zimbardo, G., Pommois, P., Veltri, P.: Astrophys. J. 639, 91 (2006)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shalchi, A., Li, G. & Zank, G.P. Analytic forms of the perpendicular cosmic ray diffusion coefficient for an arbitrary turbulence spectrum and applications on transport of Galactic protons and acceleration at interplanetary shocks. Astrophys Space Sci 325, 99–111 (2010). https://doi.org/10.1007/s10509-009-0168-6
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-009-0168-6