The Fokker-Planck Coefficient for Pitch-Angle Scattering of Cosmic Rays
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Fisk, L. A., M. L. Goldstein, A. J. Klimas, and G. Sandri. “The Fokker-Planck Coefficient for Pitch-Angle Scattering of Cosmic Rays.” The Astrophysical Journal 190 (June 1, 1974): 417–28. https://doi.org/10.1086/152893.
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This work was written as part of one of the author's official duties as an Employee of the United States Government and is therefore a work of the United States Government. In accordance with 17 U.S.C. 105, no copyright protection is available for such works under U.S. Law.
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Abstract
For the case of homogeneous, isotropic magnetic field fluctuations, it is shown that most theories which are based on the quasi-linear and adiabatic approximations yield the same integral for the Fokker-Planck coefficient for the pitch-angle scattering of cosmic rays. For example, despite apparent differences, the theories due to Jokipii and to Klimas and Sandri yield the same integral. It is also shown, however, that this integral in most cases has been evaluated incorrectly in the past. For small pitch angles, the errors in previous evaluations are fortuitously of minor importance. For large pitch angles, however, these errors become more significant; and for pitch angles of 900, the actual Fokker-Planck coefficient contains a delta-function which has been overlooked in the past. The implications of these corrections on our ability to relate cosmic-ray diffusion coefficients to observed properties of the interplanetary magnetic field are discussed.