Solar cosmic ray distribution function under prolonged particle injection

Heading: 
1Fedorov, YI
1Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
Kinemat. fiz. nebesnyh tel (Online) 2019, 35(5):3-24
https://doi.org/10.15407/kfnt2019.05.003
Start Page: Space Physics
Language: Russian
Abstract: 

The solar cosmic ray propagation on the basis of Fokker-Planck kinetic equation is considered. It is known that solar cosmic ray distribution function averaged over a period of solar proton event contains valuable information about energetic charged particles scattering by interplanetary magnetic fields. Steady state solution of kinetic equation in small angle approximation is obtained and the dependence of angular distribution function on the distance to the particle source is analyzed. This solution is only correct when the distance to the particle source is small relative to cosmic ray mean free path, and when the particles are moving preferentially in the radial direction. The particle angular distribution on large distances to the particle source (bigger than cosmic ray mean free path) is also investigated. The analytical expression of the cosmic ray distribution function in a form of a sum of isotropic and small anisotropic components is derived. It is shown that the angular cosmic ray distribution depends essentially on the anisotropy of the cosmic ray scattering. The estimates of features of energetic charged particle scattering by interplanetary magnetic field fluctuations are made based on the observational data of some solar cosmic ray flares.

Keywords: cosmic rays, interplanetary magnetic field, kinetic equation
References: 

1. Abramovitz M., Stegun I. (1979) Reference book on special functions. M.: Science. 832 p. (in Russian).

2. Galperin B. A., Toptygin I. N., Fradkin A. A. (1971) Rasseyaniye chastits magnitnymi neodnorodnostyami v sil’nom magnitnom pole. Zhurnal Eksperimentalnoi i Teoreticheskoi Fiziki, 60(3), 972 (in Russian).

3. Dorman L. I., Katz M. E. (1973) O fluktuaciyah intensivnosti solnechnyh kosmicheskih luchej. Tr. 5-go Leningradskogo mezhdunarodnogo seminara, FTI. 311 (in Russian).

4. Prudnikov A. P., Brychkov Yu. A., Marichev O. I. (1981) Integraly i ryady. M.: Nauka. 800 p. (in Russian).

5. Toptygin I. N. (1983) Kosmicheskiye luchi v mezhplanetnykh magnitnykh polyakh. M.: Nauka. 304 p. (in Russian)

6. Fedorov Yu. I. (2004) Propagation of solar cosmic rays in the interplanetary medium under conditions of prolonged particle injection. Kinematics Physics of Celest. Bodies. 20(3). P. 137—147.

7. Beeck J., Wibberenz G. (1986) Pitch angle distributions of solar energetic particles and the local scattering properties of the interplanetary medium. Astrophys. J. 311. P. 437.
https://doi.org/10.1086/164784

8. Bieber J. W. (1996) A useful relationship between time-dependent and steady state solutions of the Boltzmann equation. J. Geophys. Res. 101(NA6). P. 13523.
https://doi.org/10.1029/96JA00607

9. Bieber J. W., Earl J. A., Green G., et al. (1980) Interplanetary pitch-angle scattering and coronal transport of solar energetic particles: New information from Helios. J. Geophys. Res. 85(NA5). P. 213.
https://doi.org/10.1029/JA085iA05p02313

10. Bieber J. W., Evenson P. A., Pomerantz M. A. (1986) Focusing anisotropy of solar cosmic rays. J. Geophys. Res. 91(NA8). P. 8713.
https://doi.org/10.1029/JA091iA08p08713

11. Cramp J. L., Fluckiger E. O., Humble J. E., et al. (1997) The October 22, 1989 solar cosmic ray enhancement: An analysis of the anisotropy and spectral characteristic. J. Geophys. Res. 102(NA11). P. 2437.
https://doi.org/10.1029/97JA01947

12. Dorman L. I., Katz M. E. (1977) Cosmic ray kinetics in space. Space Sci. Rev. 70. P. 529—575.
https://doi.org/10.1007/BF02186896

13. Earl J. A. (1981) Analytical description of charged particle transport along arbitrary guiding field configurations. Astrophys. J. 251. P. 739.
https://doi.org/10.1086/159518

14. Fedorov Yu. I., Stehlik M. (2006) SCR steady state distribution function and scattering properties of the interplanetary medium. Astrophys. Space Sci. 302. P. 99.
https://doi.org/10.1007/s10509-005-9010-y

15. Hasselmann K., Wibberenz G. (1968) Scattering charged particles by random electromagnetic fields. Z. Geophys. 34. P. 353.

16. Hatzky R. (1996) Angular distributions of energetic charged particles and the scattering properties of interplanetary medium. Ph. D. Thesis, Univ. of Kiel, P. 1—247.

17. Hatzky R., Wibberenz G., Bieber J. W. (1995) Pitch angle distribution of solar energetic particles and the transport parameters in the interplanetary space. Proc. 24th Intern. Cosmic Ray Conf., Rome, v. 4, P. 261.

18. Jokipii J. R. (1966) Cosmic ray propagation. 1. Charged particle in a random magnetic field. Astrophys. J. 146. P. 480.
https://doi.org/10.1086/148912

19. Kallenrode M.-B. (1993) Particle propagation in the inner heliosphere. J. Geophys. Res. 98(NA11). P. 19037.
https://doi.org/10.1029/93JA02079

20. Kunstmann J. E. (1979) A new transport mode for energetic charged particles in magnetic fluctuations superposed on a diverging mean field. Astrophys. J. 229. P. 812.
https://doi.org/10.1086/157016

21. Miroshnichenko L. I., Perez-Peraza J. A. (2008) Astrophysical aspects in the studies of solar cosmic rays. Int. J. Modern Phys. A. 23(1). P. 1.
https://doi.org/10.1142/S0217751X08037312

22. Shakhov B. A., Stehlik M. (2003) The Fokker-Planck equation in the second order pitch angle approximation and its exact solution. J. Quant. Spectr. Radiative Transfer. 78. P. 31—39.
https://doi.org/10.1016/S0022-4073(02)00175-9