The cosmic ray distribution function on the initial stage of the solar proton event
|1Fedorov, YI |
1Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
|Kinemat. fiz. nebesnyh tel (Online) 2020, 36(3):3-20|
|Start Page: Space Physics|
The propagation of solar cosmic rays in the interplanetary medium is considered based on the kinetic equation, describing multiple small-angle scattering of charged particles. The energetic particles are assumed to be injected in the interplanetary medium by the instantaneous, point-like source. The spatio-temporal distribution of high-velocity particle density and anisotropy is studied during the anisotropic phase of solar cosmic ray enhancement. The analytical expression of cosmic ray distribution function in the small-angle approximation is derived; the evolution of energetic particle angular distribution is investigated. It is shown that under weak scattering of charged energetic particles on the interplanetary magnetic field fluctuations the impulsive enhancement of their intensity occurs. The anisotropy of angular solar cosmic ray distribution decreases with time steadily and has a maximal value in the instant of first particle arrival in the given point of space.
|Keywords: cosmic rays, interplanetary medium, kinetic equation|
1. G. A. Bazilevskaya and R. M. Golynskaya. On the propagation of solar cosmic rays in an interplanetary medium taking into account adiabatic focusing, Geomagn. Aeron. 29, 204–209 (1989).
2. B. A. Gal’perin, I. N. Toptygin, and A. A. Fradkin. Scattering of particles by magnetic inhomogeneities in a strong magnetic field, J. Exp. Theor. Phys. 33, 526–531 (1971).
3. I. N. Toptygin. On the time dependence of the intensity of cosmic rays at the anisotropic stage of solar flares, Geomagn. Aeron. 12, 989–995 (1972).
4. I. N. Toptygin, Cosmic Rays in Interplanetary Magnetic Fields (Nauka, Moscow, 1983; Reidel, Dordrecht, 1985).
5. J. Beeck and G. Wibberenz. Pitch angle distributions of solar energetic particles and the local scattering properties of the interplanetary medium, Astrophys. J. 311, 437 (1986).
6. J. W. Bieber, J. Clem, P. Evenson, et al. Giant ground level enhancement of relativistic solar protons on 2005 January 20, Astrophys. J. 771, 52 (2013).
7. J. W. Bieber, P. A. Evenson, and M. A. Pomerantz. Focusing anisotropy of solar cosmic rays, J. Geophys. Res.: Space Phys. 91, 8713 (1986).
8. D. J. Bombardieri, M. L. Duldig, J. E. Humble, and K. J. Michael. On improved model for relativistic solar proton acceleration applied to the 2005 January 20 and earlier events, Astrophys. J. 682, 1315–1327 (2008).
9. J. L. Cramp, M. L. Duldig, E. O. Fluckiger, et al. 1989 solar cosmic ray enhancement. An analysis of the anisotropy and spectral characteristic, J. Geophys. Res.: Space Phys. 102, 24 237–24 248 (1997).
10. R. J. Danos, J. D. Fiege, and A. Shalchi. Numerical analysis of the Fokker–Planck equation with adiabatic focusing. Isotropic pitch angle scattering, Astrophys. J. 772, 35 (2013).
11. H. Debrunner, J. A. Lockwood, and J. M. Ryan. The solar flare event on 1990 May 24. Evidence for two separate particle accelerations, Astrophys. J., Lett. 387, L51–L54 (1992).
12. L. I. Dorman and M. E. Katz. Cosmic ray kinetics in space, Space Sci. Rev. 70, 529–575 (1977).
13. W. Droge, Y. Y. Kartavych, B. Klecker, and G. A. Kovaltsov. Anisotropic three-dimensional focused transport of solar energetic particles in the inner heliosphere, Astrophys. J. 709, 912–919 (2010).
14. J. A. Earl. Analytical description of charged particle transport along arbitrary guiding field configurations, Astrophys. J. 251, 739 (1981).
15. Yu. I. Fedorov. Intensity of cosmic rays at the initial stage of a solar flare, Kinematics Phys. Celestial Bodies 34, 1–12 (2018).
16. Yu. I. Fedorov. Solar cosmic ray distribution function under prolonged particle injection, Kinematics Phys. Celestial Bodies 35, 203–216 (2019).
17. Yu. I. Fedorov and M. Stehlik. SCR steady state distribution function and scattering properties of the interplanetary medium, Astrophys. Space Sci. 302, 99 (2006).
18. L. A. Fisk and W. I. Axford. Anisotropies of solar cosmic rays, Sol. Phys. 7, 486–498 (1969).
19. E. Kh. Kagashvili, G. P. Zank, J. Y. Lu, and W. Droge. Transport of energetic charged particles. 2. Small-angle scattering, J. Plasma Phys. 70, 505–532 (2004).
20. J. E. Kunstmann. A new transport mode for energetic charged particles in magnetic fluctuations superposed on a diverging mean field, Astrophys. J. 229, 812 (1979).
21. G. Li and M. A. Lee. Focused transport of solar energetic particles in interplanetary space and the formation of the anisotropic beam-like distribution of particles in the onset phase of large gradual events, Astrophys. J. 875, 116 (2019).
22. M. A. Malkov. Exact solution of the Fokker–Planck equation for isotropic scattering, Phys. Rev. D 95, 023007 (2017).
23. K. G. McCracken, H. Moraal, and P. H. Stoker. Investigation of the multiple-component structure of the 20 January 2005 cosmic ray ground level enhancement, J. Geophys. Res.: Space Phys. 113, A1202 (2008).
24. L. I. Miroshnichenko and J. A. Perez-Peraza. Astrophysical aspects in the studies of solar cosmic rays, Int. J. Mod. Phys. 23, 1 (2008).
25. H. Moraal and K. G. McCracken. The time structure of ground level enhancement in solar cycle 23, Space Sci. Rev. 171, 85–95 (2012).
26. C. Plainaki, A. Belov, H. Mavromichalaki, and V. Yanke. Modeling ground level enhancement. Event of 20 January 2005, J. Geophys. Res.: Space Phys. 112, A04102 (2007).
27. D. Ruffolo. Effect of adiabatic deceleration on the focused transport of solar cosmic rays, Astrophys. J. 442, 861–874 (1995).
28. B. A. Shakhov and M. Stehlik. The Fokker–Planck equation in the second order pitch angle approximation and its exact solution, J. Quant. Spectrosc. Radiat. Transfer 78, 31–39 (2003).
29. M. A. Shea and D. F. Smart. Space weather and the ground level solar proton events of the 23-rd solar cycle, Space Sci. Rev. 171, 161 (2012).
30. G. M. Simnett. The timing of relativistic proton acceleration in the 20 January 2005 flare, Astron. Astrophys. 445, 715–724 (2006).
31. E. V. Vashenyuk, Yu. V. Balabin, J. A. Perez-Peraza, et al. Some features of the sources of relativistic particles at the Sun in the solar cycles 21–23, Adv. Space Res. 38, 411–418 (2006).
32. H. J. Völk. Cosmic ray propagation in interplanetary space, Rev. Geophys. Space Phys. 13, 547–566 (1975).