The cosmic ray intensity on the initial stage of the solar flare
1Fedorov, YI 1Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Kyiv, Ukraine |
Kinemat. fiz. nebesnyh tel (Online) 2018, 34(1):3-20 |
https://doi.org/10.15407/kfnt2018.01.003 |
Start Page: Space Physics |
Language: Russian |
Abstract: The propagation of solar cosmic rays in the interplanetary space is considered based on the solution of Fokker-Planck equation in the small-angle approximation. The particle source is assumed to be instantaneous and point-like. The spatial and temporal distributions of energetic particle density during the anisotropic phase of solar cosmic ray enhancement are studied. The prolonged particle injection in the interplanetary medium is also discussed. |
Keywords: cosmic rays, diffusion, kinetic equation, magnetic fields |
1.M. Abramovitz and I. Stigun, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables (National Bureau of Standards, Washington, DC, 1964; Nauka, Moscow, 1979).
2.G. A. Bazilevskaya and R. M. Golynskaya, “On distribution of solar cosmic rays in interstellar medium with consideration of adiabatic focusing,” Geomagn. Aeron. 29, 204–209 (1989).
3.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).
4.I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Fizmatgiz, Moscow, 1963; Academic, New York, 1965).
5.L. I. Dorman and M. E. Katz, “On intensity fluctuations of solar cosmic rays,” in Proc. Solar Cosmic Rays and Their Penetration into the Earth’s Magnetosphere: 5th Leningrad Int. Semin., Leningrad, July 26–29, 1973 (Leningrad Fiz.-Tekh. Inst. im. A. F. Ioffe, Leningrad, 1973), pp. 311–321.
6.A. F. Nikiforov and V. B. Uvarov, Special Functions of Mathematical Physics (Nauka, Moscow, 1978; Birkhäuser, Basel, 1985).
7.I. N. Toptygin, “On the time dependence of intensity of cosmic rays at the anisotropic stage of solar flares,” Geomagn. Aeron. 12, 989–995 (1972).
8.I. N. Toptygin, Cosmic Rays in Interplanetary Magnetic Fields (Nauka, Moscow, 1983; Reidel, Dordrecht, 1985).
https://doi.org/10.1007/978-94-009-5257-7
9.J. W. Bieber, J. Clem, P. Evenson, et al., “Giant ground level enhancement of relativistic solar protons on 2005 January 20. I. Spaceship Earth observations,” Astrophys. J. 771, 92 (2013).
https://doi.org/10.1088/0004-637X/771/2/92
10.J. W. Bieber, J. A. Earl, G. Green, et al., “Interplanetary pitch angle scattering and coronal transport of solar energetic particles: New information from Helios,” J. Geophys. Res.: Space Phys. 85, 2313–2323 (1980).
https://doi.org/10.1029/JA085iA05p02313
11.J. W. Bieber, P. A. Evenson, and M. A. Pomerantz, “Focusing anisotropy of solar cosmic rays,” J. Geophys. Res.: Space Phys. 91, 8713–8724 (1986).
https://doi.org/10.1029/JA091iA08p08713
12.D. J. Bombardieri, M. L. Duldig, J. E. Humble, and K. J. Michael, “An improved model for relativistic solar proton acceleration applied to the 2005 January 20 and earlier events,” Astrophys. J. 682, 1315–1327 (2008).
https://doi.org/10.1086/589494
13.J. L. Cramp, M. L. Duldig, E. O. Flückiger, J. E. Humble, M. A. Shea, and D. F. Smart, “The October 22, 1989, solar cosmic ray enhancement: An analysis of the anisotropy and spectral characteristics,” J. Geophys. Res.: Space Phys. 102, 24237–24248 (1997).
https://doi.org/10.1029/97JA01947
14.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).
https://doi.org/10.1088/0004-637X/772/1/35
15.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., Part 2 — Lett. 387, L51–L54 (1992).
https://doi.org/10.1086/186303
16.L. I. Dorman and M. E. Katz, “Cosmic ray kinetics in space,” Space Sci. Rev. 70, 529–575 (1977).
https://doi.org/10.1007/BF02186896
17.W. Dröge, 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).
https://doi.org/10.1088/0004-637X/709/2/912
18.S. P. Duggal, “Relativistic solar cosmic rays,” Rev. Geophys. Space Phys. 17, 1021–1058 (1979).
https://doi.org/10.1029/RG017i005p01021
19.Yu. I. Fedorov and B. A. Shakhov, “Solar cosmic rays in homogeneous magnetic field,” in Proc. 23rd Int. Cosmic Ray Conf., Calgary, July 19–30, 1993 (World Sci., Singapore, 1993), Vol. 3, pp. 215–218.
20.Yu. I. Fedorov, B. A. Shakhov, and M. Stehlik, “Non-diffusive transport of cosmic rays in homogeneous regular magnetic fields,” Astron. Astrophys. 302, 623–634 (1995).
21.Yu. I. Fedorov, M. Stehlik, K. Kudela, and J. Kassavicova, “Non-diffusive particle pulse transport — Application to an anisotropic solar GLE,” Sol. Phys. 208, 325–334 (2002).
https://doi.org/10.1023/A:1020581705981
22.L. J. Gleeson and G. M. Webb, “Energy changes of cosmic rays in the interplanetary region,” Astrophys. Space Sci. 58, 21–39 (1978).
https://doi.org/10.1007/BF00645373
23.E. Kh. Kaghashvili, G. P. Zank, J. Y. Lu, and W. Dröge, “Transport of energetic charged particles. Part 2. Smallangle scattering,” J. Plasma Phys. 70, 505–532 (2004).
https://doi.org/10.1017/S0022377803002745
24.J. Kota, “Coherent pulses in the diffusive transport of charged particles,” Astrophys. J. 427, 1035–1040 (1994).
https://doi.org/10.1086/174209
25.J. Y. Lu, J. P. Zank, R. Rankin, and R. Marchand, “The transport of charged particles in a flowing medium,” Astrophys. J. 576, 574–586 (2002).
https://doi.org/10.1086/341734
26.J. Y. Lu, G. P. Zank, and G. M. Webb, “Numerical solution of the time-dependent kinetic equation for anisotropic pitch-angle scattering,” Astrophys. J. 550, 34–51 (2001).
https://doi.org/10.1086/319722
27.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, A12101 (2008).
https://doi.org/10.1029/2007JA012829
28.L. I. Miroshnichenko, Solar Cosmic Rays (Kluwer, Dordrecht, 2001).
https://doi.org/10.1007/978-94-015-9646-6
29.C. Plainaki, A. Belov, H. Mavromichalaki, and V. Yanke, “Modeling ground level enhancements: Event of 20 January 2005,” J. Geophys. Res.: Space Phys. 112, A04102 (2007).
https://doi.org/10.1029/2006JA011926
30.D. Ruffolo, “Effect of adiabatic deceleration on the focused transport of solar cosmic rays,” Astrophys. J. 442, 861–874 (1995).
https://doi.org/10.1086/175489
31.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).
https://doi.org/10.1016/S0022-4073(02)00175-9
32.G. M. Simnett, “The timing of relativistic proton acceleration in the 20 January 2005 flare,” Astron. Astrophys. 445, 715–724 (2006).
https://doi.org/10.1051/0004-6361:20053503
33.G. M. Webb, M. Pantazopolou, and G. P. Zank, “Multiple scattering and the BGK Boltzmann equation,” J. Phys. A: Math. Gen. 33, 3137–3160 (2000).MathSciNet
https://doi.org/10.1088/0305-4470/33/16/307
34.G. P. Zank, J. Y. Lu, W. K. M. Rise, and G. M. Webb, “Transport of energetic charged particles in a radial magnetic field. Part 1. Large-angle scattering,” J. Plasma Phys. 64, 507 (2000).
https://doi.org/10.1017/S0022377800008709