Statistical acceleration and spatial diffusion of cosmic rays in the turbulent medium

1Fedorov, YI, 1Shakhov, BA, 2Stehlik, M
1Main Astronomical Observatory of the National Academy of Sciences of Ukraine, Kyiv, Ukraine
2Institute of Experimental Physics SAS, Košice, Slovakia
Kinemat. fiz. nebesnyh tel (Online) 2013, 29(1):3-25
Start Page: Space Physics
Language: Russian

The process of cosmic ray acceleration in the turbulent medium is studied. It is supposed that charged particles are obtaining the energy in a limited space region and are leaving the acceleration region as a result of spatial diffusion induced by cosmic ray scattering in turbulent magnetic fields. Analytical solutions of cosmic ray transport equation are obtained and equilibrium spatial-energetic distributions of high-energy particles in and outside the acceleration region are investigated.

Keywords: cosmic rays, equation, turbulent medium

1.M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions (Dover Publications, New York, 1972; Nauka, Moscow, 1979).

2.I. S. Kardashev, “Nonstationarity of Spectra of Young Sources of Nonthermal Radio Emission,” Sov. Astron. 6, 317–327 (1962).

3.A. P. Prudnikov, Yu. A. Brychkov, and O. I. Marichev, Integrals and Series. Elementary Functions (Nauka, Moscow, 1981) [in Russian].

4.B. A. Tverskoi, “Contribution to the Theory of Fermi Statistical Acceleration,” Sov. Phys. JETP 25, 317–325 (1967).

5.I. N. Toptygin, Cosmic Rays in Interplanetary Magnetic Fields (Nauka, Moscow, 1983) [in Russian].

6.Yu. I. Fedorov, “Statistical Acceleration of Cosmic Rays in Anisotropic Turbulent Medium,” Kinem. Phys. Celest. Bodies 27, 1–16 (2011).

7.A. Achterberg, “On the Nature of Small Amplitude Fermi Acceleration,” Astron. Astrophys. 97, 259–264 (1981).

8.M. J. Aschwanden, “Particle Acceleration and Kinematics in Solar Flares,” Space Sci. Rev. 101, 1–227 (2002).

9.P. A. Becker, T. Le, and C. D. Dermer, “Time-Dependent Stochastic Particle Acceleration in Astrophysical Plasmas,” Astrophys. J. 647, 539–551 (2006).

10.C. D. Dermer, J. A. Miller, and H. Li, “Stochastic Particle Acceleration near Accreting Black Holes,” Astrophys. J. 456, 106–118 (1996).

11.W. Droege and R. Schlickeiser, “Particle Acceleration in Solar Flares,” Astrophys. J. 305, 909–912 (1986).

12.Z. Fan, S. Liu, and C. L. Fryer, “Stochastic Electron Acceleration in the TeV Supernova Remnant RXJ 1713.7-3946: The High Energy Cutoff,” Mon. Not. R. Astron. Soc. 406, 1337–1349 (2009).

13.Yu. I. Fedorov, M. E. Katz, L. L. Kichatinov, and M. Stehlik, “Cosmic-Ray Kinetics in a Random Anisotropic Reflective Non-Invariant Magnetic Field,” Astron. Astrophys. 260, 499–509 (1992).

14.Yu. I. Fedorov and M. Stehlik, “Cosmic Ray Energetic Spectrum and Its Evolution in Helical Plasma Turbulence,” in Proc. 21st European Cosmic Ray Symposium, Kosice, Slovakia, 2008, Ed. by P. Kiraly, K. Kudela, M. Stehlik, and A. W. Wolfendale (Inst. of Experim. Phys. Slovak Acad. of Sci., Kosice, 2009), pp. 297–302.

15.Yu. Fedorov and M. Stehlik, “Stochastic Acceleraton by Induced Electric Field versus Fermi Acceleration,” J. Phys. B: At., Mol. Opt. Phys. 43, 185701 (2010).

16.E. Fermi, “On the Origin of the Cosmic Radiation,” Phys. Rev. 75, 1169–1174 (1949).

17.L. Fletcher and H. S. Hudson, “Impulsive Phase Flare Energy Transport by Large-Scale Alfven Waves and the Electron Acceleration Problem,” Astrophys. J. 675, 1645–1655 (2008).

18.D. Melrose, “On the Formation of Energy Spectra in Synchrotron Sources,” Astrophys. Space Sci. 5, 131–169 (1969).

19.P. Mertsch, “A New Analytic Solution for 2-nd Order Fermi Acceleration.”

20.J. A. Miller, P. I. Cargill, A. G. Emslie, et al., “Critical Issues for Understanding Particle Acceleration in Impulsive Solar Flares,” J. Geophys. Res. 102, 14631–14659 (1997).

21.J. A. Miller, N. Guessom, and R. Ramaty, “Stochastic Fermi Acceleration in Solar Flares,” Astrophys. J. 361, 701–708 (1990).

22.J. A. Miller, T. N. Larosa, and R. L. Moore, “Stochastic Electron Acceleration by Cascading Fast Mode Waves in Impulsive Solar Flares,” Astrophys. J. 461, 445–464 (1996).

23.J. A. Miller and D. A. Roberts, “Stochastic Proton Acceleration by Cascading Alfven Waves in Impulsive Solar Flares,” Astrophys. J. 452, 912–932 (1995).

24.I. Mochol and M. Ostrowski, “Validity Range of the Escape Term Approximation in the Momentum Diffusion Equation,” in Proc. 31st Int. Cosmic Ray Conf., Lodz, 2009.

25.B. T. Park and V. Petrosian, “Fokker-Planck Equations of Stochastic Acceleration: Green’s Functions and Boundary Conditions,” Astrophys. J. 446, 699–716 (1995).

26.R. Ramaty and R. J. Murphy, “Nuclear Processes and Accelerated Particles in Solar Flares,” Space Sci. Rev. 45, 213–268 (1987).

27.R. Schlickeiser, Cosmic Ray Astrophysics (Springer-Verlag, Berlin — Heidelberg, 2002).

28.P. Schneider, “A Comment on Second-Order Fermi Acceleration,” Astron. Astrophys. 269, L13–L15 (1993).

29.J. Steinacker and R. Schlickeiser, “Stochastic Acceleration of Solar Protons in the Transrelativistic Region,” Astron. Astrophys. 224, 259–266 (1989).

30.J. J. P. Virtanen and R. Vainio, “Stochastic Acceleration in Relativistic Parallel Shocks,” Astrophys. J. 621, 313–323 (2005).

31.Y. G. Zheng, L. Zhang, “Stochastic Acceleration of Relativistic Particles in a Turbulent Magnetic Field,” in Proc. 32nd Int. Cosmic Ray Conf., Beijing, 2011.