Skip to main content
Log in

Charged particle acceleration in the front of the shock wave bounding supersonic solar wind

  • Space Physics
  • Published:
Kinematics and Physics of Celestial Bodies Aims and scope Submit manuscript

Abstract

The process of cosmic ray acceleration in the front of the spherical shock wave bounding the supersonic solar wind is studied. On the basis of our analytical solution of the transport equation, the energy and spatial distributions of cosmic ray intensity and anisotropy are investigated. It is shown that the shape of accelerated particle spectrum is determined by the medium compressibility at the shock front and by cosmic ray modulation parameters.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. E. G. Berezhko and G. F. Krymskii, “Acceleration of cosmic rays by shock waves,” Usp. Fiz. Nauk 154, 49–91 (1988).

    Article  ADS  Google Scholar 

  2. A. Z. Dolginov and I. N. Toptygin, “Multiple scattering of particles in a magnetic field with random inhomogeneities,” Zh. Eksp. Teor. Fiz. 51, 1771–1783 (1966).

    Google Scholar 

  3. A. Z. Dolginov and I. N. Toptygin, “On diffusion of cosmic rays in the interplanetary medium,” Geomagn. Aeron. 7, 967–973 (1967).

    Google Scholar 

  4. Yu. L. Kolesnik and B. A. Shakhov, “Effect of the heliosheath and standing termination shock on galactic cosmic ray propagation in a stationary heliosphere model,” Kinematics Phys. Celestial Bodies 28, 261–269 (2012).

    Article  ADS  Google Scholar 

  5. G. F. Krymskii, “A regular mechanism for the acceleration of charged particles in the front of a shock wave,” Dokl. Akad. Nauk SSSR 234, 1306–1309 (1977).

    ADS  Google Scholar 

  6. G. F. Krymskii and S. I. Petukhov, “Acceleration of particles by a regular mechanism in the presence of a spherical shock wave,” Pis’ma Astron. Zh. 6, 227–231 (1980).

    ADS  Google Scholar 

  7. L. D. Landau and E. M. Lifshitz, Field Theory (Nauka, Moscow, 1973).

    Google Scholar 

  8. V. L. Prishchep and V. S. Ptuskin, “On acceleration of fast particles in the front of a spherical shock wave,” Astron. Zh. 58, 779–789 (1981).

    ADS  MATH  Google Scholar 

  9. I. N. Toptygin, Cosmic Rays in Interplanetary Magnetic Fields (Nauka, Moscow, 1983).

    Google Scholar 

  10. Yu. I. Fedorov, “Energy exchange between energetic particles and a shock wave propagating in space plasma,” Kinematika Fiz. Nebesnykh Tel 22, 323–339 (2006).

    ADS  Google Scholar 

  11. B. A. Shakhov and Yu. L. Kolesnik, “Iterative method for solving boundary-value problems in the theory of cosmic ray propagation,” Kinematics Phys. Celestial Bodies 22, 75–80 (2006).

    Google Scholar 

  12. W. I. Axford, E. Leer, and G. Scadron, “The acceleration of cosmic rays by shock waves,” in Proceedings of the 15th International Cosmic Ray Conference, Plovdiv, Bulgaria, 1977, vol. 11, p. 132.

  13. A. R. Bell, “The acceleration of cosmic rays in shock fronts,” Mon. Not. R. Astron. Soc. 182, 147–156 (1978).

    ADS  Google Scholar 

  14. J. W. Bieber, W. H. Matthaeus, C. W. Smith, et al., “Proton and electron mean free paths: the Palmer consensus revisited,” Astrophys. J. 420, 294–306 (1994).

    Article  ADS  Google Scholar 

  15. R. D. Blandford and J. P. Ostriker, “Particle acceleration by astrophysical shocks,” Astrophys. J. 221, L29–L32 (1978).

    Article  ADS  Google Scholar 

  16. P. Bobik, G. Boella, M. J. Boschini, et al., “Systematic investigation of solar modulation of galactic protons for solar cycle 23 using a Monte Carlo approach with particle drift effects and latitudinal dependence,” Astrophys. J. 745, 132 (2012).

    Article  ADS  Google Scholar 

  17. A. C. Cummings, E. C. Stone, F. B. McDonald, et al., “Voyager observations of anomalous cosmic rays in the outer heliosphere,” in Proceedings of the 32nd International Cosmic Ray Conference, Beijing, China, 2011, vol. 11, p. 2.

  18. L. I. Dorman, M. E. Katz, Yu. I. Fedorov, and B. A. Shakhov, “Variation of cosmic-ray energy in interplanetary space,” Astophys. Space Sci. 94, 43–95 (1983).

    Article  ADS  MATH  Google Scholar 

  19. W. Droege, “The rigidity dependence of solar particle scattering mean free paths,” Astophys. J. 537, 1073–1079 (2000).

    Article  ADS  Google Scholar 

  20. L. O’C. Drury, “An introduction to the theory of diffusive shock acceleration of energetic particles in tenuous plasmas,” Rep. Prog. Phys. 46, 973–1027 (1983).

    Article  ADS  Google Scholar 

  21. L. A. Fisk and G. Gloeckler, “The acceleration of anomalous cosmic rays by stochastic acceleration in the heliosheath,” Adv. Space Res. 43, 1471–1478 (2009).

    Article  ADS  Google Scholar 

  22. V. Florinski and J. R. Jokipii, “Cosmic ray spectra at spherical termination shocks,” Astrophys. J. 591, 454–460 (2003).

    Article  ADS  Google Scholar 

  23. V. Florinski and N. V. Pogorelov, “Four-dimensional transport of galactic cosmic rays in the outer heliosphere and heliosheath,” Astrophys. J. 701, 642–651 (2009).

    Article  ADS  Google Scholar 

  24. V. Florinski, G. P. Zank, and N. V. Pogorelov, “Galactic cosmic ray transport in the global heliosphere,” J. Geophys. Res. 108, 1228 (2003).

    Article  Google Scholar 

  25. J. Giacalone, J. F. Drake, and J. R. Jokipii, “The acceleration mechanism of anomalous cosmic rays,” Space Sci. Rev. 173, 283–307 (2012).

    Article  ADS  Google Scholar 

  26. L. J. Gleeson and W. I. Axford, “Solar modulation of galactic cosmic rays,” Astrophys. J. 154, 1011–1026 (1968).

    Article  ADS  Google Scholar 

  27. L. J. Gleeson and I. H. Urch, “A study of the force-field equation for the propagation of galactic cosmic rays,” Astrophys. Space Sci. 25, 387–404 (1973).

    Article  ADS  Google Scholar 

  28. B. Heber and M. S. Potgieter, “Cosmic rays at high heliolatitudes,” Space Sci. Rev. 127, 117–194 (2006).

    Article  ADS  Google Scholar 

  29. R. Kallenbach, K. Bamett, and M. Hilchenbach, “Acceleration of the anomalous component of cosmic rays revisited,” Astrophys. Space Sci. Trans. 5, 49–60 (2009).

    Article  ADS  Google Scholar 

  30. J. Kota and J. R. Jokipii, “Cosmic ray transport beyond the termination shock: Modulation in the heliosheath,” in Proceedings of the 28th International Cosmic Ray Conference, Tsukuba, Japan 2003, pp. 3863–3866.

  31. P. O. Lagage and C. J. Cesarsky, “The maximum energy of cosmic rays accelerated by supernova shocks,” Astron. Astrophys. 125, 249–257 (1983).

    ADS  MATH  Google Scholar 

  32. J. A. Le Roux and G. M. Webb, “Time-dependent acceleration of interstellar pickup ions at the heliospheric termination shock using a focused transport approach,” Astrophys. J. 693, 534–551 (2009).

    Article  ADS  Google Scholar 

  33. F. B. McDonald, “Voyager observations of galactic and anomalous cosmic rays at the termination shock and in the heliosheath,” in Proceedings of the 30th International Cosmic Ray Conference, Merida, Mexico 2007, vol. 6, pp. 167–180.

  34. I. V. Moskalenko, A. V. Strong, J. F. Ormes, and M. S. Potgieter, “Secondary antiprotons and propagation of cosmic rays in the Galaxy and heliosphere,” Astrophys. J. 565, 280–296 (2002).

    Article  ADS  Google Scholar 

  35. M. Ostrowski and R. Schlickeiser, “Cosmic-ray diffusive acceleration at shock waves with finite upstream and downstream escape boundaries,” Sol. Phys. 167, 381–394 (1996).

    Article  ADS  Google Scholar 

  36. I. D. Palmer, “Transport coefficients of low-energy cosmic rays in interplanetary space,” Rev. Geophys. Space Phys. 20, 335–351 (1982).

    Article  ADS  Google Scholar 

  37. E. N. Parker, “The passage of energetic charged particles through interplanetary space,” Planet. Space Sci. 13, 9 (1965).

    Article  ADS  Google Scholar 

  38. M. S. Potgieter and H. Moraal, “Acceleration of cosmic rays in the solar wind termination shock. 1. A steady state technique in a spherically symmetric model,” Astrophys. J. 330, 445–455 (1988).

    Article  ADS  Google Scholar 

  39. J. D. Richardson and L. F. Burlaga, “The solar wind in the outer heliosphere and heliosheath,” Space Sci. Rev. 176, 217–235 (2013).

    Article  ADS  Google Scholar 

  40. G. M. Webb, M. A. Forman, and W. I. Axford, “Cosmic-ray acceleration at stellar wind terminal shocks,” Astrophys. J. 298, 684–708 (1985).

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yu. I. Fedorov.

Additional information

Original Russian Text © Yu.I. Fedorov, 2014, published in Kinematika i Fizika Nebesnykh Tel, 2014, Vol. 30, No. 3, pp. 3–26.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fedorov, Y.I. Charged particle acceleration in the front of the shock wave bounding supersonic solar wind. Kinemat. Phys. Celest. Bodies 30, 109–125 (2014). https://doi.org/10.3103/S0884591314030040

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0884591314030040

Keywords

Navigation