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Modulation of Galactic Cosmic Ray Intensity in the Approximation of Small Anisotropy

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Abstract

The propagation of cosmic rays in the interplanetary medium based on the transport equation is considered. The solution of the cosmic ray transport equation is obtained for the known energy distribution of high-energy charged particles at the heliospheric boundary. The spectrum of galactic cosmic rays in the local interstellar medium is taken on the basis of the data from the Voyager 1 and 2 spacecraft. The flux of galactic cosmic rays in different periods of solar activity is calculated. Cosmic ray intensity gradients are estimated, and these calculations are compared to the data from space missions. The anisotropy of the angular distribution of cosmic rays is calculated. It is shown that the flux of galactic cosmic rays in the Earth’s orbit has an azimuthal direction, and the value of the anisotropy of protons with energies from 1 MeV to 1 Gev is of the order of 0.5%.

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REFERENCES

  1. A. Z. Dolginov and I. N. Toptygin, “Multiple scattering of particles in a magnetic field with random inhomogeneities,” Sov. Phys. - JETP 24, 1195–1202 (1966).

    ADS  Google Scholar 

  2. L. I. Dorman, M. E. Kats, Yu. I. Fedorov, and B. A. Shakhov, “Energy balance of charged particles multiply scattered in a randomly inhomogeneous magnetic field,” Sov. Phys. - JETP 52, 640–646 (1980).

    ADS  Google Scholar 

  3. G. F. Krymskii, “Diffusion mechanism of diurnal variation of cosmic rays,” Geomagn. Aeron. 4, 977 (1964).

    Google Scholar 

  4. B. A. Shakhov and Yu. L. Kolesnik, “Iteration method for solution of cosmic ray propagation theory boundary problems,” Kinematika Fiz. Nebesnykh Tel 22 (2), 100 (2006).

    ADS  Google Scholar 

  5. R. A. Caballero-Lopez and H. Moraal, “Limitations of the force field equation to describe cosmic ray modulation,” J. Geophys. Res.: Space Phys. 109, A01101 (2004).

    ADS  Google Scholar 

  6. L. I. Dorman and M. E. Katz, “Cosmic ray kinetics in space,” Space Sci. Rev. 20, 529 (1977).

    Article  ADS  Google Scholar 

  7. Yu. I. Fedorov, “Propagation of galactic cosmic rays in the outer heliosphere,” Kinematics Phys. Celestial Bodies 33, 63–78 (2017).

    Article  ADS  Google Scholar 

  8. Yu. I. Fedorov and M. Stehlik, “The modulation of galactic cosmic ray intensity in the outer heliosphere,” Sol. Phys. 293, 119 (2017).

    Article  ADS  Google Scholar 

  9. L. J. Gleeson and W. I. Axford, “Solar modulation of galactic cosmic rays,” Astrophys. J. 159, 1011 (1968).

    Article  ADS  Google Scholar 

  10. B. Heber, “Cosmic rays through the Solar Hale Cycle. Insights from Ulysses,” Space Sci. Rev. 176, 265 (2013).

    Article  ADS  Google Scholar 

  11. B. Heber, W. Droege, P. Ferrando, et al., “Spatial variation of > 40 MeV/n nuclei fluxes observed during ULYSSES rapid latitude scan,” Astron. Astrophys. 316, 538 (1996).

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  13. Yu. L. Kolesnyk 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 

  14. Yu. L. Kolesnyk, P. Bobik, B. A. Shakhov, and M. Putis, “An analytically iterative method for solving problems of cosmic ray modulation,” Mon. Not. R. Astron. Soc. 470, 1073 (2017).

    Article  ADS  Google Scholar 

  15. Yu. L. Kolesnyk, B. A. Shakhov, P. Bobik, and M. Putis, “An exact solution of cosmic ray modulation problem in a stationary composite heliosphere model,” Mon. Not. R. Astron. Soc. 491, 5826 (2020).

    Article  ADS  Google Scholar 

  16. R. B. McKibben, “Three-dimensial solar-modulation of cosmic rays and anomalous components in the inner heliosphere,” Space Sci. Rev. 83, 21 (1998).

    Article  ADS  Google Scholar 

  17. R. B. McKibben, J. J. Connel, C. Lopate, J. A. Simpson, and M. Zhang, “Observations of galactic cosmic rays and the anomalous helium during Ulysses passage from the south to the north solar pole,” Astron. Astrophys. 316, 547 (1996).

    ADS  Google Scholar 

  18. H. Moraal, “Cosmic ray modulation equation,” Space Sci Rev. 176, 299 (2013).

    Article  ADS  Google Scholar 

  19. E. N. Parker, “Dynamics of the interplanetary gas and field,” Astrophys. J. 128, 644 (1958).

    ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  21. M. S. Potgieter, “Very local interstellar spectra for galactic electrons, protons and helium” (2013). arxiv 1310.6133 [astro-ph].

  22. I. H. Urch and L. J. Gleeson, “Galactic cosmic ray modulation from 1965–1970,” Astrophys. Space Sci. 17, 426 (1972).

    Article  ADS  Google Scholar 

  23. E. E. Vos and M. S. Potgieter, “New modeling of galactic proton modulation during the minimum of solar cycle 23/24,” Astrophys. J. 815, 119 (2015).

    Article  ADS  Google Scholar 

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Correspondence to Yu. I. Fedorov.

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Translated by O. Pismenov

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Fedorov, Y.I., Shakhov, B.O. & Kolesnyk, Y.L. Modulation of Galactic Cosmic Ray Intensity in the Approximation of Small Anisotropy. Kinemat. Phys. Celest. Bodies 38, 181–189 (2022). https://doi.org/10.3103/S0884591322040043

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  • DOI: https://doi.org/10.3103/S0884591322040043

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