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3D AND 2D TRANSPORT EQUATIONS OF GALACTIC COSMIC RAYS IN MODERN HELIOSPHERE MODELS – I
- Authors: Kalinin M.S.1, Krainev M.B.1
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Affiliations:
- Lebedev Physical Institute of the Russian Academy of Sciences
- Issue: Vol 63, No 6 (2025)
- Pages: 601–609
- Section: Articles
- URL: https://journal-vniispk.ru/0023-4206/article/view/361956
- DOI: https://doi.org/10.7868/S3034550225060033
- ID: 361956
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Abstract
The paper presents the results of the reduction of the full three-dimensional (in spatial coordinates) transport equation of galactic cosmic rays in longitude. It is shown that in the simplest case of the quasi-stationary equation, usually used to describe the intensity of galactic cosmic rays near solar activity minima, when only the coefficient describing the particle drift depends on longitude, the resulting axisymmetric equation does not reduce to an a priori 2D-equation, in which the longitudinal component of the particle drift velocity is dropped from consideration. The presence of the drift modulation mechanism leads to the fact that in the 2D reduced equation the total drift velocity acquires a factor −1 ≤ F ≤ 1, depending on the latitude, and an additional term appears in the equation, taking into account the contribution of the three-dimensionality of the original equation.
About the authors
M. S. Kalinin
Lebedev Physical Institute of the Russian Academy of Sciences
Email: kalininns@lebedev.ru
Moscow, Russia
M. B. Krainev
Lebedev Physical Institute of the Russian Academy of SciencesMoscow, Russia
References
- Kalinin M.S., Krainev M.B. Two-Dimensional Transport Equation for Galactic Cosmic Rays as a Con- sequence of a Reduction of the Three-Dimensional Equation // Geomagnetism and Aeronomy. 2014. V. 54. Iss. 4. P. 423–429.
- Kalinin M.S., Gvozdevsky B.B., Krainev M.B. et al. On the transition from 3D to 2D transport equations for a study of long-term cosmic-ray intensity variations in the heliosphere // Proceedings of Science. 37th International Cosmic Ray Conference (ICRC). https://pos.sissa.it/. 2021. V. 395. Art.ID. 1323. doi: 10.22323/1.395.01323.
- Potgieter M.S., Vos E.E., Boezio M. et al. Modulation of Galactic Protons in the Heliosphere During the Unusual Solar Minimum of 2006 to 2009 // Solar Phys. 2014. V. 289. P. 391–406. doi: 10.1007/s11207-013-0324-6.
- Крымский Г.Ф. Диффузионный механизм суточной вариации космических лучей // Геомагнетизм и аэрономия. 1964. T. IV. № 6. C. 977–986.
- Parker E.N. The passage of energetic charged particles through interplanetary space // Planet. Space Sci. 1965. V. 13. P. 9–49.
- Jokipii J.R., Levy E.H., Hubbard W.B. Effects of particle drift on cosmic-ray transport. I. General properties, application to solar modulation // Astrophysical J. 1977. V. 213. Art.ID. 861.
- Köta J., Jokipii J.R. Effects of drift on the transport of cosmic rays VI. A three-dimensional model including diffusion // Astrophysical J. 1983. V. 265. P. 573–581.
- Burger R.A., Moraal H., Webb G.M. Drift theory of charged particles in electric and magnetic fields // Astroph. and Sp. Sc. 1985. V. 116. Iss. 1. P. 107–129.
- Burger R.A., Moraal H., Webb G.M. Notes on drift theory // Astroph. and Sp. Sc. 1985. V. 116. Art.ID. 107.
- Burger R.A., Moraal H., Potgieter M.S. On the Inclusion of a Wavy Neutral Sheet in Two-Dimensional Drift Models // Proc. 20th Internation-I Cosmic Ray Conference. Moscow. 1987. V. 3. Art.ID. 283.
- Burger R.A., Potgieter M.S. The calculation of neutral sheet drift in two-dimensional cosmic-ray modulation models // Astrophysical J. 1989. V. 339. Iss. 511. P. 501–511.
- Burger R.A. Modeling drift along the heliospheric wavy neutral sheet // Astrophysical J. 2012. V. 760. Art.ID. 60. doi: 10.1088/0004-637X/760/1/60
- Pei C., Bieber J.W., Burger R.A. et al. Three-dimensional wavy heliospheric current sheet drifts // Ap J. 2012. V. 744. Art.ID. 170. doi: 10.1088/0004-637X/744/2/170.
- Schatten K.H. Current sheet magnetic model for the solar corona. NASA Technical Report X-692-71-132. 1971.
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