Solar-Terrestrial Physics Solar-Terrestrial Physics Solar-Terrestrial Physics 2500-0535 16402 10.12737/article_58f970f2455545.93154609 Results of current research Results of current research Results of current research Heliospheric modulation of cosmic rays: model and observation Heliospheric modulation of cosmic rays: model and observation https://orcid.org/0000-0003-1247-4513 Герасимова Сардаана Кимовна Gerasimova Sardaana Kimovna danagsk@mail.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

 https://orcid.org/0000-0003-2184-8089 Гололобов Петр Юрьевич Gololobov Peter Yur'evich gpeter@ikfia.sbras.ru https://orcid.org/0000-0002-1348-4708 Григорьев Владислав Георгиевич Grigoryev Vladislav Georgievich grig@ikfia.ysn.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

 Кривошапкин Прокопий Антипович Krivoshapkin Prokopy Antipovich p_a_krivoshapkin@mail.ru

кандидат физико-математических наук;

candidate of physical and mathematical sciences;

 Крымский Гермоген Филиппович Krymsky Germogen Filippovich krymsky@ikfia.ysn.ru

доктор физико-математических наук;

doctor of physical and mathematical sciences;

 https://orcid.org/0000-0002-2343-1618 Стародубцев Сергей Анатольевич Starodubtsev Sergei Anatolyevich starodub@ikfia.ysn.ru

доктор физико-математических наук;

doctor of physical and mathematical sciences;

 Институт космофизических исследований и аэрономии им. Ю.Г. Шафера СО РАН Якутск Россия Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy SB RAS Yakutsk Russian Federation Институт космофизических исследований и аэрономии им. Ю.Г. Шафера СО РАН Якутск Россия Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy SB RAS Yakutsk Russian Federation Институт космофизических исследований и аэрономии им. Ю.Г. Шафера СО РАН Якутск Россия Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy SB RAS Yakutsk Russian Federation Институт космофизических исследований и аэрономии им. Ю.Г. Шафера СО РАН Якутск Россия Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy SB RAS Yakutsk Russian Federation Институт космофизических исследований и аэрономии им. Ю.Г. Шафера СО РАН Якутск Россия Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy SB RAS Yakutsk Russian Federation Институт космофизических исследований и аэрономии им. Ю.Г. Шафера СО РАН Якутск Россия Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy SB RAS Yakutsk Russian Federation 3 1 78 102 https://zh-szf.ru/en/nauka/article/16402/view

This paper presents the basic model of cosmic ray modulation in the heliosphere, developed in Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy of the Siberian Branch of RAS. The model has only one free modulation parameter: the ratio of the regular magnetic field to the turbulent one. It may also be applied to the description of cosmic ray intensity variations in a wide energy range from 100 MeV to 100 GeV. Possible mechanisms of generation of the mentioned turbulence field are considered. The primary assumption about the electrical neutrality of the heliosphere appears to be wrong, and the zero potential needed to match the model with observations in the plane of the solar equator can be achieved if the frontal point of the heliosphere, which is flowed around by interstellar gas, lies near the mentioned plane. We have revealed that the abnormal rise of cosmic ray intensity at the end of solar cycle 23 is related to the residual modulation produced by the subsonic solar wind behind the front of a standing shock wave. The model is used to describe features of cosmic ray intensity variations in several solar activity cycles.

This paper presents the basic model of cosmic ray modulation in the heliosphere, developed in Yu.G. Shafer Institute of Cosmophysical Research and Aeronomy of the Siberian Branch of RAS. The model has only one free modulation parameter: the ratio of the regular magnetic field to the turbulent one. It may also be applied to the description of cosmic ray intensity variations in a wide energy range from 100 MeV to 100 GeV. Possible mechanisms of generation of the mentioned turbulence field are considered. The primary assumption about the electrical neutrality of the heliosphere appears to be wrong, and the zero potential needed to match the model with observations in the plane of the solar equator can be achieved if the frontal point of the heliosphere, which is flowed around by interstellar gas, lies near the mentioned plane. We have revealed that the abnormal rise of cosmic ray intensity at the end of solar cycle 23 is related to the residual modulation produced by the subsonic solar wind behind the front of a standing shock wave. The model is used to describe features of cosmic ray intensity variations in several solar activity cycles.

 cosmic rays heliosphere modulation solar activity

Belov A.V., Shelting B.D., Gushchina R.T., Obridko V.N., Kharshiladze A.F., Yanke V.G. Global magnetic field of the Sun and long-term vatiations of galactic cosmic rays. J. Atmos. Solar-Terr. Phys. 2001, vol. 63, pp. 1923-1929. DOI: 10.1016/S1364-6826(01)00073-6. Belov A.V., Shelting B.D., Gushchina R.T., Obridko V.N., Kharshiladze A.F., Yanke V.G. Global magnetic field of the Sun and long-term vatiations of galactic cosmic rays. J. Atmos. Solar-Terr. Phys. 2001, vol. 63, pp. 1923-1929. DOI: 10.1016/S1364-6826(01)00073-6. Belov A.V., Gushchina R.T., Obridko V.N., Shelting B.D., Yanke V.G. Connection of the long-term modulation of cosmic rays with the parameters of the global magnetic field of the Sun. Geomagn. Aeron. 2002, vol. 42, pp. 693-700. Belov A.V., Gushchina R.T., Obridko V.N., Shelting B.D., Yanke V.G. Connection of the long-term modulation of cosmic rays with the parameters of the global magnetic field of the Sun. Geomagn. Aeron. 2002, vol. 42, pp. 693-700. Belov A.V., Gushchina R.T., Obridko V.N., Shelting B.D., Yanke V.G. The relation of the global magnetic solar field indices and the solar wind characteristics with the long-term variations of galactic cosmic rays. Proceeding of the 29th ICRC. Pune. 2005, vol. 2, pp. 235-238. Belov A.V., Gushchina R.T., Obridko V.N., Shelting B.D., Yanke V.G. The relation of the global magnetic solar field indices and the solar wind characteristics with the long-term variations of galactic cosmic rays. Proceeding of the 29th ICRC. Pune. 2005, vol. 2, pp. 235-238. Belov A.V., Gushchina R.T., Obridko V.N., Shel’ting B.D., Yanke V.G. Simulation of the modulation of galactic cosmic rays during solar activity cycles 21-23. Bull. Russ. Acad. Sci.: Phys. 2007, vol. 71, pp. 974-976. DOI: 10.3103/S1062873807070246. Belov A.V., Gushchina R.T., Obridko V.N., Shel’ting B.D., Yanke V.G. Simulation of the modulation of galactic cosmic rays during solar activity cycles 21-23. Bull. Russ. Acad. Sci.: Phys. 2007, vol. 71, pp. 974-976. DOI: 10.3103/S1062873807070246. Bisoi S.K., Janardhan P., Ingale M., Subramanian P., Ananthakrishnan S., Tokumaru M., Fujiki K. A study of density modulation index in the inner helioshperic solar wind during solar cycle 23. Astrophys. J. 2014, vol. 795, pp. 69-76. DOI: 10.1088/0004-637X/795/1/69. Bisoi S.K., Janardhan P., Ingale M., Subramanian P., Ananthakrishnan S., Tokumaru M., Fujiki K. A study of density modulation index in the inner helioshperic solar wind during solar cycle 23. Astrophys. J. 2014, vol. 795, pp. 69-76. DOI: 10.1088/0004-637X/795/1/69. Bravo S., Stewart G. The inclination of the heliomagnetic equator and the presence of an inclined relic field in the Sun. Astrophys. J. 1995, vol. 446, pp. 431-434. DOI 10.1086/ 175801. Bravo S., Stewart G. The inclination of the heliomagnetic equator and the presence of an inclined relic field in the Sun. Astrophys. J. 1995, vol. 446, pp. 431-434. DOI 10.1086/ 175801. Charakhch’yan A.N., Stozhkov Y.I., Svirzhevsky N.S., Charakhch’yan T.N. Anomalous effect in the 11-year ga-lactic cosmic ray modulation. Proceeding of the 13th ICRC. Denver. 1973, vol. 2, pp. 1159-1164. Charakhch’yan A.N., Stozhkov Y.I., Svirzhevsky N.S., Charakhch’yan T.N. Anomalous effect in the 11-year ga-lactic cosmic ray modulation. Proceeding of the 13th ICRC. Denver. 1973, vol. 2, pp. 1159-1164. Ferreira S.E.S., Potgieter M.S. Long-term cosmic-ray modulation in the heliosphere. Astrophys. J. 2004, vol. 603, pp. 744-752. DOI: 10.1086/381649. Ferreira S.E.S., Potgieter M.S. Long-term cosmic-ray modulation in the heliosphere. Astrophys. J. 2004, vol. 603, pp. 744-752. DOI: 10.1086/381649. Gerasimova S.K., Gololobov P.Yu., Grigoryev V.G., Krivoshapkin P.A., Krymsky G.F., Starodubtsev S.A. Heli-ospheric modulation of cosmic rays in the 23rd solar cycle and in previous cycles. Proceeding of the 32nd ICRC. Beijing. 2011, vol. 11, pp.180-183. Gerasimova S.K., Gololobov P.Yu., Grigoryev V.G., Krivoshapkin P.A., Krymsky G.F., Starodubtsev S.A. Heli-ospheric modulation of cosmic rays in the 23rd solar cycle and in previous cycles. Proceeding of the 32nd ICRC. Beijing. 2011, vol. 11, pp.180-183. Gerasimova S.K., Krymsky G.F., Krivoshapkin P.A., Gololobov P.Y., Starodubtsev S.A. A modified basic model of the heliospheric modulation of cosmic rays. Bull. Russ. Acad. Sci.: Phys. 2015, vol. 79, pp. 613-615. DOI: 10.3103/ S1062873815050214. Gerasimova S.K., Krymsky G.F., Krivoshapkin P.A., Gololobov P.Y., Starodubtsev S.A. A modified basic model of the heliospheric modulation of cosmic rays. Bull. Russ. Acad. Sci.: Phys. 2015, vol. 79, pp. 613-615. DOI: 10.3103/ S1062873815050214. Gushchina R.T., Belov A.V., Obridko V.N., Shelting B.D. Manifestations of cyclic variations in the solar magnetic field in long-term modulation of cosmic ray. Geomagn. Aeron. 2008, vol. 48, pp. 571-577. DOI: 10.1134/S0016793208050022. Gushchina R.T., Belov A.V., Obridko V.N., Shelting B.D. Manifestations of cyclic variations in the solar magnetic field in long-term modulation of cosmic ray. Geomagn. Aeron. 2008, vol. 48, pp. 571-577. DOI: 10.1134/S0016793208050022. Gushchina R.T., Belov A.V., Eroshenko E.A., Obridko V.N., Paouris E., Shelting B.D. Cosmic ray modulation during the solar activity growth phase of cycle 24. Geomag. Aeron. 2014, vol. 54, pp. 430-436. DOI: 10.1134/S0016793214040057. Gushchina R.T., Belov A.V., Eroshenko E.A., Obridko V.N., Paouris E., Shelting B.D. Cosmic ray modulation during the solar activity growth phase of cycle 24. Geomag. Aeron. 2014, vol. 54, pp. 430-436. DOI: 10.1134/S0016793214040057. Hale G.E., Nicholson S.B.: The law of sun-spot polarity. Astrophys. J. 1925, vol. 62, pp. 270-300. Hale G.E., Nicholson S.B.: The law of sun-spot polarity. Astrophys. J. 1925, vol. 62, pp. 270-300. Jokipii J.R., Levy E.H. Electric field effects on galactic cosmic rays at the heliosphere boundary. Proc. 16th Internat. Cosmic Ray Conf. Kyoto. 1979, vol. 3, pp. 52-56. Jokipii J.R., Levy E.H. Electric field effects on galactic cosmic rays at the heliosphere boundary. Proc. 16th Internat. Cosmic Ray Conf. Kyoto. 1979, vol. 3, pp. 52-56. Jokipii J.R., Kota J. Galactic and anomalous cosmic rays in the heliosphere. Invited, rapporteur and highlight pa-pers, 25th ICRC. Durban. 1997, vol. 8, pp. 151-174. Jokipii J.R., Kota J. Galactic and anomalous cosmic rays in the heliosphere. Invited, rapporteur and highlight pa-pers, 25th ICRC. Durban. 1997, vol. 8, pp. 151-174. Jokipii J.R., Thomas B. Effects of drift on the transport of cosmic rays. IV. Modulation by a wavy interplanetary current sheet. Astrophys. J. 1981, vol. 243, pp. 1115-1122. DOI: 10.1086/158675. Jokipii J.R., Thomas B. Effects of drift on the transport of cosmic rays. IV. Modulation by a wavy interplanetary current sheet. Astrophys. J. 1981, vol. 243, pp. 1115-1122. DOI: 10.1086/158675. Jokipii J.R., Levy E.H., Hubbard W.B. Effects of particle drift on cosmic-ray transport. I. General properties, ap-plication to solar modulation. Astrophys. J. 1977, vol. 213, pp. 861-868. DOI: 10.1086/155218. Jokipii J.R., Levy E.H., Hubbard W.B. Effects of particle drift on cosmic-ray transport. I. General properties, ap-plication to solar modulation. Astrophys. J. 1977, vol. 213, pp. 861-868. DOI: 10.1086/155218. Kota J., Jokipii J.R. Effects of drift on the transport of cosmic rays. VI. A three dimensional model including dif-fusion. Astrophys. J. 1983, vol. 265, pp. 573-581. DOI: 10.1086/160701. Kota J., Jokipii J.R. Effects of drift on the transport of cosmic rays. VI. A three dimensional model including dif-fusion. Astrophys. J. 1983, vol. 265, pp. 573-581. DOI: 10.1086/160701. Krajnev M.B. The solar corona expansion geometry and cosmic ray effects. IV. On the cosmic ray energy change due to the electric field. Proc. 16th Internat. Cosmic Ray Conf. Kyoto. 1979, vol. 3, pp. 236-241. Krajnev M.B. The solar corona expansion geometry and cosmic ray effects. IV. On the cosmic ray energy change due to the electric field. Proc. 16th Internat. Cosmic Ray Conf. Kyoto. 1979, vol. 3, pp. 236-241. Krainev M.B., Kalinin M.S. Arguments in support of influence of external electric field of heliosphere on galactic cosmic rays. Bull. Russ. Acad. Sci.: Phys. 2003, vol. 67, pp. 1439-1442. Krainev M.B., Kalinin M.S. Arguments in support of influence of external electric field of heliosphere on galactic cosmic rays. Bull. Russ. Acad. Sci.: Phys. 2003, vol. 67, pp. 1439-1442. Krainev M.B., Bazilevskaya G.A., Gerasimova S.K., Krivoshapkin P.A., Krymsky G.F., Starodubtsev S.A., Sto-zhkov Y.I., Svirzhevsky N.S. On the status of the sunspot and magnetic cycles in the galactic cosmic ray intensity. J. Phys .: Conf. Ser. 2013, vol. 409, 012,016. DOI: 10.1088/1742-6596/409/1/012016. Krainev M.B., Bazilevskaya G.A., Gerasimova S.K., Krivoshapkin P.A., Krymsky G.F., Starodubtsev S.A., Sto-zhkov Y.I., Svirzhevsky N.S. On the status of the sunspot and magnetic cycles in the galactic cosmic ray intensity. J. Phys .: Conf. Ser. 2013, vol. 409, 012,016. DOI: 10.1088/1742-6596/409/1/012016. Krymsky G.F. Diffusion mechanism of diurnal variation of galactic cosmic rays. Geomagn. Aeron. 1964, vol. 4, pp. 763-769. Krymsky G.F. Diffusion mechanism of diurnal variation of galactic cosmic rays. Geomagn. Aeron. 1964, vol. 4, pp. 763-769. Krymsky G.F., Krivoshapkin P.A.: 2002, Cosmic rays in the past. Geomagn. Aeron. 2002, vol. 42, pp. 305-308. Krymsky G.F., Krivoshapkin P.A.: 2002, Cosmic rays in the past. Geomagn. Aeron. 2002, vol. 42, pp. 305-308. Krymsky G.F., Krivoshapkin P.A., Mamrukova V.P., Gerasimova S.K. Heliospheric modulation of high-energy cosmic ray. I. Basic model of cosmic-ray modulation with solar cycle. J. Exp. Theor. Phys. 2007, vol. 104, pp. 189-195. DOI: 10.1134/ S1063776107020033. Krymsky G.F., Krivoshapkin P.A., Mamrukova V.P., Gerasimova S.K. Heliospheric modulation of high-energy cosmic ray. I. Basic model of cosmic-ray modulation with solar cycle. J. Exp. Theor. Phys. 2007, vol. 104, pp. 189-195. DOI: 10.1134/ S1063776107020033. Krymsky G.F., Krivoshapkin P.A., Mamrukova V.P., Gerasimova S.K. Piston shock and Forbush effect. Astron-omy Letters. 2009, vol. 35, pp. 696-700. DOI: 10.1134/ S1063773709100065. Krymsky G.F., Krivoshapkin P.A., Mamrukova V.P., Gerasimova S.K. Piston shock and Forbush effect. Astron-omy Letters. 2009, vol. 35, pp. 696-700. DOI: 10.1134/ S1063773709100065. Krymsky, G.F. Gololobov, P.Y. Krivoshapkin P.A., Gerasimova S.K., Grigoryev V.G., Starodubtsev, S.A. Variation of the cosmic ray intensity in an 11-yr solar activity cycle: Experiment and theory. JETP Lett. 2013, vol. 98, pp. 769-772. DOI: 10.1134/ S0021364013250139. Krymsky, G.F. Gololobov, P.Y. Krivoshapkin P.A., Gerasimova S.K., Grigoryev V.G., Starodubtsev, S.A. Variation of the cosmic ray intensity in an 11-yr solar activity cycle: Experiment and theory. JETP Lett. 2013, vol. 98, pp. 769-772. DOI: 10.1134/ S0021364013250139. Kurt V.G., Mironova E.N. Methods of local interstellar medium investigation. Phys. Usp. 2013, vol. 56, pp. 910-918. DOI: 10.3367/UFNe.0183.201309e.0963. Kurt V.G., Mironova E.N. Methods of local interstellar medium investigation. Phys. Usp. 2013, vol. 56, pp. 910-918. DOI: 10.3367/UFNe.0183.201309e.0963. Laurenza M., Vecchio A., Storini M., Carbone V. Drift effects on the galactic cosmic ray modulation. Astrophys. J. 2014, vol. 781, pp. 71-82. DOI: 10.1088/0004-637X/781/2/71. Laurenza M., Vecchio A., Storini M., Carbone V. Drift effects on the galactic cosmic ray modulation. Astrophys. J. 2014, vol. 781, pp. 71-82. DOI: 10.1088/0004-637X/781/2/71. Levy E.H. Theory of solar magnetic cycle wave in diurnal-variation of energetic cosmic rays: Physical basis of anisotropy. J. Geophys. Res. 1976, vol. 81, pp. 2082-2088. DOI: 10.1029/JA081i013p02082. Levy E.H. Theory of solar magnetic cycle wave in diurnal-variation of energetic cosmic rays: Physical basis of anisotropy. J. Geophys. Res. 1976, vol. 81, pp. 2082-2088. DOI: 10.1029/JA081i013p02082. Lockwood M. Solar change and climate: an update in the light of the current exceptional solar minimum. Proc. R. Soc.: A. 2010, vol. 466, pp. 303-329. DOI: 10.1098/rspa.2009.0519. Lockwood M. Solar change and climate: an update in the light of the current exceptional solar minimum. Proc. R. Soc.: A. 2010, vol. 466, pp. 303-329. DOI: 10.1098/rspa.2009.0519. Lockwood J.A., Webber W.R. The 11-year solar modulation of cosmic rays as deduced from neutron monitor variations and direct measurements at low energies. J. Geophys. Res. 1967, vol. 72, pp. 5977-5989. DOI: 10.1029/ JZ072i023p05977. Lockwood J.A., Webber W.R. The 11-year solar modulation of cosmic rays as deduced from neutron monitor variations and direct measurements at low energies. J. Geophys. Res. 1967, vol. 72, pp. 5977-5989. DOI: 10.1029/ JZ072i023p05977. Manuel R., Ferreira S.E.S., Potgieter M.S.Time-dependent modulation of cosmic rays in the heliosphere. Solar Phys. 2014, vol. 289, pp. 2207-2231. DOI: 10.1007/s11207-013-0445-y. Manuel R., Ferreira S.E.S., Potgieter M.S.Time-dependent modulation of cosmic rays in the heliosphere. Solar Phys. 2014, vol. 289, pp. 2207-2231. DOI: 10.1007/s11207-013-0445-y. Manuel R., Ferreira S.E.S., Potgieter M.S., Strauss R.D., Engelbrecht N.E. Time-dependent cosmic rays modula-tion. Adv. Space Res. 2011, vol. 47, pp. 1529-1537. DOI: 10.1016/j.asr.2010.12.007. Manuel R., Ferreira S.E.S., Potgieter M.S., Strauss R.D., Engelbrecht N.E. Time-dependent cosmic rays modula-tion. Adv. Space Res. 2011, vol. 47, pp. 1529-1537. DOI: 10.1016/j.asr.2010.12.007. Moraal H. Cosmic-ray modulation equations. Space Sci. Rev. 2013, vol. 176, pp. 299-319. DOI: 10.1007/s11214-011-9819-3. Moraal H. Cosmic-ray modulation equations. Space Sci. Rev. 2013, vol. 176, pp. 299-319. DOI: 10.1007/s11214-011-9819-3. Pacini A.A., Usoskin I.G. An unusual pattern of cosmic-ray modulation during solar cycles 23 and 24. Solar Phys. 2015, vol. 290, pp. 943-950. DOI: 10.1007/s11207-014-0645-0. Pacini A.A., Usoskin I.G. An unusual pattern of cosmic-ray modulation during solar cycles 23 and 24. Solar Phys. 2015, vol. 290, pp. 943-950. DOI: 10.1007/s11207-014-0645-0. Parker E.N. The passage of energetic charged particles through interplanetary space. Planet. Space Sci. 1965, vol. 13, pp. 9-49. DOI 10.1016/0032-0633(65)90131-5. Parker E.N. The passage of energetic charged particles through interplanetary space. Planet. Space Sci. 1965, vol. 13, pp. 9-49. DOI 10.1016/0032-0633(65)90131-5. Potgieter M.S., Burger R.A., Ferreira S.E.S. Modulation of cosmic rays in the heliosphere from solar minimum to maximum: a theoretical perspective. Space Sci. Rev. 2001, vol. 97, pp. 295-307. DOI: 10.1023/A:1011837303094. Potgieter M.S., Burger R.A., Ferreira S.E.S. Modulation of cosmic rays in the heliosphere from solar minimum to maximum: a theoretical perspective. Space Sci. Rev. 2001, vol. 97, pp. 295-307. DOI: 10.1023/A:1011837303094. Starodubtsev S.A., Grigoryev V.G. Cosmic rays and solar wind turbulence: peculiarities of the 23rd solar cycle. Geomagn. Aeron. 2011, vol. 51, pp. 1004-1009. DOI: 10.1134/ S001679321107022X. Starodubtsev S.A., Grigoryev V.G. Cosmic rays and solar wind turbulence: peculiarities of the 23rd solar cycle. Geomagn. Aeron. 2011, vol. 51, pp. 1004-1009. DOI: 10.1134/ S001679321107022X. Stozhkov Y.I., Svirzhevsky N.S., Bazilevskaya G.A., Kvashnin A.N., Makhmutov V.S., Svirzhevskaya A.K. Long-term (50 years) measurements of cosmic ray fluxes in the atmosphere. Adv. Space Res. 2009, vol. 44, pp. 1124-1137. DOI: 10.1016/ j.asr.2008.10.038. Stozhkov Y.I., Svirzhevsky N.S., Bazilevskaya G.A., Kvashnin A.N., Makhmutov V.S., Svirzhevskaya A.K. Long-term (50 years) measurements of cosmic ray fluxes in the atmosphere. Adv. Space Res. 2009, vol. 44, pp. 1124-1137. DOI: 10.1016/ j.asr.2008.10.038. Thomas S.R., Owens M.J., Lockwood M. The 22-year Hale cycle in cosmic ray flux: evidence for direct helio-spheric modulation. Solar Phys. 2014, vol. 289, pp. 407-421. DOI: 10.1007/s11207-013-0341-5. Thomas S.R., Owens M.J., Lockwood M. The 22-year Hale cycle in cosmic ray flux: evidence for direct helio-spheric modulation. Solar Phys. 2014, vol. 289, pp. 407-421. DOI: 10.1007/s11207-013-0341-5. Wibberenz G., Cane H.V., Richardson I.G., von Rosenvinge T.T. The influence of tilt angle and magnetic field variations on cosmic ray modulation. Space Sci. Rev. 2001, vol. 97, pp. 343-347. DOI: 10.1023/A:1011849605820. Wibberenz G., Cane H.V., Richardson I.G., von Rosenvinge T.T. The influence of tilt angle and magnetic field variations on cosmic ray modulation. Space Sci. Rev. 2001, vol. 97, pp. 343-347. DOI: 10.1023/A:1011849605820. Zhao L.-L., Qin G., Zhang M., Heber B. Modulation of galactic cosmic rays during the unusual solar minimum between cycles 23 and 24. J. Geophys. Res. 2014, vol. 119, pp. 1493-1506. DOI: 10.1002/2013JA019550. Zhao L.-L., Qin G., Zhang M., Heber B. Modulation of galactic cosmic rays during the unusual solar minimum between cycles 23 and 24. J. Geophys. Res. 2014, vol. 119, pp. 1493-1506. DOI: 10.1002/2013JA019550. http://hecrlab.ysn.ru http://hecrlab.ysn.ru