基于一维随机输运模型的银河宇宙射线调制研究
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摘要
本文运用随机微分方程方法,求解宇宙射线在日球层内的一维输运方程,基于太阳活动对银河宇宙射线含时扩散系数κrr的影响,计算O~(8+)粒子在地球位置的能谱,模拟了太阳活动对银河宇宙射线的调制效应.其中包括,利用κrr余弦含时变化,模拟了宇宙射线的11年周期及其滞后效应;利用κrr的线性变化函数,模拟了一次福布斯下降事件中的粒子通量曲线.
In this paper,the one-dimensional transport equation of galactic cosmic rays( GCRs) in the heliosphere was solved by the stochastic differential method. Based on the time-dependent diffusion coefficient κrrof GCRs,the energy spectrums of O8 +near the Eearth were calculated,for the study of the solar modulation of GCRs. Using the time-dependent κrrof cosine function,the 11 years periodicity and the hysteresis effect of GCRs were simulated.Based on a linear response function of κrr,the particle flux profile of a Forbush Decrease( FD) event was simulated.
In this paper,the one-dimensional transport equation of galactic cosmic rays( GCRs) in the heliosphere was solved by the stochastic differential method. Based on the time-dependent diffusion coefficient κrrof GCRs,the energy spectrums of O8 +near the Eearth were calculated,for the study of the solar modulation of GCRs. Using the time-dependent κrrof cosine function,the 11 years periodicity and the hysteresis effect of GCRs were simulated.Based on a linear response function of κrr,the particle flux profile of a Forbush Decrease( FD) event was simulated.
引文
Belov A,Abunin A,Abunina M,et al.2014.Coronal mass ejection and non-recurrent forbush decreases[J].Solar Phys.,289(10)3949-3960,doi:10.1007/s11207-014-0534-6.
Blasi P.2013.The origin of galactic cosmic rays[J].Astron.Astrophy Rev.,21(1):1-73.
Bobik P,Boella G,Boschini M J,et al.2012.Systematic investigatio of solar modulation of galactic protons for solar cycle 23 using a Monte Carlo approach with particle drift effects and latitudinal dependence[J].Astrophys.J.,745(2):132.
Bothmer V,Daglis I A.2007.Space Weather:Physics and Effects[M].Berlin:Springer.
Carslaw K S,Harrison R G,Kirkby J.2002.Cosmic rays,clouds,and climate[J].Science,298(5599):1732-1737.
Chin P P,Lee M A.1986.A perturbation approach to cosmic-ray transients in interplanetary space[J].J.Geophys.Res.,91(A3):2903-2913,doi:10.1029/JA091iA 03p02903.
Fisk L A.1971.Solar modulation of galactic cosmic rays,2[J].J.Geophys.Res.,76(1):221-226,doi:10.1029/JA076i001p00221.
Fujii Z,McD onald F B.2005.The spatial distribution of galactic and anomalous cosmic rays in the heliosphere at solar minimum[J].Adv.Space Res.,35(4):611-616.
Gil A,Iskra K,Modzelewska R,et al.2005.On the 27-day variations of the galactic cosmic ray anisotropy and intensity for different periods of solar magnetic cycle[J].Adv.Space Res.,35(4):687-690.
Gleeson L J,Axford W I.1968.Solar modulation of galactic cosmic rays[J].Astrophys.J.,154:1011,doi:10.1086/149822.
Gloeckler G,Jokipii J R.1967.Solar modulation and the energy density of galactic cosmic rays[J].Astrophys.J.,148:L41,doi:10.1086/180010.
Hattingh M,Burger R A,Potgieter M S,et al.1997.Cosmic ray latitudinal effects predicted by a three-dimensional drift model[J].Adv.Space Res.,19(6):839-896.
Jokipii J R.1986.Particle acceleration at a termination shock.I.Application to the solar wind and the anomalous component[J].J.Geophys.Res.,91(A3):2929-2932.
Jordan A P,Spence H E,Blake J B,et al.2011.Revisiting two-step Forbush decreases[J].J.Geophys.Res.,116(A11):A11103,doi:10.1029/2011JA016791.
Kane R P.2011.Hysteresis of cosmic rays with respect to sunspot numbers during the recent sunspot minimum[J].Solar Phys.,269(2):451-454,doi:10.1007/s11207-011-9712-y.
Kota J,Jokipii J R.1983.Effects of drift on the transport of cosmic rays.VI-A three-dimensional model including diffusion[J].Astrophys.J.,265:573-581,doi:10.1086/160701.
Le G M.2002.Precursor characteristics research of galactic cosmic ray intensity changes before geomagnetic storm(in Chinese)[Ph.D.thesis].Beijing:Space Science and Applied Research Center of Chinese Academy of Sciences.
Le Roux J L,Potgieter M S.1990.A time-dependent drift model for the long-term modulation of cosmic rays with special reference to asymmetries with respect to the solar minimum of 1987[J].Astrophys.J.,361:275-282.
Le Roux J L,Potgieter M S.1995.The simulation of complete 11 and 12year modulation cycles for cosmic rays in the heliosphere using a drift model with global merged interaction regions[J].Astrophys.J.,442(2):847-851,doi:10.1086/175487.
Levy E H.1976.Interplanetary magnetic-field structure[J].Nature,261(5559):394-395,doi:10.1038/2613940.
Li G,Webb G M,Le Roux J A,et al.2007.Time dependent Solar Modulation of GCRs using a Monte-Carlo simulation[J].Numerical Modeling of Space Plasma Flows,385:31-37.
Li G,webb G M,Le Roux J A,et al.2009.Modeling the transport of cosmic ray due to long term variation using a stochastic differential method[C].//Proceedings of the 31st ICRC.Huntsville,AL,USA:ICRC.
Lockwood J A,Webber W R.2005.Intensities of galactic cosmic rays of~1.5 GV rigidity at Earth versus the heliospheric current sheet tilt[J].J.Geophys.Res.,110(A4):A04102,doi:10.1029/2004JA010880.
Luo X,Zhang M,Feng X S,et al.2013.Investigation of the transient cosmic ray decreases observed by voyagers in 2007:A numerical approach[J].J.Geophys.Res.,118(12):7517-7524,doi:10.1002/2013JA019218.
Luo X,Zhang M,Rassoul H K,et al.2011.Cosmic-Ray modulation by the global merged interaction region in the heliosheath[J].Astrophys.J.,730(1),doi:10.1088/0004-637x/730/1/13.
Moraal H,Potgieter M S,Stoker P H,et al.1989.Neutron monitor latitude survey of cosmic-ray intensity during the 1986/1987 solar minimum[J].J.Geophys.Res.,94(A2):1459-1464,doi:10.1029/JA094iA 02p01459.
Nagashima K,Fujimoto K,Sakakibara S,et al.1992.Local-timedependent pre-IMF-shock decrease and post-shock increase of cosmic rays,produced respectively by their IMF-collimated outward and inward flows across the shock responsible for forbush decrease[J].Planet.Space Sci.,40(8):1109-1137,doi:10.1016/0032-0633(92)90040-U.
O’gallagher J J.1975.Time-dependent diffusion-convection model for long-term modulation of cosmic-rays[J].Astrophys.J.,197:495-507.
Parker E N.1965.The passage of energetic charged particles through interplanetary space[J].Planet.Space Sci.,13(1):9-49.
Patra S N,Bhattacharya G,Panja S C,et al.2014.A low freeparameter stochastic model of daily Forbush decrease indices[J].J.Atmos.Sol.-Terr.Phy.,107:30-35,doi:10.1016/j.jastp.2013.09.008.
Potgieter M S.2013.Solar Modulation of Cosmic Rays[J].Living Rev.Solar Phys.,10(3):1-66.
Potgieter M S,Moraal H.1988.Acceleration of cosmic rays in the solar wind termination shock.A steady state technique in a spherically symmetric model[J].Astrophys.J.,330:445-455.
Rossi B.1964.Cosmic Rays:McG raw-Hill Paperbacks in Physics[M].New York:McG raw-Hill.
Schuss Z.1980.Theory and Applications of Stochastic Differential Equations[M].New York:John Wiley.
Singh Y P,Badruddin.2007.Effects of interplanetary magnetic clouds,interaction regions,and high-speed streams on the transient modulation of galactic cosmic rays[J].J.Geophys.Res.,112(A2):A02101,doi:10.1029/2006JA011780.
Strauss R D,Potgieter M S,Büsching I,et al.2012.Modelling heliospheric current sheet drift in stochastic cosmic ray transport models[J].Astrophys.Space Sci.,339(2):223-236.
Wawrzynczak A,Alania M V.2008.Modeling of the recurrent Forbush effect of the galactic cosmic ray intensity and comparison with the experimental data[J].Adv.Space Res.,41(2):325-334.
Webb G M.1981.Time-dependent Green’s functions of the cosmic ray equation of transport[J].Astrophys.Space Sci.,80(2):323-335,doi:10.1007/BF00652933.
Wiedenbeck M E,Davis A J,Leske R A,et al.2005.The level of solar modulation of galactic cosmic rays from 1997 to 2005 as derived from ACE measurements of elemental energy spectra[C].29th International Cosmic Ray Conference Pune.Amsterdam,Netherlands,101-104.
Zank G P,Matthaeus W H,Smith C W.1996.Evolution of turbulent magnetic fluctuation power with heliospheric distance[J].J.Geophys.Res.,101(A8):17093-17107.
Zhang M.1999.A Markov stochastic process theory of cosmic-ray modulation[J].Astrophys.J.,513(1):409-420.
乐贵明.2002.地磁暴前银河宇宙线强度变化的先兆特征研究[博士论文].北京:中国科学院研究生院(空间科学与应用研究中心).
Blasi P.2013.The origin of galactic cosmic rays[J].Astron.Astrophy Rev.,21(1):1-73.
Bobik P,Boella G,Boschini M J,et al.2012.Systematic investigatio of solar modulation of galactic protons for solar cycle 23 using a Monte Carlo approach with particle drift effects and latitudinal dependence[J].Astrophys.J.,745(2):132.
Bothmer V,Daglis I A.2007.Space Weather:Physics and Effects[M].Berlin:Springer.
Carslaw K S,Harrison R G,Kirkby J.2002.Cosmic rays,clouds,and climate[J].Science,298(5599):1732-1737.
Chin P P,Lee M A.1986.A perturbation approach to cosmic-ray transients in interplanetary space[J].J.Geophys.Res.,91(A3):2903-2913,doi:10.1029/JA091iA 03p02903.
Fisk L A.1971.Solar modulation of galactic cosmic rays,2[J].J.Geophys.Res.,76(1):221-226,doi:10.1029/JA076i001p00221.
Fujii Z,McD onald F B.2005.The spatial distribution of galactic and anomalous cosmic rays in the heliosphere at solar minimum[J].Adv.Space Res.,35(4):611-616.
Gil A,Iskra K,Modzelewska R,et al.2005.On the 27-day variations of the galactic cosmic ray anisotropy and intensity for different periods of solar magnetic cycle[J].Adv.Space Res.,35(4):687-690.
Gleeson L J,Axford W I.1968.Solar modulation of galactic cosmic rays[J].Astrophys.J.,154:1011,doi:10.1086/149822.
Gloeckler G,Jokipii J R.1967.Solar modulation and the energy density of galactic cosmic rays[J].Astrophys.J.,148:L41,doi:10.1086/180010.
Hattingh M,Burger R A,Potgieter M S,et al.1997.Cosmic ray latitudinal effects predicted by a three-dimensional drift model[J].Adv.Space Res.,19(6):839-896.
Jokipii J R.1986.Particle acceleration at a termination shock.I.Application to the solar wind and the anomalous component[J].J.Geophys.Res.,91(A3):2929-2932.
Jordan A P,Spence H E,Blake J B,et al.2011.Revisiting two-step Forbush decreases[J].J.Geophys.Res.,116(A11):A11103,doi:10.1029/2011JA016791.
Kane R P.2011.Hysteresis of cosmic rays with respect to sunspot numbers during the recent sunspot minimum[J].Solar Phys.,269(2):451-454,doi:10.1007/s11207-011-9712-y.
Kota J,Jokipii J R.1983.Effects of drift on the transport of cosmic rays.VI-A three-dimensional model including diffusion[J].Astrophys.J.,265:573-581,doi:10.1086/160701.
Le G M.2002.Precursor characteristics research of galactic cosmic ray intensity changes before geomagnetic storm(in Chinese)[Ph.D.thesis].Beijing:Space Science and Applied Research Center of Chinese Academy of Sciences.
Le Roux J L,Potgieter M S.1990.A time-dependent drift model for the long-term modulation of cosmic rays with special reference to asymmetries with respect to the solar minimum of 1987[J].Astrophys.J.,361:275-282.
Le Roux J L,Potgieter M S.1995.The simulation of complete 11 and 12year modulation cycles for cosmic rays in the heliosphere using a drift model with global merged interaction regions[J].Astrophys.J.,442(2):847-851,doi:10.1086/175487.
Levy E H.1976.Interplanetary magnetic-field structure[J].Nature,261(5559):394-395,doi:10.1038/2613940.
Li G,Webb G M,Le Roux J A,et al.2007.Time dependent Solar Modulation of GCRs using a Monte-Carlo simulation[J].Numerical Modeling of Space Plasma Flows,385:31-37.
Li G,webb G M,Le Roux J A,et al.2009.Modeling the transport of cosmic ray due to long term variation using a stochastic differential method[C].//Proceedings of the 31st ICRC.Huntsville,AL,USA:ICRC.
Lockwood J A,Webber W R.2005.Intensities of galactic cosmic rays of~1.5 GV rigidity at Earth versus the heliospheric current sheet tilt[J].J.Geophys.Res.,110(A4):A04102,doi:10.1029/2004JA010880.
Luo X,Zhang M,Feng X S,et al.2013.Investigation of the transient cosmic ray decreases observed by voyagers in 2007:A numerical approach[J].J.Geophys.Res.,118(12):7517-7524,doi:10.1002/2013JA019218.
Luo X,Zhang M,Rassoul H K,et al.2011.Cosmic-Ray modulation by the global merged interaction region in the heliosheath[J].Astrophys.J.,730(1),doi:10.1088/0004-637x/730/1/13.
Moraal H,Potgieter M S,Stoker P H,et al.1989.Neutron monitor latitude survey of cosmic-ray intensity during the 1986/1987 solar minimum[J].J.Geophys.Res.,94(A2):1459-1464,doi:10.1029/JA094iA 02p01459.
Nagashima K,Fujimoto K,Sakakibara S,et al.1992.Local-timedependent pre-IMF-shock decrease and post-shock increase of cosmic rays,produced respectively by their IMF-collimated outward and inward flows across the shock responsible for forbush decrease[J].Planet.Space Sci.,40(8):1109-1137,doi:10.1016/0032-0633(92)90040-U.
O’gallagher J J.1975.Time-dependent diffusion-convection model for long-term modulation of cosmic-rays[J].Astrophys.J.,197:495-507.
Parker E N.1965.The passage of energetic charged particles through interplanetary space[J].Planet.Space Sci.,13(1):9-49.
Patra S N,Bhattacharya G,Panja S C,et al.2014.A low freeparameter stochastic model of daily Forbush decrease indices[J].J.Atmos.Sol.-Terr.Phy.,107:30-35,doi:10.1016/j.jastp.2013.09.008.
Potgieter M S.2013.Solar Modulation of Cosmic Rays[J].Living Rev.Solar Phys.,10(3):1-66.
Potgieter M S,Moraal H.1988.Acceleration of cosmic rays in the solar wind termination shock.A steady state technique in a spherically symmetric model[J].Astrophys.J.,330:445-455.
Rossi B.1964.Cosmic Rays:McG raw-Hill Paperbacks in Physics[M].New York:McG raw-Hill.
Schuss Z.1980.Theory and Applications of Stochastic Differential Equations[M].New York:John Wiley.
Singh Y P,Badruddin.2007.Effects of interplanetary magnetic clouds,interaction regions,and high-speed streams on the transient modulation of galactic cosmic rays[J].J.Geophys.Res.,112(A2):A02101,doi:10.1029/2006JA011780.
Strauss R D,Potgieter M S,Büsching I,et al.2012.Modelling heliospheric current sheet drift in stochastic cosmic ray transport models[J].Astrophys.Space Sci.,339(2):223-236.
Wawrzynczak A,Alania M V.2008.Modeling of the recurrent Forbush effect of the galactic cosmic ray intensity and comparison with the experimental data[J].Adv.Space Res.,41(2):325-334.
Webb G M.1981.Time-dependent Green’s functions of the cosmic ray equation of transport[J].Astrophys.Space Sci.,80(2):323-335,doi:10.1007/BF00652933.
Wiedenbeck M E,Davis A J,Leske R A,et al.2005.The level of solar modulation of galactic cosmic rays from 1997 to 2005 as derived from ACE measurements of elemental energy spectra[C].29th International Cosmic Ray Conference Pune.Amsterdam,Netherlands,101-104.
Zank G P,Matthaeus W H,Smith C W.1996.Evolution of turbulent magnetic fluctuation power with heliospheric distance[J].J.Geophys.Res.,101(A8):17093-17107.
Zhang M.1999.A Markov stochastic process theory of cosmic-ray modulation[J].Astrophys.J.,513(1):409-420.
乐贵明.2002.地磁暴前银河宇宙线强度变化的先兆特征研究[博士论文].北京:中国科学院研究生院(空间科学与应用研究中心).
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