Numerical studies of the interplanetary "multiple magnetic clouds (Multi-MC)" are performed by a 2.5-dimensional ideal magnetohydrodynamic (MHD) model in the heliospheric meridional plane. Both slow MC1 and fast MC2 are initially emerged along the heliospheric equator, one after another with different time interval. The coupling of two MCs could be considered as the comprehensive interaction between two systems, each comprising of an MC body and its driven shock. The MC2-driven shock and MC2 body are successively involved into interaction with MC1 body. The momentum is transferred from MC2 to MC1. After the passage of MC2-driven shock front, magnetic field lines in MC1 medium previously compressed by MC2-driven shock are prevented from being restored by the MC2 body pushing. MC1 body undergoes the most violent compression from the ambient solar wind ahead, continuous penetration of MC2-driven shock through MC1 body, and persistent pushing of MC2 body at MC1 tail boundary. As the evolution proceeds, the MC1 body suffers from larger and larger compression, and its original vulnerable magnetic elasticity becomes stiffer and stiffer. So there exists a maximum compressibility of Multi-MC when the accumulated elasticity can balance the external compression. With respect to Multi-MC geoeffectiveness, the evolution stage is a dominant factor, whereas the collision intensity is a subordinate one. The magnetic elasticity, magnetic helicity of each MC, and compression between each other are the key physical factors for the formation, propagation, evolution, and resulting geoeffectiveness of interplanetary Multi-MC.
Deep Dive into Magnetohydrodynamic simulation of the interaction between two interplanetary magnetic clouds and its consequent geoeffectiveness.
Numerical studies of the interplanetary “multiple magnetic clouds (Multi-MC)” are performed by a 2.5-dimensional ideal magnetohydrodynamic (MHD) model in the heliospheric meridional plane. Both slow MC1 and fast MC2 are initially emerged along the heliospheric equator, one after another with different time interval. The coupling of two MCs could be considered as the comprehensive interaction between two systems, each comprising of an MC body and its driven shock. The MC2-driven shock and MC2 body are successively involved into interaction with MC1 body. The momentum is transferred from MC2 to MC1. After the passage of MC2-driven shock front, magnetic field lines in MC1 medium previously compressed by MC2-driven shock are prevented from being restored by the MC2 body pushing. MC1 body undergoes the most violent compression from the ambient solar wind ahead, continuous penetration of MC2-driven shock through MC1 body, and persistent pushing of MC2 body at MC1 tail boundary. As the evolut
Space weather refers to the conditions on the Sun and in the solar wind, magnetosphere, ionosphere, and thermosphere that can influence the performance and reliability of spaceborne and ground-based technological systems or can endanger human life or health, as defined in US National Space Weather Program Implementation Plan. A seamless forecasting system for Space weather lies on the comprehensive and in-depth understanding of the Sun-Earth system. The never-stopping tremendous efforts have been made by humankind since the space age of the 1950s. A great deal of the sophisticated observations beyond the Earth are now provided, with the launching of various spacecraft into deep space, such as Yohkoh, Geotail, Wind, SOHO, Ulysses, ACE, TRACE in the 1990s, and Cluster, RHESSI, SMEI, DS, Hinode (Solar B), STEREO in the 21st century. These spacecraft missions construct an indispensable backbone in the establishment of space weather prediction system. Meanwhile, many models have been or are being developed and applied to space weather forecasting by utilizing most measurements of the above spacecraft, such as ( 1) HAF (Hakamada-Akasofu-Fry) [Fry et al., 2001[Fry et al., , 2005]]; (2) STOA (Shock Time of Arrival) [Smart and Shea, 1985]; (3) ISPM (Interplanetary Shock Propagation Model) [Smith and Dryer , 1990]; (4) an ensemble of HAF, STOA and ISPM models [Dryer et al., 2001[Dryer et al., , 2004;;McKenna-Lawlor et al., 2006]; (5) SPM (Shock Propagation Model) [Feng and Zhao, 2006]; (6) SWMF (Space Weather Modeling Framework) [Toth et al., 2005]; (7) HHMS (Hybrid Heliospheric Modeling System) [Detman et al., 2006];
(8) a data-driven Magnetohydrodynamic (MHD) model of the University of Alabama in Huntsville [Wu et al., 2005a[Wu et al., , 2006a]]; (9) a 3D regional combination MHD model with in-
puts of the source surface self-consistent structure based on the observations of the solar magnetic field and K-coronal brightness [Shen et al., 2007]; (10) A merging model of SAIC MAS and ENLIL Heliospheric MHD Model [Odstrcil et al., 2004b]; (11) an HAF + 3-D
MHD model [Wu et al., 2005c[Wu et al., , 2006c[Wu et al., , 2007b, c], c], and so on. However, great challenges are still faced to improve the prediction performance of space weather, as human civilization is relying more and more on space environment [Baker , 2002;Fisher , 2004].
The interplanetary (IP) space is a pivot node of the solar-terrestrial transport chain.
Solar transients, e.g., shocks and coronal mass ejections (CMEs), propagate in it, interact with it, and cause many consequences in the geo-space. Magnetic clouds (MCs) are an important subset of interplanetary CMEs (ICMEs), occupying the fraction of nearly ∼ 100% (though with low statistics) at solar minimum and ∼ 15% at solar maximum [Richardson andCane, 2004, 2005], and have significant geoeffectiveness [Tsurutani et al., 1988;Gosling et al., 1991;Gonzalez et al., 1999;Wu and Lepping, 2002a, b;Wu et al., 2003Wu et al., , 2006b;;Huttunen et al., 2005]. The current intense study of MCs could be traced back to the pioneer work by Burlaga et al. [1981], who firstly defined an MC with three distinct characteristics of enhanced magnetic field strength, smooth rotation of magnetic field vector, and low proton temperature, and described it as a flux rope structure. An MC is widely thought to be the IP manifestation of a magnetic flux rope in the solar corona, which loses equilibrium and then escapes from the solar atmosphere into the IP space [Forbes et al., 2006], with its both ends still connecting to the solar surface [Larson et al., 1997].
It is very likely for solar transients to interact with each other on their way to the Earth, especially at solar maximum when the daily occurrence rate of CMEs is about 4.3 in aver- Some IP complicated structures were reported, such as complex ejecta [Burlaga et al., 2002], multiple MCs (Multi-MC) [Wang et al., 2002[Wang et al., , 2003a]], shock-penetrated MCs [Wang et al., 2003b;Berdichevsky et al., 2005;Collier et al., 2007], non-pressure-balanced “MC boundary layer” associated with magnetic reconnection [Wei et al., 2003a[Wei et al., , b, 2006]], ICMEs compressed by a following high-speed stream [Dal Lago et al., 2006], multiple shock interactions [Wu et al., 2005d[Wu et al., , 2006d[Wu et al., , 2007a]]. However, all space-borne instruments, except the heliospheric imagers onboard SMEI and STEREO, observe either the solar atmosphere within 30 solar radii by remote sensing, or the in-situ space by local detecting, or both. Thus, numerical simulations are necessary to understand the whole IP dynamics.
Below is an incomplete list of numerical studies of dynamical processes of CMEs/MCs and complex structures in the IP medium mentioned before: an individual CME/MC [Vandas et al., 1995[Vandas et al., , 1996[Vandas et al., , 2002;;Groth et al., 2000;Schmidt and Cargill , 2003;Odstrcil et al., 2003Odstrcil et al., , 2004aOdstrcil et al., , 2005;;Manchester et al., 2
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