The importance and actuality of the Geomagnetosphere’s research are based on following three factors: 1. The Geomagnetosphere is the nearest giant natural laboratory, where is possible by a lot of satellites and ground measurements investigate in details many different plasmas and energetic processes in space, caused finally by interaction of high kinetic energy solar wind plasmas and its perturbations (Interplanetary Coronal Mass Ejections – ICMEs, Interplanetary Shock Waves – ISWs, Interplanetary Interaction Regions – IIR) with frozen in Interplanetary Magnetic Fields – IMF with the rotated main geomagnetic field. This interaction leads to dynamic transformation magnetic fields in Geomagnetosphere, generation and trapping high energy particles (which can be called as Magnetospheric Cosmic Rays – MCR), generation of many types instabilities and electromagnetic radiations. These processes are in principle similar to processes in magnetospheres of other planets and their moons, in the atmosphere of the Sun and other stars, in interplanetary and in interstellar space, in many different astrophysical objects, i.e. this research is important basis for fundamental Space and Astrophysical science. 2. In the modern time the Technology, Economics, Navigation, TV, Internet, Radio-Connections, Military aspects, and the life of people on our planet are strong connected with the work of many satellites, moving inside the Geomagnetosphere. Different processes and MCR in the Geomagnetosphere influenced on the satellites work and often lead to satellite malfunctions up to full destroying work of their electronics – satellites became ‘dead’. The described research can be considered as basis for developing methods of forecasting dangerous situation for satellites on different orbits and to decrease the risk of satellite malfunctions and loosing, i.e. this research has important practical application. 3. The interaction of ICME, ISW, and IIR with Geomagnetosphere leads to generation big magnetic storms accompanied with Forbush decreases and precursory effects in Galactic Cosmic Ray (GCR) intensity. These magnetic storms are dangerous not only for satellites, but also on the Earth’s surface for technology, radio-connections, car accidents, people health (e.g., increasing frequency of infarct myocardial and brain strokes). Investigations of causes of magnetic storms can help to develop methods of their forecasting and decreasing the level of magnetic storms hazards. Therefore, the other practical application of this research is connected with the problem of space weather and space climate influence on the technology, radio-connections, navigation, transportation, and people health on the Earth in dependence of altitude and geomagnetic latitude.
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