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Giant solar flares are the most powerful phenomenon in the solar system, which can strongly affect various geospheres and technical systems in the near Earth's space or its surface. During the space era, only few events with a total energy of more than 1034 erg happened, and probably, only one of these ldquowas directedrdquo to the Earth (August 4, 1972). In this paper, we report on the first attempts to simulate in a laboratory both the initial (at the Sun) and final (near the Earth) stages of relevant interaction processes between the plasma flows and magnetic fields. By using laser-produced plasmas and intense magnetic dipole, we performed two types of simulation experiments: 1) on the interaction of ejected solar plasma flows with/in dipole magnetic field and 2) on the extreme (three fold) compression of the Earth's magnetopause by giant coronal mass ejections from the Sun. General physical conditions of these phenomena are briefly described, and the developed methods of laboratory simulation and numerical modeling of various explosive processes in collisionless space plasmas are discussed on the basis of relevant dimensionless criteria of the problems.