The problems of required conditions and possible consequences of the super -compression (up to R m ∼ 3R E ) of the Earth's magnetosphere by giant CME are investigated by the methods of laboratory and computer simulations. A useful relation between an expected magnetopause location R * m and the kinetic plasma energy E 0 of spherical plasma cloud (exploded at distance R 0 ) was obtained R * m /R 0 ≈ 0, 75/ae 1/6 and tested by MHDmodel of Nikitin & Ponomarenko (1994) with the using their main energetic criterion of the problem ae = 3E 0 R 3 0 /µ 2 (for magnetic moment µ of point obstacle in vacuum). This relation could describe rather well an observed compression (R m ∼ 5−6R E for CME with energy 10 32 ergs and effective value E 0 ∼ 10 33 ergs, into 4π) and predicts R * m 3R E in a probable case of Mega Flare with the total energy release ∼ 10 34 ergs and possible E 0 ∼ 5 · 10 34 ergs according to Kane et al. (1995) and Tsurutani et al. (2003). Some most important features of the formation such Artificial Magnetosphere (AM) structure and its possible influence onto various geospheres media (or technosphere areas) could be successfully studied in the simulative experiments at KI-1 facility of ILP with Laser Plasmas (LP) of E 0 up to kJ and dipole µ ∼ 10 7 G · cm 3 as was shown by Ponomarenko et al. (2001) andZakharov (2003). But the main problem of such planned AMEX experiment (at ae ∼ 50 for R 0 = 75 cm) is the influence of finite value of ion magnetization ε m = R L /R * m based on the ion Larmor radius R L = mcV 0 /ezB d , where V 0 ∼ 100 km/s is the expansion velocity of LP and B d is the initial dipole field at the point R * m . Of coarse, ε m 1 in a real space conditions (excluding cases of Mercury or asteroids, explored by Omidi et al. (2004)) while in the laboratory to fulfill both need constrains ae 1 and ε m 1 we should use a thermonuclear plasma and devices. To overcome this problem we did a 3D/PIC -calculations by hybrid model of Kyushu University, described by Muranaka et al. (2001), to find out a critical value of ε * m (≈ 0, 2 −0, 3), which need for MHD -like interaction of exploding plasmas with magnetic dipole.We have used the MHD -model of plasma dynamics based on the approach of Raizer (1963) for deceleration of diamagnetic plasma boundary in vacuum magnetic field B d that includes two (both local) relations: for pressure balance 2nm (W − V ) 2 cos 2 χ = kB 2 d /8π at plasma boundary R and for decrease of its energy 2WẆ + kB 2 d cos χV R 2 /0, 6M = 0 (for V = dR/dt and W -velocity of plasma ions). The latter one, according to Nikitin & Ponomarenko (1994), could be obtained via usual expression for total plasma energy E(t) = E 0 − A(t), where A(t) = (1/8π) s t kB 2 d cos χ V · d S dt is its work against B d . Here χ is the angle between R and local normal to boundary, while a constant k ∼ 1 ÷ 2 characterizes a field amplification near the boundary.
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