The results of contemporary investigations of cumulative phenomena due to the collision of projectiles laser-accelerated up to the velocities significantly higher than the sound velocity in solids are reviewed. The discussion is focused on the applications directed on the development of a concept of fast ignition by projectile impact and the laboratory modeling of astrophysical phenomena. Low-entropy acceleration of a projectile in a dense state up to ‘thermonuclear’ velocity of the order of 1000 km/s is grounded. The parameters of extreme matter state induced by laser-accelerated projectiles collision, namely, energy flows, pressure and temperature, spontaneous magnetic field and thermonuclear neutron yield are discussed. Astrophysical phenomena due to collision of cosmic objects such as a creation of a crater by meteorite's impact, as well as the emerging of a shock wave to a star surface, and formation of jets, ionization and emission waves are considered.
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