An overview of non-Liouvillian mechanisms useful for application to existing high-energy accelerators is presented. An example under discussion for experiments on high-energy density in matter with intense heavy-ion beams delivered by the CERN accelerator complex is described. A possible scheme has been found for accumulation of relativistic ion beams of gamma 6–10 with total energy ca. 10 kJ and pulse duration ca. 4 ns using a combination of PS and SPS synchrotron rings. Taking into account only electromagnetic interactions of the projectiles with solid matter gives a level of specific deposition power more than 100 TW/g.
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