is one of the most interesting experimental schemes proposed for the study of equation of state and transport properties of high energy density matter in the framework of the FAIR (Facility for Antiproton and Ion Research) project . This experiment involves a cylindrical implosion of a thick shell of Au or Pb driven by a heavy ion beam with annular focal spot. The region of the shell heated by the ion beam (the absorber) expands accelerating the pusher layer that surrounds the sample in the internal axial region. During this process in which the hot and less dense absorber accelerates the denser pusher, the conditions for the growing of the Rayleigh –Taylor instability (RTI) arise. Therefore, this is an issue of possible concern that is presently under investigation. The classical RTI is a very well known phenomenon that ha
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