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Interaction phenomena of intense ion- and laser radiation with matter have a large range of application in different fields of science, extending from basic research of plasma properties to applications in energy science, especially in inertial fusion. The heavy ion synchrotron at GSI now routinely delivers intense uranium beams that deposit about 1 kJ/g of specific energy in solid matter, e.g. solid lead. Our simulations show that the new accelerator complex FAIR (Facility for Antiproton and Ion Research) at GSI as well as beams from the CERN large hadron collider (LHC) will vastly extend the accessible parameter range for high energy density states. A natural example of hot dense plasma is provided by our neighbouring star the sun, and allows a deep insight into the physics of fusion, the properties of matter at high energy density, and is moreover an excellent laboratory for astroparticle physics. As such the sun's interior plasma can even be used to probe the existence of novel particles and dark matter candidates. We present an overview on recent results and developments of dense plasma physics addressed with heavy ion and laser beams combined with accelerator- and nuclear physics technology. [ABSTRACT FROM AUTHOR]