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Intense ion beams from accelerators are now available to generate high energy density matter and to study astrophysical phenomena in the laboratory under controlled and reproducible conditions. A detailed understanding of interaction phenomena of intense ion- and laser radiation with matter is important for a large number of applications in different fields of science, extending from basic research of plasma properties to application in energy science and the investigation of processes occurring in stellar atmospheres or even in the interior of stars and planets. Energy loss processes of heavy ions in plasma and cold matter are important for the generation of high energy density states in general and especially in the hot dense plasma of an inertial fusion target. Of special interest are phase transitions and the associated time scales when matter passes the warm dense matter regime of the phase diagram at high density but relatively low temperature. We present an overview on recent results and developments of beam plasma, and beam matter interaction processes studied with heavy ion beams and laser beams combined with accelerator and nuclear physics technology. 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 with a combination of equipment and methods from accelerator technology and high resolution plasma spectroscopy. [ABSTRACT FROM AUTHOR]