The forthcoming Facility for Antiprotons and Ion Research (FAIR) at Darmstadt, is going to be a unique accelerator facility that will deliver high quality, strongly bunched, well focused, intense beams of heavy ions that will lead to unprecedented specific power deposition in solid matter. This will generate macroscopic samples of High Energy Density (HED) matter with fairly uniform physical conditions. These samples can be used to study the thermophysical and transport properties of HED matter. Extensive theoretical work has been carried out over the past decade to design numerous dedicated experiments to study HED physics at the FAIR, which has provided the basis for the HEDgeHOB (High Energy Density Matter Generated by Heavy Ion Beams) scientific proposal. This work is still in progress as the feasibility studies for more experimental schemes are being carried out.Another, very important research area that will benefit tremendously from the FAIR facility, is the production of radioactive beams. A superconducting fragment separator, Super-FRS is being designed for the production and separation of rare radioactive isotopes. Unlike the HED targets, the Super-FRS production target should not be destroyed or damaged by the beam, but should remain intact during the long experimental campaign. However, the high level of specific power deposited in the production target by the high intensity ion beam at FAIR, could cause serious problems to the target survival. These HED issues related to the Super-FRS production target are also discussed in the present paper.