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Presently large efforts are conducted towards the development of highly brilliant gamma beams via Compton back scattering of photons from a high-brilliance electron beam, either on the basis of a normal-conducting electron linac or a (superconducting ) Energy Recovery Linac (ERL). Particularly ERLs provide an extremely brilliant electron beam, thus enabling to generate highest-quality gamma beams. A 2.5 MeV gamma beam with an envisaged intensity of 10^15 s^-1, as ultimately envisaged for an ERL-based gamma-beam facility, narrow band width (10^-3), and extremely low emittance (10^-4 mm^2 mrad^2) offers the possibility to produce a high-intensity bright polarized positron beam. Pair production in a face-on irradiated W converter foil (200 micron thick, 10 mm long) would lead to the emission of 2 x 10^13 (fast) positrons per second, which is four orders of magnitude higher compared to strong radioactive ^22Na sources conventionally used in the laboratory.Using a stack of converter foils and subsequent positron moderation, a high-intensity low-energy beam of moderated positrons can be produced. Two different source setups are presented: a high-brightness positron beam with a diameter as low as 0.2 mm, and a high-intensity beam of 3 x 10^11 moderated positrons per second. Hence, profiting from an improved moderation efficiency, the envisaged positron intensity would exceed that of present high-intensity positron sources by a factor of 100.
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