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If a beam of unpolarized positrons (which is considered as a sum of twofractions with opposite helicities) passes through an intense circularpolarized laser radiation these fractions may be separated. For high laserflash intensity each positron will interact with $k_0\gg$1 laser photonssubsequently (linear multiple compton scattering process). Due to difference inthe compton cross-section for positrons polarized in opposite directions themean final energy of each fraction will be different. It allows to get apolarized positron beam using the momentum selection (with some intensityloss). Estimations show the possibility to obtain a positron beam with 35%longitudinal polarization and 25% intensity from the initial one for focussedlaser flash with total energy 5J and positron beam with energy 5 GeV.Comment: 9 pages, 3 figures. Presented at 28th ICFA Workshop "Quantum Aspects  of Beam Physics", January 7-11, Hiroshima, Japa

IS IT POSSIBLE TO OBTAIN POLARIZED POSITRONS DURING MULTIPLE COMPTON BACKSCATTERING PROCESS?