Is it possible to obtain polarized positrons during multiple Compton backscattering process?

If a beam of unpolarized positrons (which is considered as a sum of two fractions with opposite helicities) passes through an intense circular polarized laser radiation these fractions may be separated. For high laser flash intensity each positron will interact with $k_0\gg$1 laser photons subsequently (linear multiple compton scattering process). Due to difference in the compton cross-section for positrons polarized in opposite directions the mean final energy of each fraction will be different. It allows to get a polarized positron beam using the momentum selection (with some intensity loss). Estimations show the possibility to obtain a positron beam with 35% longitudinal polarization and 25% intensity from the initial one for focussed laser flash with total energy 5J and positron beam with energy 5 GeV.