For a number of physical studies which are planned to be made with the next
generation colliders, it is necessary to use polarized beams of both electrons
and positrons. The problem of producing and acceleration of polarized electrons
may be considered to be solved, but the existing approaches to create polarized
positron beams do not ensure the parameters required. This work proposes a new
approach to produce polarized positron beams, which is based on the process of
multiple Compton backscattering of unpolarized ultrarelativistic positrons in
the field of intense circularly polarized laser wave
