Generation of circularly polarized photons for a linear collider polarized positron source

Various methods of obtaining longitudinally polarized positrons for future linear col-liders are reviewed. Special attention is paid to the schemes using circularly polarized high-energy photons for positron production. Most effectively such photons are obtained from electrons passing through a helical undulator or colliding with a circularly polarized laser wave. Spectrum and polarization of radiation emitted during helical motion of electrons are considered in detail. A new simple presentation of known formulas is used to account for the influence of the wave intensity, of the electron-beam angular divergence, of the collimation of radiation, and of the lateral and temporal profiles of the laser bunch on the radiation properties.