High Energy Polarized e+e- Beams

Recently, the wide discussion about Higgs-factory design again returns to problem of high energy polarized electrons and positrons. It's good known the radiative beam polarization at LEP-collider. It was obtained after spin resonance suppression at Z(0) pick, but didn't appear at energies above 70 GeV due to an enhancement of unavoidable depolarization effects. We examine in this paper various ideas for radiative polarization at TLEP/FCC-ee and formulate some estimates for the polarization buildup time and the asymptotic polarization. Using wigglers, a useful degree of polarization (for energy calibration), with a time constant of about 1 h, may be possible up to the threshold of W pair production. At higher energies such as the threshold of Higgs production, attaining a useful level of polarization may be difficult in a planar ring. With Siberian Snakes, wigglers and some imagination, polarization of reasonable magnitude, with a reasonable time constant (of not more than about 1 h), may be achievable at very high energies.