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\subsubsection{Motivation}  Polarized beams are useful for several purposes in $\epem$ storage rings. Transverse polarization was used in single beams at LEP for beam energy calibration with 0.1 MeV intrinsic precision~\cite{ement_of_the_W_boson_mass_2005}. This ability to perform energy calibrations is unique to circular machines, and the exquisite precision of the method is essential for the precision measurements of the Z mass and width, and of the W mass. Longitudinal polarization was used at SLC in collisions for the measurement of the left-right asymmetry at the Z pole, $\ALR$, with a 1.5\% relative precision, precision~\cite{doi:10.1103/PhysRevLett.84.5945},  which in turn allowed a determination of the weak mixing angle with an accuracy similar to that of the best LEP unpolarized measurements. It is therefore of great interest to establish both transverse and longitudinal polarizations with TLEP, and be able to maintain the latter in collisions at the Z pole.