Patrick Janot edited Transverse.tex  over 10 years ago

Commit id: af81835f4c2907c253311261c387da8d03bf4e73

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Transverse beam polarization builds up naturally in a storage ring by the Sokolov-Telnov effect. A transverse polarization in excess of 5-10\%, which was obtained up to 61 GeV per beam at LEP, is sufficient for beam energy calibration purposes. It is generally accepted that this upper limit is determined by the energy spread, which becomes commensurate with the fractional part of the spin-tune $\nu_s = E_{\rm beam} {\rm [GeV]} /0.440665$. Given that the energy spread scales as $E^2_{\rm beam} / \sqrt{\rho}$ (where $\rho$ is the ring bending radius), it is expected that beam polarization sufficient for energy calibration should be readily available up to and above the WW threshold (i.e., 81 GeV per beam) at TLEP.   A new machine with a better handle on the orbit should, however, be able to increase this limit. For example, a full 3D spin tracking simulation of the electron machine of the Large Hadron-electron collider (LHeC) project in the 27 km LHC tunnel predicts in a 20\% polarization at a beam energy of 65 GeV for typical machine misalignment~\cite{1206.2913}. It is to be noted that polarization wigglers, such as those described for LEP in Ref.~\cite{cite:Blondel-Jowett-LEP606}, would be mandatory for TLEP to efficiently establish such levels of polarization. Indeed, the natural polarization building time amounted to five hours at LEP, and is predicted to increase like the third power of the ring bending radius. Without polarization wigglers, the natural polarization building time would be nearly 150 hours. The impact of the polarization wigglers on the maximum achievable luminosity will need to be studied.