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Patrick Janot edited Transverse.tex
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Transverse beam polarization builds up naturally in a storage ring by the Sokolov-Ternov effect. A transverse polarization in excess of 5-10\%, which was obtained for beam energies 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 control of 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 20\% polarization at a beam energy of 65 GeV for typical machine misalignments~\cite{1206.2913}.
At
the Z peak, LEP, the natural polarization building time amounted to five hours at
LEP. It the Z peak. This time is predicted to increase like the third power of the ring bending
radius and radius, hence will reach
the unpractical value of 150 hours at
TLEP, which is unpractical. TLEP. Asymmetric "polarization" wigglers were in use in LEP, and their effect on
beam energy spread, the polarization time and
the beam energy spread, as well as other depolarizing
effects sources, is analyzed in Ref.~\cite{cite:Blondel-Jowett-LEP606}. Such polarization wigglers could be used to reduce the polarization
time, but care should be taken not to increase time at TLEP, while keeping the energy spread
excessively. to a reasonable value. As an example, the use of the LEP polarization wigglers in TLEP with a central pole field of
0.6 T 0.6~T would reduce the polarization time to 18 hours
at the Z peak, while keeping the beam energy spread below
48 MeV 48~MeV -- a value at which polarization could routinely be obtained in LEP at
55GeV. with a beam energy of 55~GeV. In these conditions, a level of polarization sufficient to perform the resonant depolarization could be reached in a couple
hours, following which energy hours. Energy calibrations would
then be performed every
10 ten minutes if at least
12 twelve bunches of
each sign electrons and of positrons were kept "single" in the machine.
At 80 GeV For a beam energy
of 80~GeV, the polarization time
is would be 9 hours in TLEP, and the use of wigglers should not be necessary.