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In chapter 2.2 it was shown that due to synchrotron radiation an electron beam in a storage ring will polarize with a certain characteristic time constant
to the maximum level of polarization
. In chapter 2.4 depolarizing mechanisms were introduced. It was also mentioned that field errors had less influence on the level of polarization in low-energy machines like SLS, thus high polarization levels should be achievable at SLS. In this section a simple model for the equilibrium polarization build-up at SLS will be discussed.
Polarization build-up at SLS is described by equation 5:
![\begin{displaymath}
P_{pol}(t)=P_{ST}\left(1-\exp\left(-\frac{t}{\tau_{p}}\right)\right)
\end{displaymath}](img104.gif) |
(38) |
with
s at the nominal energy of 2.4 GeV. Depolarizing effects are expected to show an exponential decay of the polarization:
![\begin{displaymath}
P_{depol}(t)=P_{ST}\exp\left(-\frac{t}{\tau_{d}}\right)
\end{displaymath}](img106.gif) |
(39) |
The equilibrium state between the polarization build-up due to spin-flip radiation and depolarizing effects due to photon emission is described again by an exponential build-up:
![\begin{displaymath}
P_{tot}(t)=P_{eff}\left(1-\exp\left(-\frac{t}{\tau_{eff}}\right)\right)
\end{displaymath}](img107.gif) |
(40) |
where
![\begin{displaymath}
P_{eff}=P_{ST}\frac{\tau_{d}}{\tau_{p}+\tau_{d}} \qquad \tex...
... \qquad \frac{1}{\tau_{eff}}=\frac{1}{\tau_p}+\frac{1}{\tau_d}
\end{displaymath}](img108.gif) |
(41) |
Expecting an equilibrium polarization level of 80% at SLS one can derive the characteristic depolarization time as well as the equilibrium polarization build-up time from equation 41. In the example shown in figure 5 the following values have been used:
Figure 5:
A model for the effective polarization build-up in the SLS storage ring. The time interval shown is ten hours which corresponds to typical beam lifetimes.
It is important to note that depolarizing effects have a very long characteristic time
compared to polarization build-up
(in this situation) leading to high polarization values.
Next: Experimental Approach and Equipment
Up: Introduction
Previous: Beam Excitation and Resonances
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Simon Leemann
2002-03-15