next up previous contents
Next: Experimental Approach and Equipment Up: Introduction Previous: Beam Excitation and Resonances   Contents

A Polarization Model for the SLS Storage Ring

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 $\tau_0$ to the maximum level of polarization $P_{ST}$. 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} (38)

with $\tau_p=1865$ 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} (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} (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} (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:

\includegraphics [width=1.0\textwidth]{figures/polbuildup}
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.


$\displaystyle \tau_p$ $\textstyle =$ $\displaystyle 1865~s$  
$\displaystyle P_{eff}$ $\textstyle \approx$ $\displaystyle 80\%$  
$\displaystyle \Longrightarrow \tau_{d}$ $\textstyle \approx$ $\displaystyle 12032~s$  
$\displaystyle \Longrightarrow \tau_{eff}$ $\textstyle \approx$ $\displaystyle 1615~s$  

It is important to note that depolarizing effects have a very long characteristic time $\tau_{d}$ compared to polarization build-up $\tau_{p}$ (in this situation) leading to high polarization values.


next up previous contents
Next: Experimental Approach and Equipment Up: Introduction Previous: Beam Excitation and Resonances   Contents
Simon Leemann
2002-03-15