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:

$$P_{pol}(t)=P_{ST}\left(1-\exp\left(-\frac{t}{\tau_{p}}\right)\right)$$ (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:

$$P_{depol}(t)=P_{ST}\exp\left(-\frac{t}{\tau_{d}}\right)$$ (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:

$$P_{tot}(t)=P_{eff}\left(1-\exp\left(-\frac{t}{\tau_{eff}}\right)\right)$$ (40)

where

$$P_{eff}=P_{ST}\frac{\tau_{d}}{\tau_{p}+\tau_{d}} \qquad \tex... ... \qquad \frac{1}{\tau_{eff}}=\frac{1}{\tau_p}+\frac{1}{\tau_d}$$ (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.

$$\tau_p = 1865~s$$

$$P_{eff} \approx 80\%$$

$$\Longrightarrow \tau_{d} \approx 12032~s$$

$$\Longrightarrow \tau_{eff} \approx 1615~s$$

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.