Introduction

As first mentioned by Ternov, Loskutov and Korovina in 1961 electrons gradually polarize in storage rings due to sustained transverse acceleration while orbiting. The mechanism is the emission of spin-flip synchrotron radiation: While being accelerated, electrons radiate electromagnetic waves in quanta of photons which carry a spin. An extremely small fraction ($10^{-11}$ of the emitted power) of the synchrotron emissions is spin-flip radiation. The difference between the two possible transition rates causes an injected electron beam to get polarized anti-parallel with respect to the guiding dipole field. The maximum achievable polarization level in a planar ring without imperfections is the Sokolov-Ternov Level [2]:

$$\begin{eqnarray*} \nonumber P_{ST}=\frac{W_{\uparrow \downarrow}-W_{\downarrow \... ...ownarrow}+W_{\downarrow \uparrow}}=\frac{8}{5 \sqrt{3}}= 92.38\% \end{eqnarray*}$$

The time constant of the exponential build-up process of this equilibrium polarization by the initially unpolarized beam is:

$$\tau_p={\left(W_{\uparrow \downarrow}+W_{\downarrow \uparrow}\rig... ...rt{3}}{8}\cdot\frac{e^2\hbar}{{m_{e}}^2c^2}\right)}^{-1}\frac{\rho^3}{\gamma^5}$$ (1)

with $\tau_p=1873$ s for the SLS storage ring ($E=2.4$ GeV, effective bending radius $\rho = 11.48$ m).

However, spin-flip radiation is accompanied by depolarizing effects (for example from perpendicular fields) and therefore beam polarization must be understood as an equilibrium state. Depolarizing effects (over a time which is long enough to allow spin diffusion) are expected to show an exponential decay of the polarization with the decay time constant $\tau_d$. The equilibrium state is therefore described by an exponential build-up:

$$P_{tot}(t)=P_{eff}\left(1-\exp\left(-\frac{t}{\tau_{eff}}\right)\right)$$ (2)

where

$$P_{eff}=P_{ST}\frac{\tau_{d}}{\tau_{p}+\tau_{d}} \quad \textrm{and} \quad \frac{1}{\tau_{eff}}=\frac{1}{\tau_p}+\frac{1}{\tau_d}$$ (3)

Since depolarizing effects are small in low energy rings, we expect high equilibrium polarization values close to the Sokolov-Ternov level at the SLS storage ring.