Touschek Scattering and Polarization

Until now polarization of the electron beam as well as depolarization have been mentioned. Measuring absolute polarization however is not a simple task and requires dedicated complex hardware (Compton Polarimeter, dedicated beam line, etc.) which currently do not exist at SLS. But it is actually not necessary to measure absolute polarization in order to obtain the degree of equilibrium polarization. If a Touschek limited beam is used the degree of equilibrium polarization can be determined by observing the rate of Touschek scattering because Touschek scattering is polarization-dependent.

The three main effects which contribute to scattering of beam electrons in a storage ring are: Touschek Scattering ($\tau_{ts}$), elastic scattering ($\tau_{el}$) and bremsstrahlung ($\tau_{bs}$); these effects determine beam lifetime in the SLS storage ring [14]:

$$\frac{1}{\tau}=\frac{1}{\tau_{ts}}+\frac{1}{\tau_{el}}+\frac{1}{\tau_{bs}}$$ (42)

Recent experiments [14] have shown $\tau_{bs}$ to be so large, that it has no significant influence on the total lifetime $\tau$. For single bunch beam current of $0.5\--1.5~mA$ the dominant effect [14] is Touschek scattering; elastic scattering depends inversely on gas pressure, which in turn depends linearly on beam current. Therefore we chose to use a filling pattern of 90 bunches at about $100~mA$ which guarantees for Touschek limitation of the beam where:

$$\frac{1}{\tau_{ts}} \gg \frac{1}{\tau_{el}}+\frac{1}{\tau_{bs}}$$ (43)

Touschek scattering [15] [16] has a polarization dependent cross section:

$$\sigma_{ts}=f_1(r_e,\beta,\Theta) - P^2\cdot f_2(r_e,\beta,\Theta,\Phi)$$ (44)

where $f_i$ are functions of the electron radius $r_e$, the relativistic velocity $\beta$ and the scattering angles $\Theta$ and $\Phi$. Increasing beam polarization $P$ leads to a smaller Touschek cross section and therefore to less losses of beam particles. On the other hand, a sudden decrease in beam polarization (due to the depolarizing resonance for example) will lead to a rise of Touschek scattering losses. Therefore the change of the Touschek loss rates of the beam can be correlated with changes in the polarization level.

Furthermore, measurement of the equilibrium polarization build-up time will allow determination of the equilibrium degree of polarization nevertheless: Recall equation 40 describing this build-up process. If we observe the exponential build-up the remaining unknown ($\tau_{p}$ can be calculated, see equation 4) $\tau_d$ can be fitted. With equation 41 the equilibrium polarization level $P_{eff}$ can be obtained⁶.