Beam Current and Lifetime

Beam current and beam lifetime can both be monitored through the SLS control system. When injection into the storage ring stops the beam current slowly decays following an exponential function with a characteristic decay time:

$$I=I_0\exp(-\frac{t}{\tau})\qquad \textrm{and} \qquad \dot{I}=-I\frac{1}{\tau}$$ (45)

The beam lifetime is the inverse negative of the current derivative $-\dot{I}^{-1}$ and therefore the product of beam lifetime and beam current is the decay constant:

$$\tau = -\dot{I}^{-1} \cdot I$$ (46)

After stopping the injection one would expect a gradual decay of the current and respectively an increase in lifetime. Instead an exponential increase of this product is observed due to the fact that Touschek scattering decreases with increasing polarization (figure 6). Recall that the characteristic decay time of the beam current in the SLS storage ring is given by:

$$\frac{1}{\tau}=\frac{1}{\tau_{ts}}+\frac{1}{\tau_{el}}$$ (47)

If the current is known $\tau_{el}$ can be calculated [14] and thus we derive $\tau_{ts}$:

$$\tau_{ts}=\frac{\tau\cdot\tau_{el}}{\tau_{el}-\tau}$$ (48)

It was observed that after waiting for two to three polarization build-up times to pass, $\tau_{ts}$ reaches a constant value, precisely as expected from theory.

Figure 6: The polarization build-up after injection is clearly seen in this plot. Injection stopped shortly before timestamp 12000. The fit is depicted by the dashed line. The build-up time constant is $\tau_{ts}=(1261\pm 12)$s corresponding to an equilibrium polarization degree $P_{eff}=(62.5\pm 0.6)$%.

After the build-up of $\tau_{ts}$ has been observed and the stored beam has reached equilibrium state $\tau_{ts}$ stays constant. This changes when the beam is excited at the spin tune: The effective polarization is reduced and thus the Touschek scattering cross section rises leading to a decrease of beam lifetime (figure 7).

Figure 7: The beam is excited shortly at the depolarizing resonance at timestamp 7910 and again later at timestamp 8110 leading to sudden drops in the product of beam current and lifetime.