COUPLING CORRECTION

  

Figure: Top: Mean, rms and maximum beam ellipse twist $\theta$ for 200 seeds for 1/3rd of the lattice, bottom: corresponding sigma ratio $\sigma_{II}/\sigma_{I}$.

Betatron and emittance coupling have been estimated from the calculation of generalized emittances and sigma matrices [5]. The beam ellipse twist in the straight sections of the SLS storage ring has been found to be $\approx$40 mrad (see top graph of Figure 3).

The corresponding value for the emittance coupling in mode D1 which allows 5-8 cm horizontal dispersion in the straight sections is calculated to be 0.2% and 1% in the zero dispersion mode D0. This relatively large coupling factor for the latter mode can be explained by the fact that the vertical working point had been initially chosen very close to the integer ( $\nu_{y}=7.08$) in order to optimize the Dynamic Aperture. At the same time this results in a significant increase of the spurious vertical dispersion. A change of the vertical tune to $\nu_{y}=8.28$ (D2A lattice) leads to a reduction of the emittance coupling to 0.25%. The bottom graph of Figure 3 shows the sigma ratios $\sigma_{II}/\sigma_{I}$ for 1/3rd of the D2A lattice after the tune change. The contribution from quadrupoles is nicely compensated by the dispersion generated by the nearly adjacent orbit correctors in the sextupoles. Thus the remaining vertical dispersion of 0.3 cm is mainly induced by sextupoles. Another source of emittance coupling is the feeddown of horizontal dispersion through skew quadrupole components induced by nonzero vertical orbits in sextupoles and quadrupole roll errors. This contribution can be minimized utilizing dedicated skew quadrupoles. Foreseen are three families with two magnets per family paired around the three long straight sections. The idea is to use the foreseen additional corrector windings on the sextupoles to generate the necessary field. The effectivness of the correction scheme has been tested for the 200 seeds. The resulting histograms for the emittance ratio $\kappa$ are depicted in Figure 4. It can be seen that the mean $\kappa$ value is reduced from 0.25% (see curve labeled sextupoles+tilt error+no correction) to 0.1% (see curve labeled sextupoles+tilt error+correction). Furthermore the $\kappa$ spread has been reduced from 0.16% to 0.06%. It can be also deduced from the graph that magnet tilt errors have only a marginal influence on $\kappa$ (see curves labeled sextupoles+tilt error+(no) correction). Switching of the sextupoles results in a $\kappa$ of 0.02% (see curve labeled no sextupoles+tilt error+correction) which illustrates that the residual coupling is dominated by sextupoles. Quadrupoles plus correctors alone account for a $\kappa$ of 0.01% (see curve labeled no sextupoles+no tilt error).

  

Figure: Histograms of the emittance ratio $\kappa$ for 200 seeds with and without coupling correction.