1. Emittance Tuning Simulations in the ILC Damping Rings James Jones ASTeC, Daresbury Laboratory

2. 2 Contents Previous Work Current Work - Setup Orbit Correction Dispersion Correction Coupling Correction Ground Motion Girders Future Plans

3. 3 Previous Work Most of the previous work performing simulations on the low emittance tuning of the damping rings was performed by A. Wolski and K. Kubo, and myself. The work was presented at Snowmass 2005, and compared the 7 different lattice designs at that time. The major conclusions were that there was very little difference between the codes used (Merlin, SAD, MAD), but that there were differences in the methods of correction. The major conclusion at that time was that the OTW lattice was the only lattice unsuitable on LET arguments alone.

4. 4 Previous Work - Methods The major differences in tuning methods between Kubo and Jones were: Kubo uses a minimisation of the Orbit correction using corrector magnets Vertical orbit + vertical dispersion using correctors Coupling correction using limited skew quadrupoles and 2 horizontal kickers Jones uses Orbit correction using quadrupoles & SVD method Vertical dispersion correction using arc skew quads Coupling correction using straight section skew quads

5. 5 Previous Work - Results The results showed that the method of Kubo generated lower vertical emittances than that of Jones for the cases considered. Kubo Results – 200 seeds Jones PPA Lattice – 200 seeds

6. 6 Current Work Since Snowmass very little work has been done comparing the different techniques. Have modified my technique to produce better results for the OCS lattice Still some optimisation can occur… New technique Closed Orbit correction using dipole correctors @ every quadrupole Vertical dispersion + coupling correction using skew quads at every sextupole Both corrections use SVD response matrix inversion method

7. 7 Method – CO Correction The correction of the closed orbit is performed using a corrector and BPM pair at every quadrupole in the lattice. The matrix inversion is performed using SVD The matrix is 1251x1251 elements Use ~750 singular values in the final correction matrix Correction can also be performed using quadrupole movers, and the results are very similar. Obviously, mechanical considerations would suggest that correctors are the better choice, and they are assumed in the rest of the talk.

8. 8 Method – Dispersion and Coupling Correction To correct the dispersion a response matrix of BPM dispersion vs. skew quadrupole field was created. Skew quadrupoles were placed at every sextupole in the lattice. Coupling correction was also achieved through the same skew quadrupoles and by minimising the vertical response to the orbit induced by 4 horizontally displaced quadrupoles. The kickers were generally placed at opposite ends of the lattice and out of phase. The relative correction weight between the coupling and dispersion correction was set to 0.05, in favour of coupling correction. This number could be more fully optimised.

9. 9 Dispersion Correction Studies were performed showing the relative merits of vertical dispersion correction with corrector magnets or skew quadrupoles, whilst also correcting the orbit. Correction of the dispersion with skew quadrupoles is clearly superior in this case. For OCS2

10. 10 Results with standard errors Using the same errors as those given at Snowmass Extracted beam emittance over 50 seeds gives an rms. Emittance of 18nm-rad. Rms. = 18.3nm-rad

11. 11 Alignment Tolerances – OCS2 Calculated using the full correction systems described for a variety of errors Arbitrary amplification function No CorrectionCO Correction CO + DY + Coupling Correction

12. 12 Ground Motion To further investigate the low emittance tuning, I looked at the required correction interval under the influence of simple ground motion I use a model of the ATL-like motion of the ground developed by Wolski and Walker. This method relies on developing covariance matrices of the position of each element to the position of every other element. I assumed an A coefficient equivalent to ~100  m/10m/Year Not coincidently that used for the diamond light source. All motion is vertical – no horizontal or longitudinal motion arises from the motion of the ground. The model can use girders and allows differential motion between the two ends of the girders, and thus rotation around the x-axis.

13. 13 Girders I made some simple assumptions on the girderisation of the machine In general, most of the ring has very separate elements Not sure if girders can be used in this scenario Most girders are situated in the arcs or the wiggler magnets All BPM-Corrector-Quad/Sext assumed to be tied together Wiggler Block – assumed to be one long support structure Simple ~5m long quadrupole and sextupole structure

14. 14 Girder Amplification Factors A simple analysis of the amplification factor of the machine in terms of vertical motion shows that the girders have a limited effect: Does the machine need a better defined girder strategy? QuadrupolesAll Magnets With Girders 32.332.4 Without Girders 34.734.8

15. 15 Ground Motion Results Start by misaligning the machine with static errors: Initial correction is performed using 4 iterations of CO and then 2 iterations of DY+Coupling correction The ATL motion is then applied in steps of 1 day A full correction of 3xCO + 2xDY+Coupling is then performed every 6 days Assumed each correction step takes ~3 minutes

16. 16 Ground Motion Results Emittance oscillates around the 20nm area with correction Emittance >20nm after ~10 days without correction Uncorrected Corrected

17. 17 Results – OCS2 Emittance > 20nm after ~20 Days with no correction With correction every 6 days, we maintain the emittance for at least 120 days!

18. 18 Future Plans The ground motion model can be further developed to provide a more realistic model This can include better modelling of the girders in the machine This needs to be combined with better tuning of the correction system parameters (such as the SVD rejection criteria etc) Also further analysis of the different correction techniques should be performed – Methods used at real light sources! A realistic assessment of the number of required BPMs and correctors and skew quads for the different techniques also needs to be looked at