1. Correlated Misalignments Studies for LCLS-II SC Linac
Arun Saini, N. Solyak
Fermilab
28th Oct. 2015

2. Motivation
Misalignment of beamline elements during various stage of commissioning are mostly correlated.
Correlated misalignments result in coherent kick, and therefore may lead to much significant emittance growth than individual element misalignment with same magnitude.
Cavity
String Axis
CM Axis

3. Alignment tolerances (LCLS-II requirements)
Nominal individual RMS alignment tolerances of Beamline elements

4. Misalignment Budget During Assembly
Different aspects of error budget stack up:
Georg Gassner: Presentation Summary
Cell to cell assembly in a cavity: 0.3mm RMS/range?, every ~0.15m
Relative alignment of cavities to string: +/-0.075mm RMS; every 1.3m
Transport shifts: 0.3mm RMS, 3m pattern (I assume that the support posts don’t move)
Cold/warm uncertainty: +/-0.175mm RMS, 3m pattern (the support posts seem to be stable)
Alignment of components in the tunnel: 0.05mm RMS, every 13m
Alignment network: 0.3mm RMS, ~100m wavelength

5. Single Cavity Assembly
Single cell to cell assembly: 0.3mm RMS?, every ~0.15m
Tuning Machine
Each cavity is tuned to align electrical center in order to achieve field flatness > 97 %
Mechanical center of cavity is also aligned within 0.3 mm
Cell to cell mechanical errors results in excitation of geometrical wakes.

6. Relative alignment of elements w.r.t string
Each element on string is misaligned with RMS amplitude of mm.
Cavity
String
String to cavity = mm RMS

7. String Misalignment in Cryomodule
Cryomodule length: ~12.3m
3 supports for cold mass (1-fix. and 2-sld.)
String misalignments are measured at scale of 3 m.

8. String Misalignments w.r.t CM axis
Misalignment of string is because of
Transportation of cryomodule
Warm to cold uncertainty
Offset
String
Cold Warm Uncertainty = mm RMS, 3 m +
0.3 mm RMS after transportation.
CM Axis Dx
Tilt
Cavity
CM Axis
Tilt angle of string is : atan(
Dx/ (L/2))
dx =S*tanq
Where L is length of string, 3m in this case. q S

9. CM Alignment w.r.t Network Line
Cavity
String
CM Axis
Network Line
A Cryomodule is misaligned in tunnel that further results in correlated misalignment.
CM Alignment w.r.t Network Line = 0.05 mm RMS , 13m

10. Misalignment of Network Line
Ideal Survey Line
Due to tunnel width of only 3.3 m, Deviation over long distance is resulted mainly by reflection.
Network line is misaligned w.r.t. ideal survey line in range of 0.3 mm with wavelength of 100 m.
I have not included Network line misalignment in this study.

11. Simulation Input Parameters
Studies are performed for
L3 section
Guassian beam distribution of 50 k particles truncated at 4 sigma.
Short range wake fields are included.
Initial normalized RMS emittance =0.45 mm mrad.
Initial 1 rms beam offset of vertical centroid (y, y’) is included.
One to one steering algorithm is applied.

12. Misalignment Implementation in Lucretia
Each element is misaligned randomly in a Gaussian distribution with given RMS amplitude.
Distribution of offset of all cavities for 50 seeds when RMS misalignment of 0.5 mm is applied.
Distribution of RMS cavity-offset for 50 seeds. Most of machines exhibits RMS cavity offset close to 0.5 mm

13. Emittance growth along the linac for all seeds
Distribution of emittance growth along linac for 100 machines
Emittance growth without and with correction
Distribution of Emittance along linac after corrections

14. Distribution of Centroid trajectory along linac
Vertical Centroid trajectory
without and with correction
Mean Vertical Centroid trajectory for
different cases

15. Mean emittance growth along linac
Mean emittance is estimated by taking mean for all seeds at each location.
Emittance growth at the end of L3 section is 0.69 mm mrad without correction and 0.46 mm mrad after correction

16. 90 % emittance dilution
De = yfinal -yinitial

17. Element + String Transport Offset
Element + String Transport +Cold Offset
Element + String Transport +Cold Uncertainty Offset + CM offset

18. Element + String Transport Offset
Element + String Transport +Cold Offset
Element + String Transport +Cold Uncertainty Offset + CM offset
Mean
90 %
unit
String transport
0.19
0.37
mm mrad
String (trans+cold)
0.218
0.475
String + CM
0.23
0.50

19. Comparison with previous studies
Independent Misalignment of Each elements
Correlated Misalignment
Mean eimttance growth without correction is ~ 20 % and 70 % for non-correlated and correlated cases respectively.
Mean emittance growth after correction is ~ 1.1 % and 2.6 % for both cases respectively.

20. Corrector Strengths Independent Misalignment Correlated Misalignment
Corrector strength are within functional requirements for both cases
Design specifications for corrector is 5 mT-m

21. Summary
Correlated misalignments were introduced and studies have been performed for L3 section.
Correlation results in a coherent kick that leads to significant emittance growth ( Final emittance (average over 50 seeds) of mm mrad without correction.
One to one steering correction algorithm allows to restore emittance. Final average emittance at the end of L3 section after applying one to one steering is 0.46 mm mrad.
Correctors settings were within design specification.
In a comparison, correlated misalignments results in a larger emittance growth than uncorrelated misalignments.

22. Back-up slide
Distribution of Cavity offset after applying correlated misalignment.