1. Review of Alignment Tolerances for LCLS-II SC Linac Arun Saini, N. Solyak Fermilab 27 th April 2016, LCLS-II Accelerator Physics Meeting

2. Outline  Types of misalignments  Implications of misalignments  Studies for LCLS-II SC linac  L2 Section  L3 Section  Summary

3. Type of Misalignments Element Offset Element Tilt/Pitch/Yaw Roll Errors r z φ

4. Implications of Cavity misalignment:  Cavity Offset:  Cavity transverse offset results in a wake kick from head particles to tails particles leading emittance growth.  Impacts depends on beta functions in lattice. Strong focusing provide large tolerances on cavity misalignment.  Cavity Tilt/Pitch :  It will cause coupling of longitudinal field into transverse plane. Particles get a transverse kick.  Due to time dependent field and finite size of bunch, particles get different kicks leading to emittance growth.  Implications are significant at low energy  Bunch length is longer  Cavity Rolls: Without power and HOMs coupler, cavity is axial-symmetric structure.  Roll may help to reduce coherent coupler’s kicks effects.

5. Implication of Quadrupole misalignments  Quadrupole Offset  A misaligned quadrupole gives a dipole kick that deflects the on- axis beam.  Kick is proportional to particle energy. A finite energy spread in bunch results emittance growth due to dispersion effects.  Usually a weaker betatraon function helps to reduces dispersive emittance growth.  Quadrupole Rolls  Generate a coupling between transverse planes and therefore results in emittance exchange.  Round-beam is pretty much invulnerable to quad rolls. r z φ

6. Cryomodule misalignment: A Cryomodule accommodates several elements on the same platform. Misalignment of cryomodule results in a correlated misalignment. All elements are misaligned in same way. All misaligned elements generate coherent kicks (same direction) to the beam.

7. Sources of Misalignments(1) An accelerating LCLS-II cryomodule consists of eight 1.3 GHz cavities and a quadrupole magnet. Total length of CM ~ 12.3 m It has three cold mass supports. One at the middle is fixed while two at both ends are sliding supports.

8. Sources of misalignment(2) Cavity misalignment on the string : 75  m RMS. String w.r.t CM axis: Transportation of CM results a transverse offset of 0.3 mm RMS with repeating scale of 3 m. String w.r.t CM axis: CM is cooled down from room temperature to cryogenic temperature (2K) and it results in a transverse offset of string with respect to CM axis. It is assumed to be 0.175 mm with repeating scale of 3m. CM axis w.r.t Network line: Cryomodule is aligned w.r.t. network line in the beamline. Tolerance on CM alignment is 50  m. String transportation

9. Network line/Survey line misalignment Distribution of Network error in L2 Section A set of reference markers are positioned along the beam line. Coordinates of those markers are measured using GPS technique. A set of primary reference points are established. Collection of those reference points along the beam line makes a network line (also called survey line). Because of narrow tunnel, refraction will affect measurements and therefore, survey process may have an error that leads to deviation of network line from its true position. Network line error is distributed as wave along beamline and formulated as: where A is amplitude, is wavelength, z cm is central position of cryomodule in beamline and  is arbitrary phase of the wave.

10. Budget of Alignment Tolerance Typew.r.tmagnitudeScale ElementsString 75  m (RMS) - String: Transportation CM0.3mm (RMS)3 m String: Cold to Warm CM0.175mm (RMS)3m CryomoduleNetwork line 50  m (RMS) 13 m (CM length) Network lineIdeal Line0.3mm (wave)100 m Courtesy : George Gassner

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

12. Correlated Misalignment Studies:  Different stages of assembly and commissioning introduces correlated misalignments.  Correlated misalignments reflects most realistic scenario in beam line.  Correlated misalignments result in coherent kick, to beam and therefore may lead to much significant emittance growth than individual element misalignment with same magnitude. Independent Misalignment Correlated Misalignment

13. Correlated Misalignment Model Implementation  A Model is implemented in Matlab and interfaced with beamdyanmics code Lucretia in order to perform tracking.  Several layers of misalignments are applied in steps.  Pitch angle is estimated based on offset   where S is distance of element center from center of string.  Offset due to pitch is applied to the elements. CM Axis Offset xx String Cavity CM Axis Tilt S   x =S*tan  Thanks to Glen White for useful discussion about Lucretia

14. Correlated Misalignment Model(2) Cavity String CM Axis Network Line Ideal Survey Line CM Misalignment w.r.t Network Line Misalignment w.r.t Ideal Line

15. Validation of Correlated Misalignment model:  Each element is misaligned randomly in a Gaussian distribution with given RMS amplitude. Distribution of offset of all cavities for 100 seeds when RMS misalignment of 0.5 mm is applied. Distribution of RMS cavity-offset for 100 seeds. Most of machines exhibits RMS cavity offset close to 0.5 mm

16. Studies for LCLS-II SC Linac: Initial parameters  Studies are performed for  L2 and L3 section  Gaussian beam distribution of 50 k particles truncated at 4 sigma.  Bunch charge of 300pC  Initial normalized RMS emittance 0.45 mm mrad;  Short range wake fields are included.  Initial 1  beam offset of vertical centroid (y, y’) is included.  All misalignment errors are included.  One to one steering algorithm is applied to understand emittance compensation scheme.

17. Emittance growth without and with correction Distribution of Emittance along linac after corrections L2 Section: Emittance Evolution Distribution of emittance growth along linac for 100 machines. All types of misalignments are applied.

18. 90% emittance growth: Mean Emittance along the L2 section L2 Section: Emittance Distribution  final -  initial No Correction

19. Vertical Centroid trajectory without and with correction L2 Section: Centroid trajectories Mean Vertical Centroid trajectory for different cases Maximum displacement is 5 mm without correction. One to one steering corrects the trajectory with in 100  m

20. Mean90 % unit String + CM 0.1560.33 mm mrad Network Line 0.0080.015 mm mrad String+CM+Net work 0.160.36 mm mrad String + CM Offset Network Misalignment String+ CM + Network Misalignment Summary of Emittance Dilution for different cases

21.  Network line misalignment is given as:   For fixed amplitude, its implications on beam strongly depends on wavelength and initial phase. Network line error in L2 section for 100 m wavelength Understanding of network/ survey line Error

22. Distribution of Network line error with different phases Variation in Final emittance with initial phase variation Network line Error: Initial Phase Variation Initial large offset (large initial phase) of CMs leading to large emittance growth. Only Network line misalignment error is applied.

23. Mean emittance dilution with wavelength 90 % emittance dilution with wavelength Network Line Error: Wavelength Variation Only Network line misalignment error is applied. Maximum emittance dilution for wavelength of 200 m.

24. Emittance :UncorrelatedEmittances: Correlated A comparison bw uncorrelated/correlated misalignments Mean Emittance dilutions in case of correlated misalignments are ~36% and ~ 3.8% without and with 1-1 correction respectively Mean Emittance dilutions in case of uncorrelated misalignments are 6.7 % and 1.1 % without and with correction respectively.

25. L3 Sections: Emittance Evolution Emittance growth without and with correction Distribution of Emittance along linac after corrections Distribution of emittance growth along linac for 100 machines. All types of misalignments are applied.

26. Mean Emittance growth in presence of all misalignments L3 Section: Emittance Dilution at different stages Mean90 % unit String transport 0.190.37 mm mrad String (trans+cold) 0.2180.475 mm mrad String + CM 0.240.50 mm mrad String+CM+Net workLine 0.2470.517 mm mrad Emittance Summary

27. L3 Section: Centroid Trajectories Vertical Centroid trajectory without and with correction Mean Vertical Centroid trajectory for different cases Maximum displacement is 5 mm without correction. One to one steering corrects the trajectory with in 100  m

28. L3 Section: Uncorrelated v/s correlated misalignments Emittance :Uncorrelated Emittances: Correlated Mean Emittance dilutions in case of correlated misalignments are ~55% and ~ 2.7% without and with 1-1 correction respectively Mean Emittance dilutions in case of uncorrelated misalignments are 19% and 1.0 % without and with correction respectively.

29. L2 Section L3 section Corrector strengths: Corrector settings are well within design specification. Correctors settings for all seeds in L2 and L3 sections.

30. Summary  A model is implemented to understand implications of correlated misalignment in LCLS-II SC linac.  Correlated misalignment result in large emittance growth in both L2 and L3 sections.  Mean emittance dilutions in presence of all misalignments are 0.247 and 0.16 mm mrad in L3 and L2 section respectively.  One to One steering is applied to compensate emittance dilution.  Studies shows that corrector settings are within design specification of 5 mT-m. Thus, correctors would be able to correct beam trajectory and hence emittance dilution.  Mean emittance dilutions after 1-1 correction are 0.017 and 0.0135 mm mrad in L2 and L3 section respectively.