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

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

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

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

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.

Relative alignment of elements w.r.t string Each element on string is misaligned with RMS amplitude of 0.075 mm. Cavity String String to cavity = 0.075 mm RMS

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.

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 = 0.175 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

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

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.

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.

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

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

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

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

90 % emittance dilution De = yfinal -yinitial

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

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

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.

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

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 0.69 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.

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