1. ILC BDS Alignment and Tuning Studies Glen White SLAC/QMUL 8 November 2005 Progress report and ongoing plans for BDS alignment and tuning strategy.

2. BDS Alignment and Tuning Simulations Using most recent (pre-Snowmass) 20mrad BDS deck plus extraction line. Start with expected post-survey magnet and BPM alignment tolerances, magnet errors and BPM resolutions. Simulate BPM-Magnet alignment using Quad- shunting technique and fits to higher-order magnet moves (Sexts, Octs). Steer/move to BPM readings with measured alignment. Generate orthogonal knobs for correction of IP aberrations using Sextupole movers. Simulation tool used: Lucretia.

3. Initial Parameter Assumptions All magnets have an associated BPM and x, y and roll movers. Quads have x- and y- corrector dipoles. Magnet RMS mis-alignment: 200um. Assume initial BPM-magnet centre alignment of 30um. Magnet rotation: 300urad. RMS relative magnetic strength error: 0.1%. Magnet mover resolution (x & y): 50nm. BPM resolution: 1um. Initially, use TESLA/USC bunch parameters (ideal gaussian for now) with 0.1 % uncorl. E spread. Track 2000 macro-particles per bunch, 100 random seeds.

4. Alignment & Tuning Strategy 1.Switch off Sextupoles & Octupoles. 2.Apply 1-1 Steering algorithm to align beam to measured BPM centres in Quads. 3.Use nulling Quad-shunting technique to get BPM- Quad alignments. 4.Use Quad movers to put Quads in a straight line in x and y with beam going through Quad field centres. 5.Get BPM- Sextupole alignment with movers and use a fit to downstream BPM responses. 6.Switch on Sextupoles and use Sextupole multi- knobs to tune IP waist, dispersion and coupling. 7.Perform BPM-Octopole alignment in a similar fashion to (5).

5. Nulling Quad Shunting technique: –To get BPM-Quad offsets, use downstream 10 Quad BPMs for each Quad being aligned (using ext. line BPMs for last few Quads). –Switching on & off Quad’s power, use change in downstream BPM readouts to get Quad offset. –Move Quad and repeat until detect zero-crossing. –For offset measurement, use weighted-fit to downstream BPM readings based on ideal model transfer functions: BPM-Quad Alignment

6. Quadrupole Alignment Results Left: BPM-Quad alignments (RMS mis-alignment from 100 seeds). Right: RMS Quad position post Quad mover alignment routine. –End points not fixed -> how to achieve initial beam collisions?

7. Sextupole, Octopole Alignment Use x-, y-movers on higher-order magnets and fit 2 nd, 3 rd order polynomials to downstream BPM responses (for Sext, Oct respectively). –Alignment is where 2 nd, 3 rd derivative is 0 from fits.

8. Beam Orbit Post-Alignment Beam orbit as measured in Quad BPMs after magnet alignment

9. Generating IP Tuning Knobs Use x- and y-moves of 5 Sextupole magnets to generate IP x- and y-dispersion and waist tuning knobs and (4) x-y coupling knobs. Generate response matrix to map Sextupole movements to IP parameters. Use SVD matrix inversion to get tuning knobs. With full errors applied, found knobs to be not so orthogonal – applied iterative tuning procedure based on IP beam spot sizes. IP RMS pre-knob tuning errors are (for 100 seeds): –Waist (x,y) ~ 0.5mm –Dispersion (x) ~ 0.5 mm (y) ~ 6.5 um –X-Y Coupling:( ) ~ 0.76 ( ) ~ 0.34 – ( ) ~ 0.82 ( ) ~ 0.31

10. Test of IP Multi-Knobs

12. Application of IP Multi-Knobs Start with just aligned Sextupoles on (no Octs). Zero x- and y- IP dispersion based on IP dispersion measurements. Iteratively tune all other knobs based on IP spot sizes (~lumi). Align and switch on Octupoles. Sweep each Oct in x and y, minimizing IP spots to reduce non-linear aberrations introduced (need to develop tuning knobs for this later). Re-apply Sextupole tuning knobs.

13. Application of IP Multi-Knobs InitialSteer Quads Align Quads Align Sexts Apply MK Oct Align + MK

14. Post-Tuning IP Beam Sizes Final IP params (100 seeds): RMS Dispersion (x/y): 0.39 mm / 1.5 um RMS Coupling Terms: 0.14 0.01 0.34 0.33

15. Future BDS Alignment Work Improve IP multi-knobs –Include non-linear terms for Sextupole knobs. –Use Skew Quads in addition for coupling correction. Simulate 2 beams- tune on luminosity (pair signals). Include steering routine to get initial beam collisions. Include LINAC to get real bunch shapes. Include GM. Integrated time-evolved simulation with initial tuning + pulse-pulse FB + intra-bunch FB. –Provides information on how often re-tuning necessary and most detailed luminosity performance estimate.