ILC BDS Alignment and Tuning Studies

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

5. BPM-Quad Alignment • 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:

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 2nd, 3rd order polynomials to downstream BPM responses (for Sext, Oct respectively). • Alignment is where 2nd, 3rd 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: (<xy>) ~ 0.76 (<xy’>) ~ 0.34 • (<x’y>) ~ 0.82 (<x’y’>) ~ 0.31

10. Test of IP Multi-Knobs

11. 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 Initial Steer 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: <xy> 0.14 <x’y> 0.01 <xy’> 0.34 <x’y’> 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.