ILC BDS Alignment, Tuning and Feedback Studies

1. ILC BDS Alignment, Tuning and Feedback Studies Glen White SLAC/Oxford Feb 2006 • Progress report and ongoing plans for BDS alignment and tuning strategy.

2. BDS Alignment and Tuning Simulations • Using ILC-IR1 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). • Move to BPM readings with measured alignment and optimise orbit. • Use orthogonal knobs for correction of linear 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 with respect to model: 1e-4. • Magnet mover resolution (x & y): 50nm. • All magnets on their own movers, apart from last quad/sext/oct pair which are in cryo-module and have fixed offsets. • Cryo module bpm and magnet relative offsets 10um/100urad RMS. • Assume SD0/OC0 and SF1/OC1 co-wound with above relative magnetic centre offsets. • Assume whole module has position+angle movers. • BPM resolution: 1um for all quads, assume cavities on sextupoles with 100nm resolution. • TESLA bunch parameters (gaussian beam) with 0.1 % uncorl. E spread. • Track 2000 macro-particles per bunch.

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/Octupole alignment with movers and use a fit to downstream BPM responses. • Switch on Sextupoles/Octupoles. • Use global BDS pulse-pulse feedback system to keep betatron orbit centred in BPMs. • Use Sextupole knobs to tune IP waist, dispersion. Use skew quads (4 in coupling section + SQ3FF) for coupling correction.

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 Quad’s power (100% - 80%), use change in downstream BPM readouts to get Quad offset. • Move Quad and repeat until detect zero-crossing (using 1-d optimiser). • For offset measurement, use weighted-fit to downstream BPM readings based on ideal model transfer functions:

6. Quadrupole Alignment Results • Left: BPM-Quad alignments (1 seed). • Right: RMS Quad position post Quad mover alignment routine. • In reality, don’t want this large drift- use lattice matrix inversion to align quads in straight line centered in vacuum chamber and to collide beams.

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. (1) (2) BDS Orbit Stabilisation • A global steering algorithm throughout the BDS is used to keep the orbit centered in the magnet BPMs whilst moving Sexts/changing skew quad strengths. • Sext moves when doing IP tuning must be accompanied by set-point changes for the magnets being moved. • Feedback also counter-acts ground motion/element drift. • Correction scheme: choose set of bpm’s and correctors. Then use Matlab’s lscov routine to obtain solution to (1), where R is the matrix of coupled transfer elements , b is the vector of x and y bpm readings and c is the corrector set to solve for. • lscov does a least-squares minimisation (2); where V is proportional to the bpm covariance matrix.

9. Linear IP Tuning Knobs • Correction of linear IP aberrations (x/y waist and dispersion) performed by sextupole moves. • X-offsets in sextupoles generate additional quad-component and can be used to compensate for waist and x-dispersion aberrations. • Y-offsets general additional skew-quad components and are used to correct IP vertical dispersion. • Y-offsets also generate coupling, SQ3FF is used to compensate for this.

10. Dy IP Tuning Knobs • Use orthogonal x-moves of SF6, SF1, SD0 to tune on x/y waist and Dx. • Use orthogonal vertical moves of SD0 and SD4 and dK for SQ3FF to tune Dy and dominant coupling term (<x’y>). • Use additional 4 skew quads in BDS coupling section to perform orthogonal tweaks of other coupling terms. Waist (x) Waist (y) Dx SD0 SD4 -1 0.938

11. Application of IP Multi-Knobs • Knobs are not completely orthogonal after adding lattice errors etc. • Iteratively apply knobs, tuning on luminosity. • Starting conditions after initial alignment: • Beamsize (x/y): ~ 620/140 nm. • Dx/y : ~ 14 / 10 um. • Waist (x/y): ~ 0.3/0.6 (s1,2/3,4)). • Coupling: ~ 0.2/0.1/0.8/0.5 (xy,x’y,xy’,x’y’). • Initially fix vertical aberrations & dominant coupling (x’y) until no further improvement possible. • Then iterate through all knobs.

12. Feedback • All Quad BPMs and correctors are used in feedback. The final doublet string is steered to with the 2 Sext BPMs. • Orbit stabilised throughout tuning process with global steering algorithm. The IP is included as a BPM with resolution 1e-9 to mimic information from the beam-beam collision which allows the feedback to keep the beam within the capture range of the fast feedback system ~100nm. Lumi stability ~0.1%. • A simple, single gain feedback is applied to the BPM readings to damp RMS errors from finite BPM resolutions. This is tuned to damp on a 50 bunch timescale- to be optimised later.

13. Results • Results from single seed: • Tuning on luminosity and tuning 1 knob at a time, finding the optimal by using 1-d optimisation routine (Matlab’s fminbnd). • Convergence to beam spot size x<600nm, y<6nm- to get about 80% of geometric Luminosity is fairly quick, ~200 pulses- about 40s of beam time. • Convergence beyond this is very slow, may take many hours of optimisation to get close to design. • It may be faster to use more beam diagnostics in final tuning phase, ie. Dispersion scans and coupling measurements… • Further speed improvement also possible with fine-tuning of optimisation routines etc. • Should be possible to finally converge on very close to design Lumi. Measured normal mode emittance growth <1%.

14. Future Work • Improve speed of alignment. • Include GM. • Simulate 2 beams- tune on luminosity (pair signals). • Include steering routine to get initial beam collisions. • Include LINAC to get real bunch shapes. • 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.