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**Alignment and Beam Stability**

Magnet Alignment Tolerances Random Alignment tolerances Girder correlations Beam Based Alignment and Closed Orbit Correction Strategy Quadrupole vs Sextupole BBA schemes BPM and Correctors Placement Beam Stability and Feedback Systems Global slow and fast feedback system Local feedback system S.L. Kramer for the NSLS-II Team

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Quadrupole Alignment Misalignment of quadrupole centers, drive large Closed Orbit Distortion Closed Orbit Amplification Factors (COAF) defined as RMS(cod)/ RMS(error) ~50X in both planes or 100µm RMS Quad. misalignment 5mm offset of COD in lattice

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**Magnet Alignment Tolerances**

Quadrupole and Sextupoles have centers measured to a resolution of 10 and 15 µm with pulsed wire technique Allow 2X for resolution, alignment Tolerance <30µm on girder Girder alignment Tolerance in tunnel <100µm (as achieved elsewhere ) girder amplification factors (6,2.5) in ID are ~7 to 8X less than COAF Std(COD) for 200 seeds with girder alignment dX,dY=10µm random at both ends

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**First Turn Correction These tolerance still make closed orbit unlikely**

4 of 10 stable with baseline lattice and alignment tolerances Reduced sextupole strength or first turn correction algorithm Also possible to find reduced sensitivity Day-One lattice but should have similar tunes Magnet centers also need to be independent of powering <30µm Once stable orbit established use beam based alignment to center on magnet offsets to reduce closed orbit distortions

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Beam Based Alignment With stable orbit, measure beam position with BPMs where individual magnet strength changes has a null effect Gradient error from sextupoles is source of DA reduction, so ideal would be to align to sextupole magnetic centers First order effect is a tune shift due to gradient No tune shift with y coordinate except through coupling Resolution of tune shift dependent on energy spread and chromaticity, at best <30µm Synchro-betatron coupling could easily increase resolution to ~100µm M. Kikuchi, et.al. (KEK), introduced gradient coils to shift orbit rather than tunes

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Quadrupole BBA Quadrupoles introduce orbit steering with strength changes if closed orbit is offset by x and y then the steering with strength change K2 is Assuming 1µm BPM resolution and K2 ~2% of weakest quadrupole yields resolution on x and y of ~ 6 and 14µm or better We assume a resolution of 10µm for Dynamic Aperture studies

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**BPM Placement for Girder Alignment**

BPMs at ends of girder to reduce the 100µm girder-girder misalignment to the BBA resolution: <10µm for quads or >30µm sextupoles Resulting magnet random misalignment of <30µm from placement on girder

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**BPM and Corrector Placement**

BPMs next to Quads near ends of girders for Max. lever arm Large beta functions for BPMs and correctors

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**Number of BPMs and Correctors**

3-5 BPMs needed from tunes (νx , νy ~ 1.1, 0.54 per cell ) 6 BPMs for 3-girder alignment, 7th BPM useful for physics (peak ηx) # of Correctors = # of BPMs for deterministic correction scheme Study of reduced BPMs based on DA with tolerance errors DA for 7 BPM x 7 Correctors vs BPM x 6 Correctors

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**Roll Errors and Coupling Correction**

Johan covered magnetic field error tolerances and ID effects Girder and Dipole roll tolerance < 0.5 mrad Quadrupole and sextupole roll tolerance < 0.2 mrad BPM roll tolerance < 0.2 mrad Skew correction in the discrete orbit correction magnets Two per super-period Corrects yi << 8pm, introduce a vertical dispersion wave to increase vertical size from diffusion not coupling for increased lifetime or increase roll tolerances

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**Orbit Stability and Feedback**

Small vertical emittance (~ 8pm) yields small beam size in ID’s σy ~ 2.8µm and σy’ ~ 3µrad Centroid motion of beam cause effective emittance growth or reduced brightness for users for frequency > fsample(user)

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**Tolerance for Orbit Stability**

Many operational LSs have set 10%σ centroid motion tolerances Y < 0.1 σy ~ 0.3 µm and Y’ < 0.1 σy’ ~ 0.3 µradian COAF of ~ 15 to 25 in IDs Y(quads) < nm random motion Uncorrelated quadrupole motion Xq = 330nm and Yq =23nm adds cm ~1% o to each plane or 10% σx,y

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**Correlated Quadrupole Errors**

Beta calculates cm for correlated motion from plane wave vibration with velocity of wave, vg ~500 m/sec, amplitude for cm ~20% o shown Later N. Simos measured vg ~285 m/sec so scale frequency by 60% 1μm 1μm

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**Tolerance for Quadrupole motion without Feedback**

Girder amplification factors need to be included to reference to ground vibration limits Girder design has first resonance (horizontal) > 60 Hz. Reduction of cultural noise. Tolerance Limits dX RMS Quads dY RMS Quads X RMS (εx) Y RMS (εy) Random motion < 0.33 μm < μm 19.4 μm (0.02 nm) 0.5 μm (0.088 pm) Plane wave <3Hz < 20 μm < 2 μm 1 μm (0.4 nm) 0.3 μm (1.6 pm) Plane wave >12Hz ~ 0.5 μm ~ 0.15 μm Additional limits dS RMS Dipole dθ RMS Dipole Dipole Random motion < 10 μm < 0.1 μradians 25 μm (0.036 nm) 0.58 μm (0.12 pm)

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**Closed Orbit Feedback Systems**

To insure beam stability exceeds these specifications a global feedback has been proposed Slow motion <1 Hz handled by closed orbit correction using all BPM and Correctors Global Feedback system using 4- BPM and 4- Correctors studied using SVD fit, with assumed BW 1 to 100Hz Correctors near to dipoles have stainless steel bellow chambers low eddy current Effect of feedback simulated for random quadrupole induced motion, with RMS amplitude of 1μm

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**Global Feedback Loop Open/Closed**

Open loop and closed loop RMS beam motion Reduction of motion in IDs 22,12 0.6, 0.8 μm (worst case) Open Closed

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**Local Feedback Loop each ID**

As IDs are installed, 2-user BPMs (UBPM) and 4- Fast Correctors (FHVC) are installed for closed bump correction of local beam motion X-ray BPM inputs are available to steer beam for beam line motion without effecting other users, no linear and minimum non-linear coupling

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Summary and R&D Work Quadrupole BBA of closed orbit, exploits the excellent alignment resolution, < 30μm, of magnets on the girder Vibration and noise levels appear adequate for stable operation with girder design, thermal stability adequate but will be studied Global and Local feedbacks to insure beam stability is adequate and to handle relative motion of beam line components Tolerances and control of user motion needs better definition along with XBPM calibration and response measurements

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