brookhaven science associates alignment and beam stability s.l. kramer for the nsls-ii team magnet...
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BROOKHAVEN SCIENCE ASSOCIATES
Alignment and Beam StabilityAlignment and Beam Stability
S.L. Kramer for the NSLS-II TeamS.L. Kramer for the NSLS-II Team
• Magnet Alignment TolerancesRandom 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
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Quadrupole Alignment
Misalignment of quadrupole centers, drive large Closed Orbit DistortionClosed 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 TolerancesMagnet Alignment Tolerances
• Quadrupole and Sextupoles have centers measured to aresolution 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 BPMswhere 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
2 3
1 1( ) ( ) ( ) ( )
4 2x x xQ s K L x s b L x
2 3
1 1( ) ( ) ( ) ( )
4 2y y yQ s K L x s b L x
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
2 2
( ) ( )( ) 5.2
2sin( )x x
x
s quadx s K L x K L x
Q
2 2
( ) ( )( ) 7.2
2sin( )y y
y
s quady s K L y K L y
Q
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 misalignmentto 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 armLarge 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 6 BPM x 6 Correctors
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Roll Errors and Coupling Correction
• Johan covered magnetic field error tolerances and ID effectsGirder 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 toincrease 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’sσy ~ 2.8µm and σy’ ~ 3µrad
• Centroid motion of beam cause effective emittance growth or reduced brightness for users for frequency > fsample(user)eff o cm
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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) < 10-20 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
Tolerance Limits
dX RMS Quads dY RMS Quads X RMS (εx) Y RMS (εy)
Random motion < 0.33 μm < 0.023 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 1 μm (0.4 nm) 0.3 μm (1.6 pm)
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)
•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.
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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 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