1. 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

2. 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

3. 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

4. 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

5. 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

6. 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

7. 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

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

9. 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

10. 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

11. 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)

12. 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

13. 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 

14. 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)

15. 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

16. 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

17. 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

18. 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