# Presentation: 205057

## Alignment and Beam Stability

**S.L. Kramer for the NSLS-II Team**

- 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

## 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

## 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

## 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

## 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

## Quadrupole BBA 

- Quadrupoles introduce orbit steering with strength changes if closed orbit is offset by *x* and *y *then the steering with strength change *K**2 *is

- Assuming 1μm BPM resolution and *K**2* ~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

## 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

## BPM and Corrector Placement 

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

## Number of BPMs and Correctors

- 3-5 BPMs needed from tunes (*ν**x** , **ν**y** ~ *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

## 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

## 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)

## 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

## Correlated Quadrupole Errors

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

- 1μm 

- 1μm 

## 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.

## 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

## Global Feedback Loop Open/Closed 

**Global Feedback Loop Open/Closed **

**Open loop and closed loop RMS beam motion**
**   ****Reduction of motion in IDs 22,12 ********0.6, 0.8 ****μ****m (worst case)**

-  Open

-  Closed

## 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

## 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