# Presentation: 344034

- Issues on Closed Orbit Feedback for NSLSII
- NSLS-II Stability Workshop
- April 18-20, 2007
- Li-Hua Yu

## 1. Calculation on the performance showing vibration problem can be solved by fast feedback
2. Requirement on power supply strength

- 2. Requirement on power supply strength

**Outline**

## Goal

- Beam stability requirement based on 10%  beam size
- The minimum beam size is 2.7 m at  =1m ,
- assuming y  0.1nm/4.

## Machine model used in feedback system performance calculation for DBA30

- Qx =   32.35          Qy           =         16.28

## Orbit feedback system calculation: BPM vibration and noise errors are included

- BPM signals without feedback

- BPM signal is used to calculate the corrector trim kick strength and the orbit movement with feedback:

- Trim kick strength

- BPM output
- signal

- Beam position

## Response Matrix

- In matrix form:

- Frequency response of trims and vacuum chamber eddy current T(): (T(0)1)

## Effect of feedback 

**Effect of feedback**** **

- Without feedback:

- If G is a large positive number, with feedback loops on, the error 	signal is reduced by a factor of 1+G at DC (T(0)=1).
- At higher frequency, TG is a complex number and has to be 	designed to avoid oscillation.
- Assume all the trims have the same frequency response

- With feedback:

## Amplification factor with and without feedback system on

- Assuming 1 micron random vibration of quads and BPMs
- Trim strength is expressed in unit of micro-radian. The calculation uses 4 correctors next to sections of stainless vacuum chamber for each half superperiod.

- off

- on

- Required trim strength is 1 μrad

## Ratio of vertical beam motion over beam size with the feedback system on shows the stability is almost satisfied except at short straight sections it is slightly larger if quads and BPMs motion is 0.4 micron. The calculation uses 4 correctors next to sections of stainless vacuum chamber for each half superperiod

- y  0.1nm/4.

- Z (m)

- y y

- If we design the BPM support in short straight sections such that temperature change of 0.1 ̊C causes 0.3 motion, the beam motion will be less than10% of beam size there.

## BMPs and Trims in the design after CDR

- Fast trim to be used in fast feedback system

- BPM to be used in fast feedback system

## Tolerance on Vertical Trim Power Supply Resolution

- Orbit motion due to trim power supply noise of 1 nrad rms

**If we require beam motion due to the trim noise at the beam waist where ********y****=1m is less than 0.25μm=250nm, the rms trim noise should be less than 10nrad.**
**The last digit should be less than 10 nrad/0.29 = 30nrad**
**If the maximum trim strength is 1 mrad, we need the last digit to be 30 ppm**
** ****	****                                         ****0.1mrad                                               300 ppm**

- 

- Δ

- y

- (nm)

- 

- (nm)

## Maximum motion of quads and BPM that feedback can correct: < 0.3μm
Power Supply Specification:

                                 Frequency        Strength - RMS  		<  5   Hz               800   μrad    		20     Hz	           100   μrad  		100   Hz               10     μrad 		1000 Hz	             1     μrad 		Resolution of last bit:  0.01 μrad		Noise Level : 0.003 urad    ( ~ 4 ppm of 800 μrad

May need special BPM supports in short straight sections to reduce temperature 
	dependence to <0.1 for 0.1 ̊C change. 
All trims (magnet, power supply, vacuum chamber Eddy current included) required 
	to have same frequency response with bandwidth 60-100Hz.

- Power Supply Specification:
-                                  Frequency        Strength - RMS  		<  5   Hz               800   μrad    		20     Hz	           100   μrad  		100   Hz               10     μrad 		1000 Hz	             1     μrad 		Resolution of last bit:  0.01 μrad		Noise Level : 0.003 urad    ( ~ 4 ppm of 800 μrad
- May need special BPM supports in short straight sections to reduce temperature
- 	dependence to <0.1 for 0.1 ̊C change.
- All trims (magnet, power supply, vacuum chamber Eddy current included) required
- 	to have same frequency response with bandwidth 60-100Hz.

**Summary of Requirements**

## Specially designed BPM support at 5m straights to reduce temperature dependence

- Assuming 1.2 micron random motion of quads and BPMs, and assuming
- UBPMs in the short straight are used in the feedback to replace the BPM next to Q22 and support with invar so that the motion due to temperature change is 0.4 micron, the beam motion in the short straight is reduced to less than 0.3 micron.

- BPM in 5m straight