1 brookhaven science associates issues on closed orbit feedback for nslsii nsls-ii stability...

1 BROOKHAVEN SCIENCE ASSOCIATES

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

Outline


Beam stability requirement based on 10% beam size

The minimum beam size is 2.7 m at =1m ,

assuming y 0.1nm/4.

Goal


Machine model used in feedback system performance calculation for DBA30

Qx = 32.35 Qy = 16.28


k

kik

iQiii

i ss

yklss

sy

|))(|cos(sin2

)()|)()(|cos(

sin2

)()(

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:

i

Qiiji

ij

Bjj yKlyy )|)(|cos(sin20

BPM motion+noise

Quad motion

Quad strength

Trim kick strength

BPM outputsignal

Beam position


k

kjk

kj

jy

|)|cos(sin2

Response Matrix

Ry

tT

In matrix form:

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


noisee yUWTG

f~

1

1 1

Effect of feedback

noisee yUWf~1

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:

V

R

U

W-1 V

fe fc

y

PID

R

W-1fe fc

y

-G

T()

t

VUWR~


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

10 20 30 40 50 60

20

40

60

80

Δ

y (

m)

Δ

y (

m)

Δ

y (

m)

tri

m(

rad )

trim

( )

()

y14

Δ

y BPM position

10 y 10 trim

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)

20 40 60 80 100 120

0.02

0.04

0.06

0.08

0.1

0.12 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


10 20 30 40 50 60

25

50

75

100

125

150

175

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

Δy

(nm

)

(nm

)BPM

Trim position

y

Tolerance on Vertical Trim Power Supply Resolution


• 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 μradNoise 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.

10 20 30 40 50 60

20

40

60

80

off

on

Δ

y (

m)

Δ

y (

m)

Δ

y (

m)

tri

m(

rad )

trim

( )

()

y17

Δ

y BPM

position

10 y 10 trim

Required trim strength is 1 µrad

BPM in 5m straight

1 brookhaven science associates issues on closed orbit feedback for nslsii nsls-ii stability...

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