NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-1 TLS and TPS Vertical Beam Size...

NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-1

TLS and TPS Vertical Beam Size Control and Beam Stability Issues

C.C. Kuo

NSRRC XBPM and Beam Stability Mini WorkshopSeptember 11-12, 2008

NSRRC


Outline

1. Challenges of a high-performance light source

2. Sources of the beam perturbations

3. Emittance coupling control

4. Orbit stability and beam instabilities control


Challenges of a high-performance LS

• High brilliance, low emittance, low emittance coupling ratio, high nonlinear lattice effects

• Small beam size, stringent stable beam orbit

• High current, low beam impedance, good vacuum

• Many insertion devices with small sizes of vacuum pipes

• High reliability, reproducibility and flexibility

• Reasonable beam current lifetime and top-up injection

NSRRC TLS

TPSTPS

effyeffxpypypxpx

photon IdtdNB

,,,,,,

2''4

/

[photon/sec/mm2/mrad2/0.1%bandwidth]


TLS and TPS Optical functions OPTICAL FUNCTIONS TPS 79H2

0 10 20 30 40 50 60 70 800

5

10

15

20

25

30

S(m)

Op

tica

l F

un

cti

on

s (

m)

x

y

x*10

emittance = 1.6 nm-rad

TLS: 25.6 nm-rad @1.5 GeV TPS: 1.6 nm-rad @ 3GeV


TLS and TPS ParametersTLS TPS

Energy (GeV) 1.5 3.0

Beam current (mA) 300 400

Circumference (m) 120 518.4

Nat. emittance x (nm-rad) 25.6 1.6

Cell / symmetry / structure 6 / 6 / TBA 24 / 6 / DBA

Straights 6m*6 12m*6+7m*18

Betatron tune x /y 7.18 / 4.13 26.2 / 13.25

Mom. comp. (1, 2) 6.678×10-3, -3.89×10-3 2.4×10-4, 2.1×10-3

Nat. energy spread E 7.45×10-4 8.86×10-4

Damping time (ms) ( x / y / s) 7.2 / 9.3 / 5.5 12.20 /12.17 / 6.08

Nat. chromaticity x / y -15.3 / - 7.9 -75 / -27

RF frequency (MHz) 500 500

RF voltage (MV) 1.6 3.5

Harmonic number 200 864

SR loss/turn, dipole (keV) 128 852.6

Synchrotron tune s 1.52×10-2 6.09×10-3

Bunch length (mm) 6.5 2.86


Electron beam size

Emittance ratio=1% due to betatron coupling

Source point σx (μm) σx’ (μrad) σy (μm) σy’ (μrad)

TPS1.6 nm-r

ad

12 m straight center

165.1 12.4 9.8 1.6

7 m straight center

120.8 17.2 5.1 3.1

Dipole 39.7 76.1 15.8 1.1

TLS25.6 nm-

rad

6 m straight center

526.9 50.3 27.7 9.5

Dipole 125.1 287.8 55.8 8.5


Sources of the beam perturbations

• Emittance coupling change

• Collective instabilities – single-bunch and coupled-bunch, longitudinal and transverse

• Beam-ion instabilities

• Orbit perturbations


Emittance Coupling Sources• Linear betatron coupling due to skew quadrupole err

ors from (1) quadrupole rotation errors and (2) vertical closed orbit distortion in sextupoles.

• Linear betatron coupling from solenoid field.• Spurious vertical dispersion caused by

(A) (1) vertical bend error from bending rotation errors and (2) vertical closed orbit errors in th

e quadrupoles(B) dispersion coupling due to skew quadrupole

errors in the dispersive region which are from (3) quadrupole rotation errors in the dispersiv

e region and (4) vertical closed orbit distortion in sextupoles in the dispersive region.


)cos(,1,1 lJJGJJH yxyxlyx

or 2 where

,2

1

21

])([

,1,1

coss

lisyx

i

l

ykkkk

dsek

eG yxyx

B

the minimum separation of the normal mode tunes is || ,1,1 lG

yx .

Coupling ratio is defined as:22

2

2G

G

.

i

iyixsetcoi

iyixquad lkylkG ,,2

2,,,,2

12

2 22

1

Betatron Coupling driving strength：

Betatron Coupling


Betatron coupling

3,,2

109.0101.5

:TLS

13,,2

1061.31079.7

:TPS

22

2

2

,

5-24-2

22

2

2

,

3-24-2

yx

sexcoquad

yx

sexcoquad

G

G

yG

G

G

yG

Two major sources:(1) Quad rotation (2) Vertical orbit through sextupoles

TPS

TLSQaud roll=0.1 mrad rms


Spurious Vertical Dispersion

mCc

cIc

qdipoleyy

q

dipoleyyyyyy

qyq

y

132

2

2'2

22

10832.3,/2

/])([

:dispersion vertical todue emittance Vertical

iiiyi

y

icoi

ixiiyiii

ixiiyi

icoi

iiyii

i

iyi

ydipoley

LF

yLkLk

yLkL

22

2

2

,

22

2

222

1

2

,

2

1

2

2

2

2

2

sin8

1

,

sin8

1/

sexticoxii

quadixii

quadicoi

dipolesi

i

yk

k

ykF

,,2

,1

,,1

2

,

Vertical dispersion generated from all error sources can be expressed as:

2

,

-12-32

,

-12-3

y 107.1106.71078.4 10 18.5)( sextcoquadquadcodipole yyradnm TPS:

2

,

-12-22

,

-12-2

y 103.2101.1103.1 10 2.1)( sextcoquadquadcodipole yyradnm TLS:

Unit: mm, mrad


Spurious Vertical Dispersion2

,

-12-32

,

-12-3

y 107.1106.71078.4 10 18.5)( sextcoquadquadcodipole yyradnm TPS:

2

,

-12-22

,

-12-2

y 103.2101.1103.1 10 2.1)( sextcoquadquadcodipole yyradnm TLS:

Unit: mm, mrad

TPSTLS

Dipole roll=0.2 mrad rmsQuad roll=0.1 mrad rms


Cross Orbit Response MatrixCross Orbit Response Matrix

Vertical orbit and dispersion response

ymcc GyxKxKsG 2

~

1)(

,

xcxcy yKKyKGsF 2

~

11)(


Response Matrix skew quads and sextupoles only

k

HjHkj

Vikk

sHj

Hsj

Vissmic RRlKRRlyKy ,)()()( )()(

1

~)()(

2

,)()()( )(~

1)(

2 xVikk

kx

Vissm

siy RlKRlyK

VMK

TPS:M: 16296 X 24 or 48 K: 24 or 48 skew quads V: 16296 (96*168+168)168 Monitors, 4 correctors per section, 96 in total. Using SVD method to get K as wanted correction.

TLS:M: 1176 X 8 K: 8 skew quads V: 1176 (24*48+48)48 Monitors, 4 correctors per section, 24 in total. Using SVD method to get K as wanted correction.

M : unified response matrix for a set of horizontal steering and installed (or virtual) skew quadsV : measured normalized vertical orbit and dispersion, K : skew quad array in the ring can be obtained using SVD for a linear equation such that the betatron coupling and vertical dispersion can be minimized simultaneously.


Experimental results (TLS)

correctionafter

0016.0||

correction before

0119.0||

3,1,1

3,1,1

G

G

Coupling ratio is defined as:

22

2

2G

G

C.C. Kuo, et. al EPAC2002

No de-convolution yet


C.C. Kuo, et. al EPAC2002

TLS results


Vertical beam size from interferometer at NSRRC

um

Top-upFBs ON

2008/8/29


Sensitivity to alignment in TPSError Type (rms) (<bend>m Quantity F(Driving Term) <2>[m] <y>[mm] y[m-rad] y/x

Dipole Rotation: 0.2 mrad 2.38E-05 6.57E-08 1.02E+00 2.07E-13 0.01%

Quadrupole Rotation: 0.1mrad x 1.97E-05 2.41E-08 6.20E-01 7.60E-14 0.00%

Vertical Quadrupole Position: 0.1mm y y 1.41E-04 1.52E-06 4.92E+00 4.78E-12 0.30%

Vertical Sextupole Position: 0.1mm y xy 2.33E-04 5.41E-07 2.94E+00 1.70E-12 0.11%

Total: 0.43%

Error Type (rms) G (%)

Quadrupole Rotation: 0.1 mrad 5.04E-02 1.40E-03 1.53E-01

Vertical Sextupole Position: 0.1 mm 5.04E-02 3.00E-03 7.07E-01

Spurious dispersion

Betatron coupling

Increase tune separation to 0.1 will reduce K by a factor about 4


CORRECTION OF VERTICAL DISPERSION AND BETATRON COUPLING

Lattice: TPS 79H2

Using cross-plane response matrix and SVD method to correct both betatron coupling and vertical dispersion with a set of skew quadrupoles.

With 48 skew quads, <1% emittance ratio can be achieved, and the maximum strength is < 5.4x10-3 m-1

100 machinesBefore correction

100 machinesAfter correction


Efforts for Beam Stabilization in TLS

1. Orbit stability:Elimination of sources

Feedback system 2.Coupled-bunch instability:

RF gap voltage modulation ( ~ Oct. 2004)Superconducting RF ( Dec. 2004 ~)Coupled-bunch feedback systems (FPGA-based processor)

Transverse (Nov. 2005), 300 mA top-upLongitudinal (Feb. 2006)


TLS orbit


Orbit at NSRRC:

COD - y

-10

-8

-6

-4

-2

0

2

4

6

8

10

0 20 40 60 80 100 120

s(m)

cod-

y (m

m)

cod before correction

cod after correction

cod mad simulation before correction

COD - X

-8

-6

-4

-2

0

2

4

6

8

10

0 20 40 60 80 100 120s(m)

cod-

x (m

m)

cod-x before correction

cod-x after correction

cod mad simulation before correction

)()()3.9()()6.22()(

)10()()5.3()()3.32()(

2,

22,

22,

3222,

22,

mradmmzmmz

B

Bmmxmmx

rmsBMsrmsqrmsco

rmsrmsqrmsco

COD before correction (compared with model simulation with errors input) in SRRCStorage ring at commissioning stage in1993. Corrected COD is shown.Qx=7.18, Qy=4.1347 BPM, 24HC, 30 VC


32 micron, rms (H) and 40 micron, rms (V) after correction32 micron, rms (H) and 40 micron, rms (V) after correction


Some examples related to orbit perturbations at NSRRC

22

23

24

25

26

27

28

29

30

0 2000 4000 6000 8000 10000

Tem

pera

ture

(de

gree

C)

Time (sec)

inlet temperatureoutlet temperature

chamber temperature

-10

-5

0

5

10

15

20

25

30

0 2000 4000 6000 8000 10000

Hori

zonta

l orb

it (

um

)

Time (sec)

0.1

0.105

0.11

0.115

0.12

0.125

0 100 200 300 400 500 600 700

Vert

ical orb

it a

t r3

bpm

5Y

(m

m)

Time(sec) 10 minutes around the ring

crane movement effect on the orbit

Cooling water temp. variation While adjusting PID controller

Orbit oscillationsdue to cooling water temp.

Vertical orbit changes during crane motion

Orbit drift during ID gap changew/ and w/o feedback

One turn


Y Orbit Distortion (inbound)

U5 Gap (mm)0 50 100 150 200 250

dYrms (micron)

0

1

2

3

Yrms at 138mA 98/10/02 Yrms at 157mA 98/10/02 Yrms at 108mA 98/10/08 Yrms at 124mA 98/10/14 Yrms at 138mA 98/10/28

Orbit feed-forward for ID gap change:H. Chang, SRRC

X Orbit Distortion (inbound)

U5 Gap (mm)0 50 100 150 200 250

dXrms (micron)

0

1

2

3

4

5

Xrms at 138mA 98/10/02 Xrms at 157mA 98/10/02 Xrms at 108mA 98/10/08 Xrms at 124mA 98/10/14


Girder Displacement

• Main cause: air temperatureSensitivity to air temp.: ~10 μm / ℃Induced beam orbit drift: 20-100 μm / ℃

• Current status: < ± 0.1 μm per 8 hr shift Air temp. : < ± 0.1 (utility control system impro℃

ved) Thermal insulator jacket

-200 0 200 400 600 800 1000 1200 14000.92

0.94

0.96

0.98

1.00

-200 0 200 400 600 800 1000 1200 140024.0

24.5

25.0

25.5

26.0

Beam Position

mm

min

Air Temperature

De

gre

e (

C)

0 25 50 75 10024

25

26

27

28

Dis

plac

emen

t (£g

m)

Tunnel Air Temp. Girder Disp. Outer Girder Disp. Inner

Time (Hours)

Tem

pera

ture

(¢J)

-20

-15

-10

-5

0

J.R. Chen et. al.


Magnet (Water Temp.)

100 200 300 40022

24

26

28

Mag-Water Temp. Beam Position

Time(min.)

Tem

pera

ture

(¢J)

0.22

0.23

0.24

0.25

0.26

Posi

tion

(mm

)

Caused by the temperature fluctuations of magnet cooling waterMagnet deformed ~10μm/ ℃Induced beam orbit drift: 5-50 μm / ℃

Current statusCooling water temp.: ~ ± 0.1℃

J.R. Chen et. al.


Expansion of Vacuum Chamber

• Caused by synchrotron light irradiation. Sensitivity to water temp.: ~10 μm / ℃

Move the girder (~0.3μm/ ) and BPM (~1℃ μm/ ) ℃Induced beam orbit drift: ~10-30 μm / ℃

• Current statusVacuum cooling water temp.: ~ ± 0.5℃

0 6 12 18 2419.5

20.0

20.5

21.0

21.5 Girder Displacement Beam Current

Time (Hours)

Dis

plac

emen

t (£g

m)

0

100

200

Bea

m C

urre

nt (m

A)

0 200 400 600 800 1000 1200 1400-0.08-0.06-0.04-0.02

0 200 400 600 800 1000 1200 14000.51.01.52.0

0 200 400 600 800 1000 1200 14002425262728

0 200 400 600 800 1000 1200 14000

100200

Beam Position

mm

min

BPM Displacement

um

Vac-chamber Temp

Tem

p (

C)

Beam Current

mA

J.R. Chen et al.


TLS beam response to ground wave and mechanical vibration

0 10 20 30 40 50 60 70 80 9010

-10

10-5

100

105

Frequency[Hz]

Px(f)

[ m

2 /Hz]

Horizontal Ground Vibration at NSRRC Site.

Measured on Ground

Measured on Magnet

e-Beam(Rmax

* Measured on Magnet)

0 10 20 30 40 50 60 70 80 9010

-4

10-2

100

102

Frequency[Hz]

I x(f) [u

m]

Measured on Ground

Measured on Magnet

e-Beam(Rmax


0 10 20 30 40 50 60 70 80 9010

-10

10-5

100

105

Frequency[Hz]

Py(f)

[ m

2 /Hz]

Vertical Ground Vibration at NSRRC Site.

0 10 20 30 40 50 60 70 80 9010

-4

10-3

10-2

10-1

100

101

Frequency[Hz]

I y(f) [u

m]

Measured on Ground

Measured on Magnet

e-Beam(Rmax


Measured on Ground

Measured on Magnet

e-Beam(Rmax


V=500 m/s


Closed Orbit : tens microntens micron rms w.r.t. target orbit with DC

correction schemes.

Orbit distortions: < 10 micron rms during insertion gap s

can can be compensated for using look-up correction ta

bles.

Beam orbit stability: a few micrometer level (peak-to-pe

ak) with a global feedback system. (temperature control,

electricity upgrade, etc.)

Closed Orbit and Orbit Stability Closed Orbit and Orbit Stability (low frequency)(low frequency)


TLS orbit log (0.1Hz sampling)2008/08/29

mm

mm

K.T. Hsu will talk about high frequency behavior

mm

mm

mm


TLS instabilities and cures


Ref -20 dBm Att 10 dB

*

*

A

SGL

RBW 3 kHzVBW 30 kHzSWT 11.5 s

Center 499.654 MHz Span 100 MHz10 MHz/

1 APCLRWR

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

A22

Date: 12.APR.2005 02:19:56

Ref -20 dBm Att 10 dB

*

*

A

SGL

RBW 3 kHzVBW 30 kHzSWT 11.5 s

Center 499.654 MHz Span 100 MHz10 MHz/

1 APCLRWR

-120

-110

-100

-90

-80

-70

-60

-50

-40

-30

-20

A22

Date: 12.APR.2005 02:19:06

TFB OFF

TFB ON

TLS - Transverse Performance

Beam Spectrum

Courtesy by K.T. Hsu


TLS - Transverse Performance

Transverse Feedback OFF Transverse Feedback ON

Synchrotron Radiation Monitor



Loop Closed

Loop Open

Snapshot of Synchrotron Radiation

Beam Profile(w/o Longitudinal

Feedback)

Grow/Damp test results @ 300 mA

0

5

10

50

100

150

2000

10

20

30

40

50

60

Time (ms)

a) Osc. Envelopes in Time Domain

Bunch No.

Arb

. U

nit

0

5

10

0

50

100150

0

2

4

6

8

Time (ms)

b) Evolution of Modes

Mode No.

Arb

. U

nit

0

5

10

50

100

150

2000

5

10

15

Time (ms)

a) Osc. Envelopes in Time Domain

Bunch No.

mm

0

5

10

0

50

100150

0

1

2

3

4

Time (ms)

b) Evolution of Modes

Mode No.

mm

0 50 100 150 2000

0.05

0.1

0.15

0.2

0.25

0.3

0.35

Mode Number

Rela

tive M

agnitude

Horizontal Plane

0 50 100 150 2000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Mode Number

Rela

tive M

agnitude

Vertical Plane

Horizontal

Vertical

VerticalHorizontal

ModalSpectrum



TLS - Longitudinal Performance

Courtesy by P.J. Chou and M.H. Wang



Evolution of the stable longitudinal mode during user shiftNo longitudinal feedback

SRF 5 ~ 10 increase in threshold current



Conventional RF cavity + RF gap voltage modulator => Longitudinal stable beam

Superconductor RF cavity => Longitudinal stable beam no feedback

Time dependence of beam profile (SR monitor @ ≠ 0)


Time dependence of beam profile (SR monitor @ ≠ 0)



Streak Camera Observation

Loop Open

Loop Closed

One Turn

One Turn

Loop Closed -> Open -> ClosedOne Turn

Loop Open

Loop Open

Snapshot of the Synchrotron

Radiation Beam Profile

Loop Closed

Loop Open


TLS performance with longitudinal feedback


Photon Beam stability through 50 um pinhole

2008/08/29

Top-up 300 mA,Orbit feedback ONTransverse and longitudinal feedbacks ON


TLS operation


TLS photon beam stability


TLS orbit reproducibility from pinhole monitor


TPS orbit


TPS COD Correction Scheme

Precision ~ 15 m

7 BPM each cell3 HC(+1) and 4 VC(+1) each cell for SVD but all sextupoles are with HC and VC.

CV CH CV CH CV CH CVSQ SQ


COD Error Sources and Amplification Factor

Error Source (rms) 3 sigma truncated

Girder displacement x, y (mm) 0.1

Girder roll θ (mrad) 0.1

Quad and sext displacement x,y w.r.t. girder (mm)

0.03

Dipole displacement x,y (mm) 0.5

Dipole roll θ (mrad) 0.1

Dipole field error (10-3) 1

BPMs displacement x, y (mm) 0.1

Amplification factor Axrms (max)

Ay rms (ma

x)

Quad displacement 55 (97) 40 (51)

Girder displacement 30 (54) 8 (10)

Dipole roll θ - 5.8 (7.8)

Dipole field error 1.1 (1.9) -

COD due to Errors:Horizontal: 3.8 mm r.m.s.Vertical : 2.2 mm r.m.s.


COD Correction

　 Before Correction COD and Optics correction

After CorrectionXC=2,4,6/YC=1,3,5,7

　 Horizontal Vertical Horizontal Vertical

COD at BPMs mm (r.m.s.) 3.79 2.22 0.0807 0.0676

Max. COD mm 21.11 9.27 0.371 0.338

Max. Cors Strength mrad 　　 0.402 0.245

Mean Cors Strength mrad 　　 0.0788 0.0484


Correction Capability and Residual COD

Correctors

Used

Number of

eigenvalues

used

Mean of

<|cor. Str.|>

(mrad)

Max of

|cor. Str.|

(mrad)

Max |COD| at

BPM (mm)

rms COD at

BPM (mm)

(2,4,6) 72 7.88E-02 4.02E-01 3.71E-01 8.07E-02

(1,4,6) 72 7.34E-02 3.97E-01 3.46E-01 8.35E-02

(2,4,7) 72 7.35E-02 4.34E-01 3.66E-01 8.32E-02

(1,4,7) 72 6.69E-02 3.41E-01 3.67E-01 8.55E-02

72 3.20E-02 1.70E-01 3.53E-01 8.17E-02

96 5.44E-02 4.35E-01 2.92E-01 6.87E-02

144 1.22E-01 7.93E-01 2.12E-01 4.06E-02

Hor

izon

tal

168,

(C1-C7)x24

168 1.63E-01 9.73E-01 4.92E-02 7.71E-03

(1,3,5,7) 96 4.84E-02 2.45E-01 3.38E-01 6.76E-02

(2,3,5,7) 96 5.64E-02 3.51E-01 3.36E-01 7.18E-02

48 1.35E-02 8.73E-02 3.95E-01 9.23E-02

72 1.98E-02 1.43E-01 3.42E-01 7.97E-02

96 3.08E-02 1.92E-01 3.10E-01 6.82E-02

144 7.21E-02 4.43E-01 2.99E-01 4.13E-02

Ver

tical

168,

(C1-C7)x24

168 1.10E-01 8.95E-01 7.52E-02 1.43E-02


Ground vibration effects

To guarantee the photon brilliance, beam orbit disturbance due to ground wave need to be controlled.

V

H

Amplification v=500 m/sec, girder transmission = 1


TPS Collective Effects

• SC RF cavities will not cause coupled bunch instability in nominal operation.

• Resistive wall impedance will cause transverse coupled bunch instability. To stabilize the beam requires positive chromaticity( > 5), not recommended.

• At present the microwave instability is the dominant limitation of single bunch current.

• The more insertion devices we install, the more detrimental the transverse instabilities are.

• Active transverse feedback system is required for stable operation.

• We must strive to keep good vacuum condition in the storage ring.

P.Chou


Major sources of broadband impedance and microwave instability threshold

Total broadband impedance: |Z/n|= 0.36

A. Rusanov

(K. Oide’s code)


summary

• The beam size control including coupling correction, instability cures or feedback system in TLS and TPS are discussed. Some orbit perturbation issues included in this talk. Orbit feedback issues will be covered by Kuotung Hsu.

• With a set of skew quadrupoles in the ring, one can control both betatron coupling and vertical dispersion.

• ID gaps and phases will change coupling strength and orbit.

• Both TLS and TPS need transverse feedback systems to stabilize the beam in the transverse planes.

• In TLS, we need longitudinal feedback system for high current operation (>200 mA) even we replaced the room-temperature cavity with superconduting type.

• With SRF in TPS, we might not need longitudinal feedback system if the vacuum components are well taken care of.


Thank you

NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-1 TLS and TPS Vertical Beam Size...

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Transcript of NSRRC XBPM and Beam Stability Mini Workshop 2008/09/11~12 cckuo-1 TLS and TPS Vertical Beam Size...