sls at the paul scherrer institute (psi), villigen,...

Orbit Stability at the SLS

IWBS2004

SLS at the Paul Scherrer Institute (PSI), Villigen,Switzerland

Michael Boge 1


IWBS2004

Contents

• SLS Layout

• Booster & Storage Ring (SR)

– Lattice Calibration

– Stability∗ Requirements∗ Noise Sources∗ Short Term∗ BBA/Golden Orbit∗ Orbit Correction∗ Medium Term (“Top-up”)∗ Transition Slow→ Fast Orbit Feedback∗ Feed Forward, X-BPM & Bunch Pattern Feedback∗ Long Term

• Conclusions

Michael Boge 2


IWBS2004

SLS Layout

• Pre-Injector Linac

– 100 MeV

• Booster Synchrotron

– 100 MeV – 2.4 (.7) GeV @ 3 Hz

– ǫx = 9 nm rad

• Storage Ring

– 2.4 (.7) GeV, 400 mA

– ǫx = 5 nm rad

• Eight Beamlines:MS – 4S, µXAS – 5L,DIAG – 5D, PX – 6S,LUCIA – 7M, SIS – 9L,PXII – 10S, SIM – 11M

Michael Boge 3


IWBS2004

Booster - Design

– 3 FODO arcs with 48 BD (+SD) 6.4410◦and 45 BF (+SF) 1.1296◦

– 3× 6 Quadrupoles for Tuning, 54 BPMs, 2× 54 Correctors–± 15 mm× ± 10 mm Vacuum Chamber– Energy:100 MeV→ 2.7 GeV, Repetition Rate:3 Hz, Circumference:270 m– Magnet Power:205 kW, ǫx @ 2.4 GeV:9 nm rad

Injection

StorageRing

Linac

BoosterInjection

0 5 10 15 20 25m

OTR

Maximum Energy GeV 2.7

Circumference m 270

Lattice FODO with 3straight s of 8.68 m

Harmonic number (15x30=) 450

RF frequency MHz 500

Peak R F voltage MV 0.5

Maximum current mA 12

Maximum rep. Rate Hz 3

Tunes 12.39 / 8.35

Chromaticities −1 / −1

Momentum compaction 0.005

pread, rms

t 2.4 GeVEquilibrium v

Emittance 9

Radiation l oss keV/ turn 233

Energy s 0.075 %

Partition numbers (x,y, (1.7, 1, 1.3)

Damping times (x,y, ms (11, 19, 14)

alues a

nm rad

ε )

ε)

Michael Boge 4


IWBS2004

SR - Design

• 12 TBA: 8◦ / 14◦ /8 ◦

• 12 Straight Sections:

– 3 × 11 m(nL )

∗ Injection , 2×UE212, U19

– 3 × 7 m (nM )

∗ 2×UE56, UE54

– 6 × 4 m (nS)

∗ 2× RF, W61, 2×U19

• Energy: 2.4 (.7) GeV

• ǫx: 5 nm rad

• Current:350 mA (400 mA)

• Circumference: 288 m

• Tune:20.43/ 8.73(Femto Optics)

• Natural Chromaticity:-66 / -21

βyη

x

βx

0 48arc (TBA 8−14−8)arc (TBA 8−14−8) s[m]0

10

20

30

40

Beta functions [m]

−0.2

Dispersion [m]

−0.4

0.2

0.4

0

Energy [GeV]Circumference [m] 2

2.4 (2.7)88

RF frequency [MHz] 500Harmonic number (25x3x5 =) 480Peak RF voltage [MV] 2.6Current [mA] 400Single bunch current [mA] ≤ 10Tunes 20.38 / 8.16

Natural chromaticity −66 / −21

Momentum compaction 0.00065Critical photon energy [keV] 5.4Natural emittance [nm rad] 5.0Radiation loss per turn [keV] 512Energy spread [10−3] 0.9Damping times (h/v/l) [ms] 9 / 9 / 4.5Bunch length [mm] 3.5

Michael Boge 5


IWBS2004

SR - Lattice Calibration - Energy Spread, Energy

1e+06

1.01e+06

1.02e+06

1.03e+06

1.04e+06

1.05e+06

1.06e+06

1.07e+06

1.08e+06

1.09e+06

2.434e+092.4345e+092.435e+092.4355e+092.436e+092.4365e+092.437e+092.4375e+092.438e+09

Cur

rent

*Tou

sche

k_Li

fetim

e [m

A*s

]

Energie [eV]

DataFroissart−Stora Fit

Polarized LevelDepolarized Level

• 7th Harmonic ofU24 at 8 mm gap:

– σe = 0.9·10−3

– Beam EnergyE = 2.44 GeV

• Resonant Spin Depolarization:νspin = 5.45,Peq ≈ 91 % withτp = 30 min

– Beam EnergyE = 2.4361±5·10−5 GeV

Michael Boge 6


IWBS2004

SR - Lattice Calibration - Beta Functions

174 Quadrupoles with Individual PS→→

Gradient Correction:

• Procedure:

1. Measure< βi > for i=1..174δν = − 1

4π

∮

β(s)δk(s)ds

Precision:≈ 1.5/ 1.0%

2. Fit Errorsδki to < βi > (SVD)

3. Correct< βi > with -δki

4. Measure< βi > again

• Results:

– Horizontalβ Beat:≈ 4 %

– Verticalβ Beat:≈ 3 %

0

0

5

5

10

10

15

15

20

20

25

25

30

30

0 50 100 150 200 250

aver

age

beta

x [m

]av

erag

e be

tay

[m]

s [m]

measurement

measurement

model

model

measurement−model

measurement−model

betax beat ~4%

betay beat ~3%

Michael Boge 7


IWBS2004

SR - Stability - Requirements

• βx = 1.4 m, βy = 0.9 mat ID position of section nS→

σx = 84µm, σy = 7 µm assuming emittance couplingǫy/ǫx = 1 %

• With stability requirement∆σ = 0.1× σ →

Michael Boge 8


IWBS2004

SR - Stability - Noise Sources

• Short term (<1 hour):Ground vibration induced by human activities, mechanical devices likecompressors and cranes or external sources like road trafficpotential-ly attenuated by concrete slabs, amplified by girder resonances and s-patial frequency dependent orbit responses, ID changes (fast polariza-tion switching IDs<100 Hz), cooling water circuits, power supply (PS)noise, electrical stray fields, booster operation, slow changes of ID set-tings, “top-up” injection.

• Medium term (<1 week):Movement of the vacuum chamber (or even magnets) due to changesof the synchrotron radiation induced heat load especially in decayingbeam operation, water cooling, tunnel and hall temperaturevariations,day/night variations, gravitational sun/moon earth tide cycle.

• Long term (>1 week):Ground settlement and seasonal effects (temperature, rainfall) resultingin alignment changes of accelerator components including girders andmagnets.

msec

sec

hours

days

weeks

years

Michael Boge 9


IWBS2004

SR - Stability - Short Term

f [Hz] Noise Source

3 booster stray fields

12.4 helium-refrigerator

15-50 girder resonances

50 power supplies&pumps

0 10 20 30 40 5010

−1

100

101

102

103

104

27.7 Hz

35.2 Hz

50.5 Hz

15.5 Hz

21.6 Hz

groundpower spectrum

FE calculation girder response

44.0 Hz

Frequency [ Hz ]

Py

( f

) [ n

m2 /

Hz

]

Ground

Quadrupole

Vertical vibration PSD (1-55 Hz)measured on the slab and a girder(Redaelli et al.).

Vertical orbit amplification factor Ay for planar waves:

orbi

t am

plifa

ctio

n A

y 10 Hz without girder

with girder

60 Hz

x20

x8

ground wave frequency (c=500 m/s) [Hz]

90 Hz

νy =8.28 (=14 Hz)

Vertical orbit PSD(1-60 Hz) without and with orbit feed-back @ BPM (βy=18 m):

µm1.7

Booster

Mains

Girder Resonances

IntegratedRMS noise

→ Integrated RMS motion σy only ≈0.4µm ·√

βy !

Michael Boge 10


IWBS2004

SR - BPM/Corrector Layout

sector

8 814

Quadrupole

Sextupole

Dipole

Horizontal / Vertical Correctors

BPMs

• 12sectors

• 6 BPMsand 6Horizontal/Vertical Correctors persector

• Correctors inSextupoles, BPMsadjacent toQuadrupoles

Michael Boge 11


IWBS2004

SR - Stability - BBA/Golden Orbit

phase [rad/2pi]

2 4 6 8

posy [mm]

−0.5

0

0.5b

pm

01

lbb

pm

01

leb

pm

01

ldb

pm

01

sdb

pm

01

seb

pm

01

sb

bp

m0

2sb

bp

m0

2se

bp

m0

2sd

bp

m0

2m

db

pm

02

me

bp

m0

2m

b

bp

m0

3m

bb

pm

03

me

bp

m0

3m

db

pm

03

sdb

pm

03

seb

pm

03

sb

bp

m0

4sb

bp

m0

4se

bp

m0

4sd

bp

m0

4ld

bp

m0

4le

bp

m0

4lb

bp

m0

5lb

bp

m0

5le

bp

m0

5ld

bp

m0

5sd

bp

m0

5se

bp

m0

5sb

bp

m0

6sb

bp

m0

6se

bp

m0

6sd

bp

m0

6m

db

pm

06

me

bp

m0

6m

b

bp

m0

7m

bb

pm

07

me

bp

m0

7m

db

pm

07

sdb

pm

07

seb

pm

07

sb

bp

m0

8sb

bp

m0

8se

bp

m0

8sd

bp

m0

8ld

bp

m0

8le

bp

m0

8lb

bp

m0

9lb

bp

m0

9le

bp

m0

9ld

bp

m0

9sd

bp

m0

9se

bp

m0

9sb

bp

m1

0sb

bp

m1

0se

bp

m1

0sd

bp

m1

0m

db

pm

10

me

bp

m1

0m

b

bp

m1

1m

bb

pm

11

me

bp

m1

1m

db

pm

11

sdb

pm

11

seb

pm

11

sb

bp

m1

2sb

bp

m1

2se

bp

m1

2sd

bp

m1

2ld

bp

m1

2le

bp

m1

2lb

−1

0

−0.5

2

0

4

0.5

6

1

8

0

10

50

12

100

14

150

−1

200

−0.5

250

vert

ical

BP

M o

ffset

[mm

]

0

s [m]

offset

0.5 1

num

ber

of B

PM

svertical BPM offset [mm]

fit (<y>=−0.11 mm, √<y2>=0.24 mm)

error

]πphase [rad/2

m !RMS offset even for well aligned machines >100 µ

Vertical Golden Orbit @ SLS

−0.5 mm

0.5 mmy

[mm

]

0 8.47

m240µRMS

1mm

−1mm0 288

VerticalBBAOffset

−0.5 mm 0.5mm

ring position [m]

+BBA Orbit

BBA offset = convolution of mechanical and electronical properties of BPM

alter focusing of individual quadrupoles, resulting RMS orbit change

DC RMS corrector strength reduced when correcting to BBA orbit !

is proportional to initial orbit excursion at location of quadrupole.

offset BPM − adjacent quadrupole centerBeam−based alignment (BBA) techniques to find

Golden Orbit: goes through centers of quadrupolesand sextupoles in order to minimize optics distortionsleading to spurious vertical dispersion and betatroncoupling (emittance coupling) + extra steering @ IDs

Extra Steering

4S 6S 7m 9L 11M

Michael Boge 12


IWBS2004

SR - Stability - Orbit Correction

• “Response Matrix”Aij , mappingCorrector j(1 ≤ j ≤ n) to the corresponding BPM patternBPM i (1 ≤ i ≤ m) (from model or orbit measurements) needs to be “inverted” in order to getCorrector jfor givenBPM i

– n = m: square matrix withn independent eigenvectors not ill-conditioned→ uniquesolution by matrix inversion

– n 6= m: non-square matrix by design or due to BPM failures and/or correctorsaturation→ solution:

• Singular Value Decomposition (SVD)- Decomposes the “Response Matrix”

Aij =

√βiβj

2 sin πνcos [πν − |φi − φj |] containing the orbit “response” inBPM i to a change of

Corrector jinto matricesU ,W ,V with A = U ∗ W ∗ V T . W is a diagonal matrix containingthe sorted eigenvalues ofA. The “inverse” correction matrix is given byA−1 = V ∗ 1/W ∗ UT

– n > m: minimizes RMS orbit and RMS corrector strength changes

– n < m: minimizes RMS orbit

– n = m & all eigenvalues: matrix inversion

– “Most Effective Corrector” combinations by means of cutoffs in the eigenvalue spectrum→ SVD makes other long range correction schemes like “MICADO”superfluous

Michael Boge 13


IWBS2004

SR - Stability - Orbit Correction

Remarks on matrix inversion:

• Since modern light sources are built with very tight alignment tolerances and BPMs are wellcalibrated with respect to adjacent quadrupoles, orbit correction by matrix inversion in thenxn

case has become an option since

– resulting RMS corrector strength is still moderate (typically ≈100µrad)

– BPMs are reliable and their noise is small (no BPM averaging is performed which is similarto a local feedback scenario)

• This allows to establish any desired “golden orbit” within the limitations of the availablecorrector strength and the residual corrector/BPM noise.

Remarks on horizontal orbit correction:

• Dispersion orbits due to “path length” changes (circumference, model-machine differences, rffrequency) need to be corrected by means of the rf frequencyf .

• A gradual build-up of a dispersionD related corrector pattern∑

A−1

jiDi with a nonzero mean

must be avoided→ leads together with rf frequency change to a corrected orbitat a differentbeam energy.

• Subtract pattern∑

A−1

jiDi from the actual corrector settings before orbit correctionin order to

remove ambiguity.

Michael Boge 14


IWBS2004

SR - Stability - Medium Term

In this regime high mechanical stability is needed to achieve stability on the sub-micron level:

• Stabilization of tunnel, cooling water temperature and digital BPM electronics to≈ ±0.1◦andthe experimental hall to≈ ±1.0◦.

• Minimization of thermal gradients by discrete photon absorbers and water-cooled vacuumchambers.

• Stiff BPM supports with low temperature coefficients and monitoring of BPM positions withrespect to adjacent quads (POMS).

• Monitoring of girder positions (Hydrostatic Leveling System (HLS), Horizontal PositioningSystem (HPS)).

• Full energy injection and stabilization of the beam currentto≈0.1 % (“top-up” operation):

300(+1) mA top−up @ SLS ~6 daysA.Lüdeke THPKF012

Michael Boge 15


IWBS2004

SR - Stability - Medium Term - Top-up

• “Top-up” operation guarantees a constan-t electron beam current and thus a constan-t heat load on all accelerator components. Italso removes the current dependence of BP-M readings under the condition that the bunchpattern is kept constant (B. Kalantari)

• Horizontal mechanical offset (≈0.5 µm res-olution) of a BPM located in an ar-c of the SLS storage ring with respec-t to the adjacent quadrupole in the case ofbeam accumulation,“top-up” @ 200 mA anddecaying beam operationat 2.4 GeV:

– Accumulation and decaying beam opera-tion: BPM movements of up to 5µm.

– “Top-up” operation: no BPM movemen-t during “top-up” operation at 200 mAafter the thermal equilibrium is reached(≈1.7 h).

µP

OM

SH

−02S

E r

eadi

ng [

m]

3.5 µm

1.5 h

15 h

−4

0

−2

−6

−8

−10

−12

beam

cur

rent

[mA

]

200

150

250

100

50

0

200 mA

top−up @ 200 mA decaying beam120 mA

no movement !

5µm

dump beam dump beam

µPOMSH−02SE reading [ m]beam current [mA]

• 0.3 % current variation (350 (+1) mA) @τ ≈ 11 h

• Injection every≈ 2 min for≈ 4 sec

Michael Boge 16


IWBS2004

SR - Stability - Transition from Slow to Fast Orbit Feedback

Temporal mean of the RMS orbit deviation from the BPM reference settingsxrms / yrms and thecorresponding RMS corrector strengthxkrms / ykrms in 2003 for three different operation modes:

horizontal vertical

mode xrms xkrms yrms ykrms

SOFB(250) 1.0µm 410 nrad 750 nm 230 nrad

SOFB(co) 1.0µm 120 nrad 300 nm 80 nrad

FOFB 0.7µm 17 nrad 60 nm 15 nrad

Michael Boge 17


IWBS2004

SR - Stability - Fast Orbit & X-BPM Feedback

-3

-2

-1

0

1

2

3

4

06/12/200400:00:00

06/12/200412:00:00

06/13/200400:00:00

06/13/200412:00:00

06/14/200400:00:00

24.5

25

25.5

26

26.5

27

vert

ical

orb

it r

efer

ence

off

set

[µm

]

tem

per

atu

re [

oC

]

time [h]

orbit ref. offset 05SBorbit ref. offset 06SBhall air temperature

-3

-2

-1

0

1

2

3

4

04/29/200400:00:00

04/29/200412:00:00

04/30/200400:00:00

04/30/200412:00:00

05/01/200400:00:00

25

25.5

26

26.5

27

27.5

28

vert

ical

orb

it r

efer

ence

off

set

[µm

]

tem

per

atu

re [

oC

]

time [h]

orbit ref. offset 05SBorbit ref. offset 06SBhall air temperature

filling pattern feedback off

-5

0

5

10

15

20

25

06/12/200400:00:00

06/12/200412:00:00

06/13/200400:00:00

06/13/200412:00:00

06/14/200400:00:00

5

6

7

8

9

10

ph

oto

n b

eam

po

siti

on

[µm

]

ID g

ap [

mm

]

time [h]

xy

ID gapvertical

horizontal

10 µ m

Feedback on X−BPM @ U24FOFB reference orbitchanges

without filling pattern feedback

~~500 nm RMS @ 8.60 m from ID (<0.5 Hz)

2 days top−up @ 300 mA

2 deg

gap change

with filling pattern feedback

X−BPM reading @ U24

J. Krempasky et al. THPLT023, B. Kalantari et al. THPLT024, T.Schilcher et al. THPLT186

PSDs on tune BPM (off−loop)

µ m

temperatureBPM rack

2

Michael Boge 18


IWBS2004

SR - Stability - X-BPM & Bunch Pattern Feedback

• The bunch pattern feedback maintains the bunch pattern (390bunches (≈1 mA)) within <1 %

• The X-BPM feedback (slave) stabilizes the photon beam (≈9 m from source point) by means ofchanges in the reference orbit of the fast orbit feedback (master) to≈0.5µm for frequencies upto 0.5 Hz

-15

-10

-5

0

5

10

0 2 4 6 8 10 12 14 16 18

Time [h]

U19 gap [mm]

X−BPM reading [um]

RF−BPM reference [um]

5 um

top−up @ 350+1 mA22/11/04

ONbunch pattern feedback OFF

bunch patternrestoration

−1.5−1

−0.5

m]X [µ0

0.51

1.5 −1.5−1

−0.50

0.51

1.5

Y [µm]

2σ1σ

Michael Boge 19


IWBS2004

SR - Stability - Feed Forward & X-BPM Feedback

• The feed forward tables (here forU24) ensure a constant X-BPM reading for the desired gaprange (here 6.5-12 mm) within a fewµm. The remaining distortion is left to the X-BPMfeedback

50

60

70

80

90

100

110

6.5 7 7.5 8 8.5 9 9.5 10 10.5 11 11.5 1210

20

30

40

50

60

70

X06

SA

-FE

-BM

1:X

[µm

]

X06

SA

-FE

-BM

1:Y

[µm

]

X06SA-ID-GAP:READ [mm]

X-BPM X, X-BPM FB off, FF offX-BPM Y, X-BPM FB off, FF offX-BPM X, X-BPM FB off, FF onX-BPM Y, X-BPM FB off, FF onX-BPM X, X-BPM FB on, FF onX-BPM Y, X-BPM FB on, FF on

FF+X−BPM FB off

FF+X−BPM FB on

FF+X−BPM FB on

FF+X−BPM FB off

Michael Boge 20


IWBS2004

SR - Stability - Medium Term - Top-up

• Change of the vertical BPM reference within the X-BPM feedback loop for decaying beamoperation (0-4 h) and “Top-up” (Time constant for getting back to thermal equilibriumτ=1.7 h):

240

260

280

300

320

340

360

380

0 2 4 6 8 10 12 14 16 18

-0.015

-0.01

-0.005

0

0.005cu

rren

t [m

A]

vert

ical

ref

eren

ce A

RID

I-B

PM

-03S

B [m

m]

time [h]

current [mA]vertical reference ARIDI-BPM-03SB [mm]

τ~1.7h

-0.015

-0.01

-0.005

0

0.005

260 280 300 320 340 360

vert

ical

ref

eren

ce A

RID

I-B

PM

-03S

B [m

m]

current [mA]

350 -> 250 mA (~1e-4 mm/mA)250 -> 350 mA (~7e-5 mm/mA

µ 0 m

µ−15 m

0.1 m/mAµ

τ=1.7time constant h

250 mA

350 mA

Michael Boge 21


IWBS2004

SR - Stability - Long Term Stability

• Horizontal BPM/Quadrupole offsets for BPM upstream ofU24 over 14 weeks @ differenttop-up currents (180, 200, 250, 300 mA) with 3 shutdowns (left plot)

• Circumference change over 3 years of SLS operation (→ ∆ circumference≈ 3 mm) (right plot)

0

50

100

150

200

250

300

350

400

33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

curr

ent [

mA

] and

pom

s [1

/10

mu

m]

Week #/2002

currentpomsypomsx

10 µm

µm10

300250250180mA

180 200 300mµ0.5

step

• Severe problems with the cooling capacity of the SLS during the hot summer 2003 (#82)! Again“scheduled” problems in 2004 (#130) due to the cooling system upgrade!

Michael Boge 22


IWBS2004

SR - Stability - Long Term Stability

• Fitted circumference change over 3 years of SLS operation (→ ∆ circumference≈ 2 mm) as afunction of the fittedoutside temperature(left plot)

• Circumference change as a function of the averagetunnel temperature (right plot)

-0.5

0

0.5

1

1.5

2

2.5-4 0 4 8 12 16 20 24 28

∆ pa

thle

ngth

[mm

]

outside temperature [°C]

∆ pathlength( outside temperature )Circumference Changeof the SLS Storage Ring

01/ 2003

over 3 Years

07/ 2002

07/ 2003

07/ 2004

01/ 2004

01/ 2002

• Stabilization of thetunnel temperature to ≈ ±0.1◦is needed to guarantee sub-micronmovement !

Michael Boge 23


IWBS2004

Conclusions

• The fast orbit feedback and X-BPMfeedbacks guarantee excellentshortterm stability up to 100 Hz.

• “Top-up” Operation allows to maintainthis degree of stability on themediumterm scaleover weeks.

• Long term stability suffered fromproblems with the cooling system dur-ing the summer months over the last 2years.

Michael Boge 24

sls at the paul scherrer institute (psi), villigen,...

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