Swiss Light Source @ PSI

Design and Performance of the Global Fast Orbit Feedback at the SLS

NSLS-II Stability WS

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

Swiss Light Source

SLS

@ PSI

http://sls.web.psi.ch/

Michael Boge 1



Outline

• Introduction

– SLS Layout

– Booster Design

– Storage Ring (SR) Design

– SR BPM/Corrector Layout

– SR Lattice Errors

– SR Lattice Calibration

• Fast Orbit Feedback (FOFB)Motivation

– Ground Noise Measurement in 1993

– User Requirements & Worst Case Es-timate

• FOFBTheory & Simulations

– Orbit Correction Schemes

– Response Matrices

– Path Length Correction

– Model for a Closed Orbit Feedback

• FOFBSubsystems

– Digital BPM System

– POsition MonitoringSystem

– Digital Power Supplies (PS)

– Hardware Layout

– System Integration

• FOFBOperation

– BBA & Golden Orbit

– Transition from Slow (SOFB) →FastOrbit Feedback

– Closed Loop Performance

– Feed Forward & X-BPM Feedback

– Effect of Top-up Operation

– X-BPM & Bunch Pattern Feedback

– Long Term Stability

• FOFBOutlook

– Limitations & Upgrades

Michael Boge 2



Introduction - 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 = 5.1(7.3) nm rad (FEMTO)

• Ten Beamlines:MS – 4S, µXAS / FEMTO – 5L,

DIAG – 5D, PX – 6S,

LUCIA – 7M, SIS– 9L,

PXII – 10S, SIM – 11M,

TOMCAT – 2DA, POLLUX — 7DA

Michael Boge 3



Introduction - 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



Introduction - Storage Ring (SR) Design

• 12 TBA: 8◦ / 14◦ /8 ◦

• 12 Straight Sections:

– 3 × 11 m(nL )

∗ Injection ,2×UE212,W128,U19

– 3 × 7 m (nM )

∗ 2×UE56, UE54

– 6 × 4 m (nS)

∗ 2× RF, W61, 2×U19

• Energy: 2.4 (.7) GeV

• ǫx: 5.1 (7.3) nm rad(with W128)

• 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



Introduction - SR Lattice Errors - Error Specifications & Dynamic Acceptance

dipole quadrupole0.04%

0.03%

0.007%

0.01%

0.006%

−0.008%

multipole errors

dynamic acceptance [mm mrad]

A. Streunwithout multipoles

with multipoles

Specified alignment tolerances (RMS, Gaussian with cut @2σ):

• Girders: 300µm (100µrad),Girder joints: 100µm (girder to girder)

• Magnets on girders: 30µm (25µrad) (with respect to magnetic center)

Michael Boge 6



Introduction - SR Lattice Errors - “Bare Orbit”

0

5

10

15

20

25

0 2 4 6 8 10 12

num

ber

of s

eeds

xrms [mm]

0.050 mm displacement0.030 mm displacement

measurement

• Right/Top: Horizontal Orbit:xRMS= 1.8 mm

• Right/Bottom: Vertical Orbit:yRMS= 0.7 mm

• Left: Consistent with quadrupole displacements of 30µm RMS (simulationfor 200 seeds)

Michael Boge 7



Introduction - SR BPM/Corrector Layout

sector

8 814

Quadrupole

Sextupole

Dipole

for FEMTO straight

+1 BPM/Correctors

U19

W128

��

Horizontal / Vertical Correctors

BPMs

• 12sectors

• 6 BPMsand 6Horizontal/Vertical Correctors persector

• Correctors inSextupoles, BPMsadjacent toQuadrupoles

• +1 BPM/Correctors set for 5L (FEMTO) straight

Michael Boge 8



Introduction - SR Lattice Errors - Sources of Vertical Dispersion

0

5

10

15

20

25

30

35

40

-0.001 0 0.001 0.002 0.003 0.004 0.005 0.006

num

ber

of s

eeds

ηyrms and ηymean [m]

co+qu 1.25198e-03+/-4.59177e-04

total 2.88592e-03+/-1.02626e-03

quadrupoles+correctors ηyrmsquadrupoles+correctors ηymean

total ηyrmstotal ηymean

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0 50 100 150 200 250 300

η y [m

]

s [m]

quadrupolescorrectors

total

measurement

4.5 mmDy~

quads+correctors

quadscorrectors

• Left: Dispersion waves from quadrupoles and correctors in antiphase ifBPM-quadrupole errors are small (<50µm RMS) (→ Beam-BasedAlignment) after correction to quad centers

• Main contribution to dispersion from sextupoles through betatron coupling(simulation for 200 seeds)

Michael Boge 9



Introduction - SR Lattice Errors - Betatron Coupling

0

10

20

30

40

50

60

70

80

0.0001 0.001 0.01

num

ber

of s

eeds

emittance ratio κ

sextupoles, tilt, no corrsextupoles, tilt, corr

sextupoles, no tilt, no corrsextupoles, no tilt, corr

no sextupoles, tilt, no corrno sextupoles, tilt, corr

no sextupoles, no tilt

0.002

emittance couplingbetatron couplingmeasurementno sextupoles

with standard

misalignments

• Betatron coupling: dQ=0.007

– Emittance coupling in absence of spurious vertical dispersion: 0.2%(Guignard)

• Left: Emittance coupling after betatron coupling correction with skewquadrupoles≈ 0.1% (simulation for 200 seeds)

Michael Boge 10



Introduction - 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 11



FOFB - Motivation - Ground Noise Measurement in 1993

280 nm !

500 nm

300 nm

130 nmNS

EW

Vertical

NS

EW

Vertical

250 nm

100 nm

25 s

0.01 Hz 100 Hz

frequency domain

time domain

TRUCK

Measurement 1993

Michael Boge 12



FOFB - Motivation - User Requirements & Worst Case Estimate

• 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 13



FOFB - Measured Short Term Noise Sources in 2004

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 =8.73 (=15 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 14



FOFB - T&S - Orbit Correction Schemes

• Sliding Bump - Phase advances betweenCorrectors0◦ < ∆φ < 180◦, Correctors 1,2,3allowto zero the orbit inBPM 2nearCorrector 2. 1 opens “Orbit Bump”,2 provides kick for3 toclose it again. Continue (“Slide”) with2,3,4to zero orbit inBPM 3... iterate until orbit isminimized in allBPMs!

Corrector BPM

12 3

1 2 3

Orbit Bump

4

< 180 deg∆Φ

• MICADO - Finds a set of “Most Effective Correctors”, which minimizethe RMS orbit in allBPMsat a minimum (“most effective”) RMSCorrectorkick by means of the SIMPLEXalgorithm. The number ofCorrectors(= iterations) is selectable.

• 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 . SVD makes the other presented schemes obsolete !-)

Michael Boge 15



FOFB - T&S - Response Matrices

72 hcm 5 0 -5

010

2030

4050

6070

mon index 010

2030

4050

6070

hcm index

-15

-10

-5

0

5

10

15

72 vcm 10 5 0 -5 -10

010

2030

4050

6070

mon index 010

2030

4050

6070

vcm index

-15

-10

-5

0

5

10

15

Aij =

√βiβj

2 sin πνcos [πν − |φi − φj |] = (U ∗ W ∗ V T )ij

• νx = 20.43 (≈3 BPMs/Correctors per unit phase,φ = 360◦)

• νy = 8.73 (≈9 BPMs/correctors per unit phase)

Michael Boge 16



FOFB - T&S - Inverse Response Matrices

72 hcm 0.5 0

-0.5

010

2030

4050

6070

hcm index 010

2030

4050

6070

mon index

-1

-0.5

0

0.5

1

72 vcm 0.5 0

-0.5

010

2030

4050

6070

vcm index 010

2030

4050

6070

mon index

-1

-0.5

0

0.5

1

A−1

ij = (V ∗ 1/W ∗ UT )ij

• A−1

ij is a sparse “tridiagonal” matrix (3 large (+1 small) adjacent coefficients are nonzero sinceBPM and Corrector positions are slightly different)→“Sliding Bump Scheme” iteratively invertsA

• A−1

ij containsglobal information although it is a “tridiagonal” matrix !→ Implementation of a Fast Orbit Feedback (FOFB)

Michael Boge 17



FOFB - T&S - Inverse Measured Response Matrices

72 hcm 0.5 0

-0.5

010

2030

4050

6070

hcm index 010

2030

4050

6070

mon index

-1

-0.5

0

0.5

1

72 vcm 0.5 0

-0.5

010

2030

4050

6070

vcm index 010

2030

4050

6070

mon index

-1

-0.5

0

0.5

1

• Horizontalβ Beat:≈ 4 %

• Verticalβ Beat:≈ 3 %

→ A(real)−1

ij is still a sparse “tridiagonal” matrix plus some noise

Michael Boge 18



FOFB - T&S - SVD Eigenvalues

0.001

0.01

0.1

1

10

100

1000

0 10 20 30 40 50 60 70 80

rms/

max

orb

it [m

m] a

nd w

[inde

x]

index of w[index]

whhorbit

wvvorbit

• Range of Eigenvalues0.5 < W < 500

• Eigenvalue Cutoff @i0 (Wi = 0 for i > i0) determines the minimum achievable RMS Orbitand Corrector Strength after Correction→ “MICADO” like: the largest Eigenvalues correspondto the “Most Effective Corrector” patterns

• No Cutoff corresponds to “Matrix Inversion”. The RMS Orbit after Correction is Zero !

Michael Boge 19



FOFB - T&S - Path Length Correction

• In a homogeneous magnetic field (a) the radius of the Closed Orbit is proportional to the Energyp (shown arep < p0, p = p0 undp < p0). The Orbit gets shorter or longer (“Path Length”change∆L/L0)

• In the case of “strong focussing” (b) the Orbit Deviation @ a locations is given byx0(s) = D(s)∆p/p0 with ∆p = p− p0, D(s) denotes the Dispersion.∆L/L0 = αc∆p/p0

with the momentum compaction factorαc = 1/L0

∫ L0

0D(s)/ρ(s)ds (≈ 6 · 10−4)

• p variations due to “Path Length” (thermal or modelling effects) changes have to be correctedby means of the RF Frequencyf with ∆f/f = −αc∆p/p0 and NOT by the Orbit Correctors !

→ Fit ∆p/p0 part of the Orbit using SVD on a 1 column response matrix containing dispersion

valuesDi0 @ the BPMs and change the RF frequency by−∆f to correct for∆p/p0 !

Michael Boge 20



FOFB - T&S - Model for a Fast Closed Orbit Feedback

BPM

Read out

SVD

Feedback

+

+

Algorithm

Digital PID

Beam Jitter

Electron

Settings Eddy Currents

in Magnet YokeBeam Chamber

Corrector

Readings

Beam Position

Orbit

Offsets

Corrector

Fields Machine

Optics

Michael Boge 21



FOFB - T&S - Calculated Corrector Transfer Functions

• MAFIA estimated Eddy Current Effects induced by the Vacuum Chamber (3 mm Stainless Steal(finally reduced to 2 mm)) and the Laminated Iron of the Sextupoles:

0.65

0.7

0.75

0.8

0.85

0.9

0.95

1

f/Hz

|B|

0 10 20 30 40 50 60 70 80 90 100

Only vacuum chamberIncluding lamination, d=1mm

0.3

0.4

|B|

f/Hz

0.5

0.6

0.7

0.8

0.9

1

0 10 20 30 40 50 60 70 80 90 100

w/o magnet losseswith magnet losses

Horizontal Polarization Vertical Polarization

Michael Boge 22



FOFB - T&S - Model based Orbit Noise Suppression

Frequency/Hz

20

10

0

-10

-20

-30

-40

-50

-601000100101

Vertical Orbit Feedback Loop

20 dB Bandwidth: 90 Hz

Sample Rate: 4 KSamples/sec.

dB

0 dB point @ >100Hz

attenuation factor 10 @ 90Hz

• 4 KHz Sampling Rate needed in order to have a gain≈20 dB @ 90 Hz

Michael Boge 23



FOFB - T&S - PS Resolution & RMS Orbit Distortion

TRACY estimated Residual Vertical RMS Orbit after Orbit Correction as seen by the BPMs(histograms for 200 seeds introducing RMS girder misalignment of 1µm):

60

55

50

45

40

35

30

25

20

15

10

5

00 4321 Yrms [um]

15 ppm30 ppm60 ppmRMS Girder Error: 0.001mm

• 1 ppm in amplitude corresponds to a resolution of 10−6 at a maximum Current of 7 A(≈ 860µrad in the vertical plane)

• 60 ppm: yrms = 0.75µm, 30 ppm: yrms = 0.5µm, 15 ppm: yrms = 0.25µm

→ 15 ppm (≈ 10 nrad or 100µA) sufficient

Michael Boge 24



FOFB - T&S - PS Resolution and RMS Position/Angle @ IDs

RMS Position @ Insertion Devices withβx ≈ 1.4m,βy ≈ 0.9m (x/yrms= 0.5µm for 15 ppm):

0

5

10

15

20

25

30

35

40

45

50

55

60

0 5e-07 1e-06 1.5e-06 2e-06

num

ber

of s

eeds

xrms [m]

vcm/hcm 15 ppmvcm/hcm 60 ppmvcm/hcm 0 ppm

0

5

10

15

20

25

30

35

40

45

50

55

60

0 5e-07 1e-06 1.5e-06 2e-06

num

ber

of s

eeds

yrms [m]

vcm/hcm 15 ppmvcm/hcm 60 ppm

vcm/hcm 0 ppm

RMS Angle at the Insertion Devices (αx/yrms= 0.08µrad for15 ppm):

0

5

10

15

20

25

30

35

40

45

50

55

60

0 5e-08 1e-07 1.5e-07 2e-07 2.5e-07 3e-07

num

ber

of s

eeds

αx rms [rad]


0

5

10

15

20

25

30

35

40

45

50

55

60

0 5e-08 1e-07 1.5e-07 2e-07 2.5e-07 3e-07

num

ber

of s

eeds

αy rms [rad]


Michael Boge 25



FOFB - Subsystems - Digital BPM System

Closed Orbit:

Mode for All Machinesin Different OperationOnly One BPM System

Turn−by−Turn:

Vital forCommissioning

Turn−by−Turn:

PSI +

Closed Orbit Mode −> Fast Orbit Feedback

µ

1 MSample/s, <20 mµ

4 KSample/s, <0.8 m~300 nm <100 Hz

Michael Boge 26



FOFB - Subsystems - POMS

Measure BPM/Quadrupole offsets with

BPM blocks

FEA−simulations indicate:chamber moves ~2 m/K @ BPM blocksµ

µµ0.5 m resolution in x and y !

0.1 m resolution @ short straights

• 6 BPMs per sector (+1BPM in 5L / FEMTO)

• BPMs rigidly attached to girders (BPM supportmounted ongirder alignment rail)

• BPM supportsserve as supports for the vacuum system (→ BPM chamber)

• Initially planned to be used within theFOFBloop (NOT necessary→Top-Up)

Michael Boge 27



FOFB - Subsystems - Digital Power Supplies

Short/Long−term: <10/30 ppm

One Digital Control Unit for ~600 power supplies of the SLS

Michael Boge 28



FOFB - Partitioning of Inverse Response Matrix

monitor index

corrector index

SLS

• 12sectors

• 6(7)BPMsand 6(7)Horizontal/Vertical Correctors persector(+1 BPM/Correctors set FEMTO)

Michael Boge 29



FOFB - Schematic View

A-L = Submatrices of A -1PC

measuredtheoretical

A

B

CD

E

F

G

H

IJ

K

L Response Matrix A

= Signal Processors

Fast Link 40Mb/s

PC

= SVD Engine

Slow Link

1Mb/s

Slow Link

or

• DedicatedSignal ProcessorsperformMatrix Multiplications in parallel !

Michael Boge 30



FOFB - Hardware Layout

Michael Boge 31



SOFB/FOFB - System Integration

peratoroco

BPM

Server

TRACYServer

Client

Event

Event

@ 3Hz

Poll

CORBA Server

CorrectorsBPMs

Client

Feedback

FB LogClient

Model Server

Console

Server

CDEV

BPMFast Orbit Feedback

LowLevel Hardware

EZCA Server

FOFB

Ded

icat

edV

ME

/DS

PLe

vel

UN

IX H

osts

Event

@ 0.5Hz

Event@ 1Hz

@ 1Hz

• Development within aClient-Server(Common Object Request BrokerCORBA) environment

• Hard Correction (“Matrix Inversion” on the Model based Response Matrix using SVD)

• SOFB: BPM Datasets @ 3 Hz, average over 3 successive Datasets => ≈ 1 Hz correction rate(toggle between x/y plane => 2 s for full cycle). Corrects orbit to<5 µm beforeFOFBlaunch.

Michael Boge 32



SOFB/FOFB- Operator Interface (Tcl/Tk) “oco Client”

oco(Mode=RI,co; Server=slsbd8; Domain=slsac.psi.ch)

Feedback ON Mode FOFB active

Tklogger(Group=slsbd; Server=slsbd8; Domain=slsac.psi.ch)

Reference Orbit

EVENT

Blinking !!!

POLL

Daq ON !!!

Continue !!!

Stop FeedbackStart FeedbackCorrect

Michael Boge 33



SOFB/FOFB - Beam-Based Alignment & 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 1nu

mbe

r of

BP

Ms

vertical 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 8.73

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 34



SOFB/FOFB - Transition from Slow →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 35



FOFB - Open & Closed Loop Transfer Functions

100

102

104

−20

−15

−10

−5

0

5hor. open loop transfer function

frequency [Hz]

ampl

itude

[dB

]

BW 1 = 355 Hz

BW 2 = 2014 Hz

measuredfit

100

102

104

−20

−15

−10

−5

0

5ver. open loop transfer function

frequency [Hz]

ampl

itude

[dB

]

BW 1 = 827 Hz

BW 2 = 2010 Hz

measuredfit

100

102

104

−800

−600

−400

−200

0

200

frequency [Hz]

phas

e [d

eg]

measuredfit

100

102

104

−600

−500

−400

−300

−200

−100

0

100

frequency [Hz]

phas

e [d

eg]

measuredfit0 dB point @ 100 Hz

Michael Boge 36



FOFB - Closed Loop Performance & 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

1Hz X−BPM feedback changes the referenceof BPMs adjacent to IDs within the FOFB loopin order to stabilize the photon beam positionat the X−BPMs −> cascaded feedback

Michael Boge 37



FOFB - 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 38



FOFB - Effect of Top-up Operation

• “Top-up” operation guarantees a constantelectron beam current and thus a constant heatload on all accelerator components. It also re-moves the current dependence of BPM read-ings under the condition that the bunch patternis kept constant

• Horizontal mechanical offset (≈0.5 µm res-olution) of a BPM located in an arcof the SLS storage ring with respect tothe 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 movementduring “top-up” operation at 200 mAaf-ter 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 39



FOFB - Top-up - 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 (Example beam line6S: 1 X-BPM≈9 m from source point (U19)) by means of changes in the reference orbit of the fast orbitfeedback (master) to ≈0.5µm for frequencies up to 0.5 Hz.

• X-BPM feedbacks are operational @ the ID beam lines4S,6S,10S(1 X-BPM→angle only) andthe dipole beam lines2DA,7DA (2 X-BPMs→angle & position).

-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 40



FOFB - Top-up - Thermal Equilibrium

• 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

0.005

curr

ent [

mA

]

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

τ=1.7time constant h

250 mA

350 mA

µ0.15 m/mA

ther

mal

DB

PM

• Large (≈0.1µm/mA) contribution originating from current dependence ofdigital BPMs

Michael Boge 41



FOFB - Long Term Stability - Annual Variations

• 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 42



FOFB - Long Term Stability - Temperature 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 43



FOFB - Outlook - Limitations

X−BPM FOFB @ 4 kHz

Michael Boge 44



FOFB - Outlook - Upgrades

Plans for integration of 48 skew quadswithin the FOFB loop in order to make

& to correct local coupling.user bumps "coupling transparent"

Michael Boge 45

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