Overview - Indico

Emittance Control at the SLS

XVII ESLS Workshop 26/11/09

Overview

• SR - Lattice Errors

– Sources of Vertical Emittance

– Sources of Vertical Dispersion

• SR - Lattice Calibration

– Beta Function Measurement

– Beta Function Correction

• SR - Multipole Correctors

• SR - Dispersion Correction

• SR - Betatron Coupling Correction

• SR - Emittance (Sigma) Monitor

• SR - Sigma and Emittance

• SR - Summary

• SR - Lattice Errors

– SR - Sextupole Beam-Based Alignment

– SR - Girder Re-alignment

It’s a long way to go ...

Michael Boge 1



SR - Lattice Errors - Sources of Vertical Emittance I

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 (in commissiong year 2001)

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

• Left: Emittance coupling after betatron coupling correction with initially 6 skew quadrupoles≈ 0.1%

(simulation for 200 seeds)

Michael Boge 2



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

4.8 mmDy~

quads+correctors

quadscorrectors

• Left: Dispersion waves from quadrupoles and correctors in antiphase if BPM-quadrupole errors aresmall (<50µm RMS) (→ Beam-Based Alignment) after correction to quad centers using “hardcorrection” (all SVD weighting factors used).

• Right: Main contribution to dispersion fromsextupolesthrough betatron coupling (simulation for 200seeds) ! Contributions from quads and correctors cancel !

Michael Boge 3



SR - Lattice Calibration - Beta Function Measurement I

Hysteresis Correction based on tune measurement before and after the quadvariation. Allows to restore the original

−> important in order to minimize opticsdistortions during the measurement !

average beta function in the quad.

(177 Quads with individual PS)

Courtesy: A. Streun

Michael Boge 4



SR - Lattice Calibration - Beta Function Correction I

-0.004

-0.002

0

0.002

0.004

0 50 100 150 200 250

δk/k

s [m]

"QfdK.10.dat" u 3:12"QfdK.10.dat" u 3:12

0.1

1

10

100

1000

0 20 40 60 80 100 120 140 160

wei

ghtin

g fa

ctor

wi

index i

allused

quad

rupo

le #

1−#n

dk

Average Beta Variation @ quadrupoles #1−#n

Quadrupole − Average Beta Response Matrix

x horizontal y vertical

From Model or Measured

− plug the measured average beta functions into

− calculate quadrupole variations dk_i which fit modelthe "inverted" matrix

best to the measured average beta functions (cutweighting factors since quadrupoles are not the onlythe only source of beta variations !)

− measure average beta functions in quadrupoles

SLS: 177 x (2x177=354) = 62658 coefficients

− Invert 177 x 354 Matrix using SVD

cutoff <13

quadrupole variations

weighting factors

not used

dk/k +−0.2% p−p

− apply the −dk_I to the machine in order to correct thebeta beat.

Recent Beta Function Measurement @ the SLS

2.8 / 2.3 % beat with respect to model

Michael Boge 5



SR - Lattice Calibration - Beta Function Measurement II

First measurements at the SLS

Courtesy: M. Aiba, CERN

!

1 2

Michael Boge 6



SR - Lattice Calibration - Beta Function Correction II

Orbit Response MatrixCoupled

SLS: 146x146

quadrupole #3 dkquadrupole #2 dk

quadrupole #1 dk

Corrector Index x+y

BP

M In

dex

x+y

quadrupole #n−1 dk

which fit the model best to the Orbit− calculate quadrupole variations dk_i

From Model or Measured Doing it the LOCO way

J. Safranek, SSRL

Linear Optics from Closed Orbits

quadrupole #n dk (SLS: 177)

− measure the Orbit Response MatrixCorrector Index x+y

quad

rupo

le #

1−#n

dk

Quadrupole − Coupled Orbit Response Matrix


BPM Index x+y

− plug ORP into the "inverted" Matrix− invert 177 x 21316 Matrix using SVD

Note:No DipoleErrors

handled !can be

Response Matrix (cut weight. facs)

to correct the beta beat.− apply −dk_i to the machine in order− iterate within model for large errors

Michael Boge 7



SR - Multipole Correctors

Michael Boge 8



SR - Dispersion Correction I

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0 50 100 150 200 250 300

vert

ical

dis

pers

ion

[m]

s[m]

Measurement before correction (rms=0.0048)Measurement error (mean=0.0009)

-0.015

-0.01

-0.005

0

0.005

0.01

0.015

0 50 100 150 200 250 300

vert

ical

dis

pers

ion

[m]

s[m]

Model prediction (rms=0.0023)Measurement after correction (rms=0.0023)

Measurement error (mean=0.0009)

Vertical DispersionVertical Dispersionbefore correctionafter correction

x2.1

RMS 2.3 mmRMS 4.8 mm

Measurement Error MEAN 0.9 mm !Model Prediction RMS 1.4 mm

Vertical Dispersion @ BPMs

Dis

p S

kew

Qua

ds

Skew Quad − Dispersion Response Matrix

− measure difference orbits for various dp/p

− feed measured dispersion into it to determineDispersive Skew Quads values for correction

− determine vertical dispersion knowing dp/p

− invert Skew Quad − Dispersion Response Matrix

− Get a Model Prediction

− Apply correction and remeasure

SLS: 12 x 73 coefficients

Michael Boge 9



SR - Dispersion Correction II

BPM Tilt = Factor * Current Ratio

Corrector currentswithin FOFB loopwhile changing thethe BPM referenceby +−0.150 mm

Dispersion before Tilt Correction: 2.1 mm rmsDispersion after Tilt Correction: 1.3 mm rms

BPM Tilt * Horizontal Dispersion

Measured DispersionDispersion from BPM Tilt vs.Correlation

15 mrad rms BPM Tilt

Michael Boge 10



SR - Betatron Coupling Correction

0

2

4

6

8

10

12

14

16

0 5 10 15 20

wei

ghtin

g fa

ctor

wi

index i

all + used

Orbit Response MatrixCoupled

SLS: 146x146

Corrector Index x+y

BP

M In

dex

x+y

which fit the model best to the Orbit− calculate quadrupole variations dk_i

From Model or Measured

− measure the Orbit Response MatrixCorrector Index x+yBPM Index x+y

skew quad #n−1 dkskew quad #n dk (SLS: 24)

skew quad #3 dkskew quad #2 dk

skew quad #1 dksk

ew q

uad

#1−#

n dk

Skew Quad − Coupled Orbit Response Matrix


horizontal

vertical

Alternative: just fit skew terms

− plug ORP into the "inverted" Matrix− invert 24 x 21316 Matrix using SVD

SLS Alternative: 24 x (73x73=5329) = 127896 coefficients

Response Matrix

weighting factors

no cutoff

to correct the betatron coupling.− apply −dk_i to the machine in order− iterate within model for large errors

factor 5reduction !

Michael Boge 11



SR - Dispersion/Betatron Coupling Correction

Empirical Optimizationof skew quads by mini−mization of driving termsin the hamiltonian byobserving beamsize overlifetime. (court. A. Streun)

Michael Boge 12



SR - Betatron Coupling Feed-Forward

-100

-50

0

50

100

0 50 100 150 200 250

beam

elli

pse

twis

t [m

rad]

ring position [m]

before coupling correctionafter coupling correction

PolLux-0.0006

-0.0004

-0.0002

0

0.0002

0.0004

0.0006

150 152 154 156 158 160 162

vert

ical

bea

m p

ositi

on [m

]

ring position [m]

dipole

900 m−300 rad

skew quadrupole

µ

monitor

sextupolecorrector

µ

PolLux

4−Bump Coupling

Coupling correction

• Left: Layout of the vertical asymmetrical “polarization” bump consisting of four successive dipolecorrectors (magentabars) for the dipole (thickbluebar) beamline PolLux. Dedicated skew quadrupoles(redbars) are used to locally compensate for the betatron coupling induced by the sextupoles (greenbars) within the bump (→coupling feed-forward).

• Right: Twist of the electron beam ellipse as a function of the longitudinal SLS storage ring position fora -300µrad steering for the PolLux beamline before (greenline) and after (redline) betatron couplingcorrection. The arrow denotes the location of the 4-bump forthe PolLux beamline.

• The 4-bump is implemented as a reference change of 2 BPMs within the framework of the Fast OrbitFeedback with a feed-forward table for the skew quadrupoles(< 2 Hz switching frequency).

Michael Boge 13



SR - Emittance (Sigma) Coupling Monitor

Michael Boge 14



SR - Sigma and Emittance

After Coupling

Before CouplingCorrection

Correction

ey = 12.6 pm.rad

ey = 8.1 pm.rad

• Does the minimization of the beam sizeσy @ one dipole imply the minimization of the emittanceǫy ?Yes, at least for a small number of skew quadrupoles (22 skew quads, simulation for 100 seeds)→ leftplot !

• Is it equivalent to minimize the beam sizeσy instead of the emittanceǫy ?Yes, it nearly is (22 skew quads, simulation for 100 seeds)→ right plot !

Michael Boge 15



SR - Dispersion/Betatron Coupling Correction - Summary

Michael Boge 16



SR - Sigma and Emittance - Operation

Michael Boge 17



SR - Lattice Errors - Sources of Vertical Emittance II

• Term K + Sηx related tolocal chromaticityξ (≈0 forcorrected localξ).

• Term Gy≈0 for well (tocenters of quadrupoles) cor-rectedyc.

• TermKsqηx is small sincethe quadrupole roll errorsare small.

• Local ξ ONLY ≈0 if yc

is corrected in quadrupolesand sextupoles simultane-ously !

Michael Boge 18



SR - Lattice Errors - Sextupole Beam-Based Alignment I

Courtesy:S.L. Kramer,NSLS−II

Michael Boge 19



SR - Lattice Errors - Sextupole Beam-Based Alignment II

Beam Based Alignment at the KEK ATF, M. Ross et al.

sextupoleunder test

Center of sextupole

Reading of adjacent BPM [um]

0

0

measurement error~6 um

• At KEK ATF skew quadrupole trims (K=0.01 m−1) on the sextupoles were used (sextupole center =skew quad center). The kick induced by the offset of the beam in the skew quad is determined from thedifference orbit using the machine model. This fit is done forseveral closed orbit bump amplitudes atthe location of the sextupole under test.At the SLS 36 out of 120 sextupoles are equipped withauxiliary skew quadrupoles (K=0.03 m−1) for betatron coupling and dispersion correction.

Michael Boge 20



SR - Lattice Errors - Girder Re-alignment

BX_09: 71 um BX_11: 95 um

BX_12: 83 umBX_06: 57 um

BX_01: 102 um BX_05: 95 um

BX_10: 48 um

Girder n

Girder n+1

Vertical Orbit

• Corrector Pattern can be used to determine alignment errors(→No Cutoff).

• Prominent girder-girder alignment errors related to localcorrector patterns (circles).

• Girder-girder errors introduce mechanical steps driving the adjacent correctors.

• Leads to saturation of correctors in machines with large alignment errors (→Eigenvalue Cutoff =“Long Range Correction”).

• →Beam-based girder alignment (magnets on girders as super-correctors).

Michael Boge 21

Overview - Indico

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