Bingxin Yang Large aperture spectrum [email protected] Beam-based undulator measurement workshop, Nov. 14, 2005 Undulator Effective-K Measurements

Bingxin Yang

Large aperture spectrum measurements [email protected]

Beam-based undulator measurement workshop, Nov. 14, 2005

Undulator Effective-K MeasurementsUsing Angle-Integrated Spontaneous Radiation

Bingxin Yang and Roger Dejus

Advanced Photon Source

Argonne National Lab

Bingxin Yang



Some History of the Conceptual Development1998 - 2002: APS Diagnostics Undulator e-beam energy measurement

– Using angle-integrated undulator radiation measure stored e-beam energy changeJan. 20, 2004: UCLA Commissioning workshop

– Galayda wish list for spontaneous radiation measurementsFeb. 10, 2004: X-ray diagnostics planning meeting (John Arthur)

– Roman: Not possible to measure Keff with required accuracy K/K~1.5×10-4

Sep. 22, 2004: SLAC Commissioning workshop– Bingxin Yang: Keff can be measured with required accuracy

• Large aperture improves accuracy• Electron energy jitter is the main experimental problem• Two undulator differential measurement improves speed and accuracy over single undulator

measurements.

Oct., 2004: LCLS– Jim Welch: Keff can be measured with required accuracy

• Small aperture is better• Spectrometer allows fast data taking

Apr. 18, 2005: Zeuthen FEL Commissioning workshop– Bingxin Yang: Undulator mid-plane can be located within 10 m

• Regular observation can monitor systematic changes in undulators– Jim Welch:

Bingxin Yang



Hope for this workshopForm a consensus – Spontaneous spectral measurements can be used to measure Keff

with required accuracy (K/K~1.5×10-4)

Aperture size should not be an issue – Operational experience will decide it naturally

Make decisions on the monochromator / spectrometer issues– Monochromator (simple, low cost, robust)– Differential measurements (ultra-high resolution, dependable, other

uses: vertical alignment, monitor field change / damage quickly– Spectrometer (scientific experiments)

• Need to evaluate specs / cost / schedule / R & D / risk factors / operational availability / maintenance effort– Decisions may depend on other functions– My personal bias: machine diagnostics

Bingxin Yang



Features of the spontaneous spectrum and effect of beam quality: numerical calculations

Average properties: e-beam divergence (x’, y’), x-ray beam divergence (), and energy spread ()Aperture geometry: width and height, center offset, and undulator distancesMagnetic field errors

Effects of e-beam jitter: simulated experimentsBeamline Option 1: crystal monochromator with charge, energy and trajectory angle readoutBeamline Option 2: crystal monochromator with differential undulator setupHigh-resolution experiment: locating magnetic mid-plane of the undulator. Dependence on beam centroid position (x, y)

Summary

Outline

Bingxin Yang



Spontaneous Radiation Spectrum

+

PHOTON ENERGY (eV)

7800 8000 8200 8400 8600

FL

UX

+ ... ... =

FL

UX

ANGLE-INTEGRATED PHTON FLUX

PHOTON ENERGY (eV)7800 8000 8200 8400 8600

FL

UX

10 rad

20 rad

30 rad

100 rad

0

10 rad

RADIATION SPECTRUM IN CM FRAME

PHOTON ENERGY

FL

UX

0/N

0

Bingxin Yang



Angle-integrated? How large is the aperture!

Pinhole (sinc) < << Angle-integrated (numeric)BXY: Large enough for the edge feature to be stable

UNDULATOR SPECTRA THRU SQUARE WINDOW

PHOTON ENERGY (eV)

8000 8050 8100 8150 8200 8250 8300 8350 8400

FL

UX

(10

6 PH

OT

ON

S/n

C/0

.01%

BW

)

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6APERTURE = 140 rad

K = 3.5000E = 13.64 GeV

30 rad

25 rad

20 rad

15 rad 10 rad

C A B

160 rad

(5mm@167m)

(5mm@35m)

1 N

Bingxin Yang



Momentum compaction measurementsB.X. Yang, L. Emery, and M. Borland, “High Accuracy Momentum Compaction Measurement for the APS Storage Ring with Undulator Radiation,” BIW’00, Boston, May 2000, AIP Proc. 546, p. 234.

Energy spread measurementsB.X. Yang, and J. Xu, “Measurement of the APS Storage Ring Electron Beam Energy Spread Using Undulator Spectra,” PAC’01, Chicago, June 2001, p. 2338

RF frequency / damping partition fraction manipulations

B. X. Yang, A. H. Lumpkin, ‘Visualizing Electron Beam Dynamics and Instabilities with Synchrotron Radiation at the APS,” PAC’05

K/K simulationsB. X. Yang, “High-resolution undulator measurements Using angle-integrated spontaneous radiation,” PAC’05

1Resolution

N

Related publications 1 1

2 200

F F

N F F

Bingxin Yang



How large is the aperture! FEL-relevant

37 mRMS cone-radius 7.4 rad

5 mx

GL

Capture the radiation cone: 2.35 – 5 rms radius 17 – 37 radMeasured radiation spectrum is more important that calculated from field data!


PHOTON ENERGY (eV)8000 8050 8100 8150 8200 8250 8300 8350 8400

FL

UX

(106 P

HO

TO

NS

/nC

/0.01%B

W)

0.2

0.4

0.6

0.8

1.0

1.2

1.4


K = 3.5000E = 13.64 GeV

30 rad

25 rad

20 rad

15 rad 10 rad

C A B

160 rad

(5mm@167m)

(5mm@35m)

Bingxin Yang



Marking the location of a spectral edge

We will watch how the following property changes:

HALF PEAK PHOTON ENERGY

FEATURES OF LCLS UNDULATOR SPECTRUM (n = 1)

PHOTON ENERGY (eV)

8000 8100 8200 8300 8400 8500

FL

UX

(10

6 P

HO

TO

NS

/nC

/0.0

1%B

W)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

Peak Flux

HALF PEAK ENERGY

Peak Energy

(8267.2 eV)

= 3.5000

= 13.64 GeV

1 = 8265.7 eV

Bingxin Yang



Effects of Aperture Change (Size and Center)Plot the half-peak photon energy vs. aperture sizeEdge position stable for 25 – 140 rad 100 rad best operation pointIndependent of aperture size Independent of aperture center position

X-RAY SPECTRAL FEATURE OBSERVED (OBSERVED THROUGH A SQUARE APERTURE)

APERTURE (rad)

0 50 100 150 200

HA

LF

-PE

AK

EN

ER

GY

(eV

)

8264

8266

8268

8270

8272

K/K = 2.4 x 10-4

K/K = 2.4 x 10-5


PHOTON ENERGY (eV)8000 8050 8100 8150 8200 8250 8300 8350 8400

FL

UX

(106 P

HO

TO

NS

/nC

/0.01%B

W)

0.2

0.4

0.6

0.8

1.0

1.2

1.4


K = 3.5000E = 13.64 GeV

30 rad

25 rad

20 rad

15 rad 10 rad

C A B

160 rad

(5mm@167m)

(5mm@35m)

Bingxin Yang



Effects of Aperture Change (Source distance)

Calculate flux through an aperture satisfying:

≤ 100 rad ≤ allowed by chamber ID

Plot half-peak photon energyRectangular aperture reduces variation

X-RAY SPECTRAL FEATURE OBSERVED THROUGH A RECTANGULAR APERTURE

UNDULATOR TO APERTURE DISTANCE (M)

40 60 80 100 120 140 160

HA

LF

-PE

AK

EN

ER

GY

(eV

)

8266.6

8266.8

8267.0

8267.2

8267.4

K = 3.5000, E = 13.64 GeV, 1 = 8265.7 eV

Maximum vertical aperture = 4.8 mmMaximum horizontal aperture = 8 mmMaximum angle aperture = 100 rad SQ

K/K ~ 2.4 x 10-5

Bingxin Yang



Effects of Finite Energy ResolutionFour factors contribute to photon energy resolution

Electron beam energy spread (0.03% RMS X-ray energy width = 11.7 eV FWHM)

Monochromator resolution ( ~ 0.1% or 8 eV)

Photon beam divergence rad

Electron beam divergence y’ rad

222

22 2'

2.352 cot 2.35Total M

B y

Bingxin Yang



Effect of Finite Energy Resolution

Edge position moves with increasing energy spreadX-RAY SPECTRAL FEATURE OBSERVED (THROUGH 100 rad SQUARE APERTURE)

PHOTON ENERGY BOXCAR WIDTH (eV)0 10 20 30 40 50

HA

LF

-PE

AK

EN

ER

GY

(eV

)

8264

8266

8268

8270

8272

K/K = 2.4 x 10-4

K/K = 2.4 x 10-5

Bingxin Yang



Effects of Undulator Field Errors

Electron beam parameters

E = 13.640 GeV

x = 37 m

x’ = 1.2 rad

= 0.03%

Detector

Aperture

80 rad (H)

48 rad (V)

Monte Carlo integration for 10 K particle histories.

Bingxin Yang



Comparison of Perfect and Real Undulator SpectraFilename: LCL02272.ver; scaled by 0.968441 to make Keff = 3.4996

First harmonic spectrum changes little at the edge.

Bingxin Yang



Comparison of Perfect and Real Undulator Spectra

Changes in the third harmonic spectrum is more pronounced. But the edge region appears to be usable.Changes in the fifth harmonic spectrum is significant. Not sure whether we can use even the edge region.

Bingxin Yang



The following beam qualities are not problems for measuring spectrum edge:

e-beam divergence (x’, y’),

x-ray beam divergence (), energy spread () and monochromator resolution,aperture width and height, center offset, and undulator distances

Magnetic field errorsPreliminary results show that the first harmonic edge is usable. Third harmonic edge may also be usable.How to define effective K in the presence of error is not a trivial issue. I need to learn more to understand it (BXY).

Next we move on jitter simulations.

Summary of calculations so far

Bingxin Yang



Bunch charge jitterX-ray intensity is proportional to electron bunch charge (0.05% fluctuation).

Electron energy jitterLocation of the spectrum edge is very sensitive to e-beam energy change (10-5 noise): = 2·

Electron trajectory angle jitterTrajectory angle (0.24 rad jitter) directly changes grazing incidence angle of the crystal monochromator

Jitters and Fluctuations

Damaging effect! Use simulation to assess impact.

2

1 u22 2

2( , ) ,

12

u

u

hc

K

Bingxin Yang



Beamline Option 1: Poor man’s solution

One reference undulator One flat crystal monochromator (asymmetrically cut preferred)One flux intensity detectorOne hard x-ray imaging detectorBeamline slits (get close to 100 rad)

Operation procedure for setting Keff

Pick one reference undulator (U33) and measure a full spectrum by scanning the crystal angle (angle aperture ~ 100 rad)Position the crystal angle at the mid-edge and record n-shot (n = 10 –100) data of the x-ray flux intensity (FREF) with electron energy, trajectory angle, and charge Roll out reference undulator and roll in other undulator one at a time.

Set slits to 100 rad or best available

Adjust x-position until the n-shot x-ray flux intensity data matches FREF. Use the measured electron bunch data in real-time to correct for jitters


PHOTON ENERGY (eV)8000 8050 8100 8150 8200 8250 8300 8350 8400

FL

UX

(106

PH

OT

ON

S/n

C/0.01%

BW

)0.2

0.4

0.6

0.8

1.0

1.2

1.4


K = 3.5000E = 13.64 GeV

30 rad

25 rad

20 rad

15 rad 10 rad

C A B

160 rad

(5mm@167m)

(5mm@35m)

Bingxin Yang



Measure fluctuating variables

Charge monitor: bunch charge

OTR screen / BPM at dispersive point: energy centroid

Hard x-ray imaging detector: electron trajectory angle (new proposal)

Bingxin Yang



One Segment Simulation: ApproachELECTRON BUNCH CHARGE BY SHOT

BUNCH NUMBER

100 200 300 400 500

BU

NC

H C

HA

RG

E (

nC

)

0.0

0.5

1.0

1.5

2.0ELECTRON BUNCH CHARGE HISTOGRAM

BUNCH CHARGE (nC)0.0 0.5 1.0 1.5 2.0

FR

EQ

UE

NC

Y

0

100

200

300

400

500MEAN = 1.001 nCSTDEV = 0.201 nC

ELECTRON BUNCH ENERGY CENTROID

BUNCH NUMBER100 200 300 400 500

BU

NC

H E

NE

RG

Y (

nC

)

13.58

13.60

13.62

13.64

13.66

13.68

13.70

ELECTRON BUNCH ENERGY HISTOGRAM

BUNCH ENERGY (GeV)13.58 13.60 13.62 13.64 13.66 13.68 13.70

FR

EQ

UE

NC

Y

0

100

200

300

400

500 MEAN = 13.640 GeVSTDEV = 0.0137 GeV

NOMINAL PHOTON ENERGY HISTOGRAM

NOMINAL PHOTON ENERGY (eV)8200 8220 8240 8260 8280 8300 8320

FR

EQ

UE

NC

Y

0

100

200

300

400

500MEAN = 8265.3 eVSTDEV = 16.6 eV

MODEL UNDULATOR SPECTRA

PHOTON ENERGY (eV)8000 8100 8200 8300 8400

FL

UX

(10

6 PH

OT

ON

S/n

C/0

.01%

BW

)

0.2

0.4

0.6

0.8

1.0

1.2

1.4

K = 3.5000E = 13.64 GeVWINDOW > 50 rad

A BC

Bingxin Yang



Effect of electron energy “correlation”

Define “Correlated Electron-Photon Energy”

NORMALIZE & CORRECTED COUNTS (K = 3.5000)

CORRECTED PHOTON ENERGY (eV)8100 8200 8300 8400

PH

OT

ON

CO

UN

TS

PE

R S

HO

T

0

2e+5

4e+5

6e+5

8e+5

1e+6

CHARGE NORMALIZE COUNTS (K = 3.5000)

PHOTON ENERGY (eV)8100 8200 8300 8400

PH

OT

ON

CO

UN

TS

PE

R S

HO

T

0

2e+5

4e+5

6e+5

8e+5

1e+6

01

2cotCORR

y y

D

RMS error from simulation

RAW COUNTS (K = 3.5000)

PHOTON ENERGY (eV)

8100 8200 8300 8400

PH

OT

ON

CO

UN

TS

PE

R S

HO

T

0.0

2.0e+5

4.0e+5

6.0e+5

8.0e+5

1.0e+6

1.2e+6

Bingxin Yang



Summary of 1-undulator simulations(charge normalized and energy-corrected)

Applying correction with electron charge, energy and trajectory angle data shot-by-shot greatly improves the quality of data analysis at the spectral edge.

Full spectrum measurement for one undulator segment (reference)

The minimum integration time to resolve effective-K changes is 10 – 100 shots with other undulator segment (data processing required)

As a bonus, the dispersion at the flag / BPM can be measured fairly accurately.

Not fully satisfied:Rely heavily on correction calibration of the instrumentNo buffer for “unknown-unknowns”Non-Gaussian beam energy distribution ???

Bingxin Yang



Beamline Option 2: Ultra-high ResolutionReference Undulator (U33)

Period length and B-field same as other segments

Zero cant angle

Field characterized with high accuracy

Upstream corrector capable of 200 rad steering (may be reduced if needed).

Broadband monochromator (E/E ~ 0.03%)Improves photon statistics

Suppress coherent intensity fluctuations

Big area, large dynamic range, uniform, linear detector

Hard x-ray imaging detector (trajectory angle)

Bingxin Yang



Operation Procedures for setting Keff (BL2)Steer the beam to be away from the axis in the reference undulator (U33) and measure a full spectrum by scanning the crystal angle (angle aperture ~ 100 rad)Position the crystal angle at the mid-edge Roll in other undulator one at a time (test undulator).

Adjust the x-position of the test undulator until the x-ray intensities of the two undulator matches (difference < threshold).Use the measured electron beam angle data in real-time to correct for angle jitters if necessary


PHOTON ENERGY (eV)8000 8050 8100 8150 8200 8250 8300 8350 8400

FL

UX

(106

PH

OT

ON

S/n

C/0.01%

BW

)

0.2

0.4

0.6

0.8

1.0

1.2

1.4


K = 3.5000E = 13.64 GeV

30 rad

25 rad

20 rad

15 rad 10 rad

C A B

160 rad

(5mm@167m)

(5mm@35m)

Bingxin Yang



Differential Measurements of Two Undulators

Insert only two segments in for the entire undulator.

Steer the e-beam to separate the x-raysUse one mono to pick the same x-ray energy

Use two detectors to detect the x-ray flux separatelyUse differential electronics to get the difference in flux

Bingxin Yang



Signal of Differential Measurements

Select x-ray energy at the edge (Point A).Record difference in flux from two undulators.Make histogram to analyze signal qualitySignals are statistically significant when peaks are distinctly resolved


PHOTON ENERGY (eV)8000 8100 8200 8300 8400

FL

UX

(10

6 PH

OT

ON

S/n

C/0

.01%

BW

)

0.2

0.4

0.6

0.8

1.0

1.2

1.4

K = 3.5000E = 13.64 GeVWINDOW > 50 rad

A BC

DIFFERENCE COUNTS (K = 3.5005)

BUNCH NUMBER

100 200 300 400 500

CO

UN

TS

(10

3 P

ER

BU

NC

H)

-80

-60

-40

-20

0

K = 3.5005E = 13.64 GeVQ = 1.0 nC

HISTOGRAM OF DIFFERENCE COUNTS

DIFFERENCE COUNTS (103 PER BUNCH)

-100 -50 0 50 100

FR

EQ

UE

NC

Y

0

500

1000

1500

PHOTON ENERGY = 8265.7 eVTOAL COUNTS = 0.644 106

N_avg = 1 (bunch)

K = 3.5005



-100 -50 0 50 100

FR

EQ

UE

NC

Y

0

500

1000

1500

K = 3.4995


N_avg = 1 (bunch)

K = 3.5005

K/K = 1.5 10-

4

Bingxin Yang



Summing multi-shots improves resolution

Summing difference signals over 64 bunches

Distinct peaks make it possible to calculate the difference K at the level of 10-5.



-8 -6 -4 -2 0 2 4 6 8

FR

EQ

UE

NC

Y

0

500

1000

1500

K = 3.499965


N_avg = 1 (bunch)

K = 3.500035



-8 -6 -4 -2 0 2 4 6 8

FR

EQ

UE

NC

Y

0

500

1000

1500

K = 3.499965


N_avg = 64 (bunches)

K = 3.500035

Example: Average improves resolution for K/K = 10-5

Bingxin Yang



Differential Measurement Recap Use one reference undulator to test another undulator simulataneouslySet monochromator energy at the spectral edgeMeasure the difference of the two undulator intensity



-4 -2 0 2 4

FR

EQ

UE

NC

Y

0

500

1000

1500K = 3.49999


N_avg = 64 (bunches)

K = 3.50001

Simulation gives approximately:

• To get RMS error K/K < 0.710-4, we need only a single shot (0.2 nC)!

• We can use it to periodically to log minor magnetic field changes, for radiation damage.

• Any other uses?

Bingxin Yang



Other application of the techniques:

Search for the neutral magnetic plane

Set the monochromator at mid-edge (Point A).Insert only one test segment in.Move the undulator segment up and down, or move electron beam up and down with a local bump.When going through the plane of minimum field (neutral plane), the spectrum edge is highest in energy. Hence the photon flux peaks.After the undulator is roughly positioned, taking turns to scan one end at a time, up and down, to level it.


PHOTON ENERGY (eV)8000 8100 8200 8300 8400

FL

UX

(10

6 PH

OT

ON

S/n

C/0

.01%

BW

)

0.2

0.4

0.6

0.8

1.0

1.2

1.4

K = 3.5000E = 16.34 GeVWINDOW > 50 rad

A BC

Bingxin Yang



Simulation of undulator vertical scan

Charge normalization only: ~ 20K shots / pointCharge-normalized and electron-energy corrected: ~ 512 shots / pointDifferential measurements (two undulators): ~ 16 shots /point gives us RMS error ~ 1.0 m ?!

UNDULATOR VERTICAL SCAN (20K x 0.2 nC)/PT

VETICAL POSITION

-50 -40 -30 -20 -10 0 10 20 30 40 50

FL

UX

(1

06 P

HO

TO

NS

/nC

)

0.395

0.400

0.405

0.410

0.415

UNDULATOR VERTICAL SCAN (16 x 0.2 nC)/PT

VETICAL POSITION

-50 -40 -30 -20 -10 0 10 20 30 40 50

DIF

FE

RE

NC

E S

IGN

AL

-0.03

-0.02

-0.01

0.00

0.01

2

5 60 110 10

0 2 u

K y K y

K

UNDULATOR VERTICAL SCAN (512 x 0.2 nC)/PT

VETICAL POSITION-50 -40 -30 -20 -10 0 10 20 30 40 50

EL

EC

TR

ON

EN

ER

GY

CO

RR

EC

TE

D

416000

418000

420000

422000

424000

426000

428000

430000

Bingxin Yang



Conclusion for Locating Magnetic Neutral Plane

Both techniques can be used to search the magnetic neutral plane, each has its own advantages and disadvantages:

Single undulator measurement (with charge-normalization and e-beam energy correction) can get required S/N ratio after averaging. Differential measurement has best sensitivity, need shortest time (keep up with mechanical scan), but required more hardware.

Finite beam sizes and centroid offset (in undulator) shift spontaneous spectrum: the apparent K is given by

22 20

02

( , ) (0,0)

(0,0)apparent eff y eff eff

n n xeff u

K x y K y K Ka x b

K x x

Bingxin Yang



Summary (The Main Idea)We propose to use angle-integrated spectra (through a large aperture, but radius < 1/) for high-resolution measurements of undulator field.

Expected to be robust against undulator field errors and electron beam jitters.

Simulation shows that we have sufficient resolution to obtain K/K < 10-4 using charge normalization. Correlation of undulator spectra and electron beam energy data further improves measurement quality. A Differential technique with very high resolution was proposed: It is based on comparison of flux intensities from a test undulator with that from a reference undulator.

Within a perfect undulator approximation, the resolution is extremely high, K/K = 3 10-6 or better. It is sufficient for XFEL applications.It can also be used for routinely logging magnet degradation.

Bingxin Yang



Summary (Continued)Either beamline option can be used for searching for the effective neutral magnetic plane and for positioning undulator vertically. The simulation results are encouraging (resolution ~1 m in theory for now, hope to get ~ 10 m in reality).

What’s next

Sources of error need to be further studied. Experimental tests need to be done.

More calculation and understanding of realistic fieldLongitudinal wake field effect,Experimental test in the APS 35IDMore?

Bingxin Yang



Monochromator RecommendationA dedicated monochromator for undulator measurement (low cost and robust, permanently installed).

Use it for K/K measurementsUse it for regular vertical alignment checkUse it for routine magnetic field measurements at regular intervals (after routine BBA operation).

Logging magnetic field changes to see trend of damage, identify sources / mechanism for damageLook for most damaged undulator segments for service for next shutdown

Location of the monochromatorFront end easy to service. Too crowded?In tunnel OK.

Differential measurement strongly recommendedBut steering magnet can be added later as an upgrade. Differential measurement saves time, improves accuracy.

Spectrometer will be easily justified by the science it supports.

Documents

Bingxin Yang Large aperture spectrum [email protected] Beam-based undulator measurement workshop, Nov. 14, 2005 Undulator Effective-K Measurements