Bingxin Yang High resolution effective K [email protected] September 22-23, 2004 High-Resolution Effective K Measurements Using Spontaneous

Bingxin Yang

High resolution effective K measurements [email protected]

September 22-23, 2004

High-Resolution Effective K MeasurementsUsing Spontaneous Undulator Radiation

Bingxin Yang

Advanced Photon Source

Argonne National Lab

Bingxin Yang



Two Essential Elements for Far-Field Measurements

(Adapted from x-ray diagnostics planning meeting, Feb. 2004, SLAC)

Roll away undulatorsSpontaneous radiation is most useful when background is clean, with each undulator rolled in individually.

Adequate Far-field X-ray Diagnostics extracts the beam / undulator information– Electron trajectory inside the undulator (m / rad accuracy)

– Undulator K-value (K/K ~ 1.5 × 10-4)

– Relative phase of undulators ( ~ 10°)

– X-ray intensity measurements (E/E ~ 0.1%, z-dependent)

– Micro-bunching measurements (z-dependent)

Bingxin Yang



Scope

Introduction: A simple feature of the spontaneous spectrumEffect of beam quality: emittance, energy spread…Simulated experiments (K/K ~ 10-6?!)Key componentsFinal remarks (conditional conclusion)

Contents

Relative measurements of undulator effective K using far-field spontaneous radiation (8 keV, 40 m to 60 m from undulator exit). Bonus: Wide bandwidth monochromator for z-dependent x-ray intensity measurement (E/E ~ 0.1%).

Bingxin Yang



Main Tools

Analytical work (back of an envelope)

Numerical simulations (MathCAD)

Undulator Radiation Modeling (XOP)Angle integrated spectra: XOP/XUS

Undulator radiation intensity profile: XOP/XURGENT

Reference: M. Sanchez del Rio and R. J. Dejus "XOP: Recent Developments," SPIE proceedings Vol. 3448, pp.340-345, 1998.

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



A Closer Look at the Spectral EdgeMonitor the edge of angle-integrated spectrum

Shifts E/E ~ – 2K/K.50 – 100 data points, 5 – 15 minutes to acquire a spectrum!

Monitor the intensity at fundamental photon energyChange F/F ~ 400 K/K < 6% intensity change neededTakes 1 – 2 seconds to acquire data?

INTENSITY SPECTRUM OF AN LCLS UNDULATOR SEGMENTTHROUGH A 100 RAD SQUARE WINDOW

PHOTON ENERGY (eV)8200 8250 8300 8350

FL

UX

(P

HO

TO

NS

/nC

/0.0

1%B

W)

200.0x103

400.0x103

600.0x103

800.0x103

1.0x106

1.2x106

1.4x106

K=3.501

K=3.499

ANGLE-INTEGRATED X-RAY BEAM INTENSITY (OBSERVED AT FUNDAMENTAL PHOTON ENERGY)

EFFECTIVE K (Keff)3.496 3.498 3.500 3.502 3.504

RE

LA

TIV

E I

NT

EN

SIT

Y

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

100 RAD APERTURE

Bingxin Yang



Impact of Aperture Change (Size and Center)Lower energy photons come in larger angles.Spectra independent of aperture size / location as long as the beam is fully contained.Spectra independent of emittance for adequate aperture.

INTENSITY PROFILES IN MOMENTUM SPACE

ANGLE (MICRO-RADIAN)-30 -25 -20 -15 -10 -5 0 5 10 15 20 25 30

FL

UX

(A

RB

. UN

ITS

)

0

20000

40000

60000

E=8210(eV)

E=8266(eV)

E=8295(eV)

UNDULATOR SPECTRA THRU SQUARE WINDOW

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

FL

UX

(10

6 P

HO

TO

NS

/nC

/0.0

1%B

W)

0.2

0.4

0.6

0.8

1.0

1.2

1.4APERTURE = 160 rad

K = 3.5000E = 16.34 GeV

35 rad

30 rad

20 rad

15 rad

10 rad

C A B

Bingxin Yang



Impact of Finite Energy ResolutionElectron beam energy spread (0.06% RMS)

X-ray energy spread = 25 eV FWHM

Monochromator resolution (E/E ~ 0.1% or 8 eV)Small effect on 70-eV wide edge!

INTENSITY SPECTRUM OF AN LCLS UNDULATOR SEGMENTTHROUGH A 100 RAD SQUARE WINDOW

PHOTON ENERGY (eV)

8200 8250 8300 8350

FL

UX

(P

HO

TO

NS

/nC

/0.0

1%

BW

)

200.0x103

400.0x103

600.0x103

800.0x103

1.0x106

1.2x106

1.4x106

E = 0 eV

E = 8 eV

K = 3.5000E = 16.34 GeV

E = 25 eV

X-RAY INTENSITY THROUGH A 100 RAD(OBSERVED AT FUNDAMENTAL PHOTON ENERGY)

EFFECTIVE K (Keff)

3.496 3.498 3.500 3.502 3.504

RE

LA

TIV

E I

NT

EN

SIT

Y

0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

1.3

1.4

1.5

E = 0 eV

E = 8 eV

K = 3.5000E = 13.64 GeV

E = 25 eV

Bingxin Yang



Impact of Electron Energy Jitter Location of the spectrum edge is very sensitive to e-beam energy change (0.1% jitter): / = 2·/

2

1 u22 2

2( , ) ,

12

u

u

hc

K

X-ray intensity is proportional to electron bunch charge. Current monitor data (20% fluctuation) can be used to normalize the x-ray intensity data.

Impact of Electron Bunch Charge Fluctuation

Most damaging instrument effect!

Bingxin Yang



A Simulation: Input and 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 = 16.34 GeVWINDOW > 50 rad

A BC

Bingxin Yang



A look at the output intensity jitterMODEL UNDULATOR SPECTRA

PHOTON ENERGY (eV)

8000 8100 8200 8300 8400

FL

UX

(10

6 P

HO

TO

NS

/nC

/0.0

1%B

W)

0.2

0.4

0.6

0.8

1.0

1.2

1.4

K = 3.5000E = 16.34 GeVWINDOW > 50 rad

A BC

PHOTON COUNTS AT SPECTRUM PEAK (8210 eV)

COUNTS (106 PER BUNCH)

0.0 0.5 1.0 1.5 2.0 2.5

FR

EQ

UE

NC

Y

0

200

400

600

800

1000 MEAN = 1.20 106

STDEV = 0.25 106

EXPECTED COUNTS = 1.226 106

(C) MONO @ 8210eV

CHARGE NORMALIZED PHOTON COUNTS NEAR SPECTRUM PEAK (8210 eV)

COUNTS (106 / nC)

0.0 0.5 1.0 1.5 2.0 2.5

FR

EQ

UE

NC

Y

0

1000

2000

3000

4000

5000

6000

MEAN = 1.201 106

STDEV = 0.064 106


(C) MONO @ 8210eV

PHOTON COUNTS AT SPECTRUM EDGE (8265.7 eV)


0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

FR

EQ

UE

NC

Y

0

200

400

600

MEAN = 0.645 106

STDEV = 0.297 106


(A) MONO @ 8265.7 eV

CHARGE NORMALIZED PHOTON COUNTS AT SPECTRUM EDGE (8265.7 eV)

COUNTS (106 / nC)

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6

FR

EQ

UE

NC

Y

0

200

400

600

MEAN = 0.646 106

STDEV = 0.265 106


(A) MONO @ 8265.7 eV

PHOTON COUNTS AT SPECTRUM EDGE (8295 eV)


0.0 0.2 0.4 0.6 0.8

FR

EQ

UE

NC

Y

0

200

400

600

800

MEAN = 0.238 106

STDEV = 0.190 106


(B) MONO @ 8295 eV

CHARGE NORMALIZED PHOTON COUNTS BEYOND SPECTRUM EDGE (8295 eV)

COUNTS (106 / nC)

0.0 0.2 0.4 0.6 0.8

FR

EQ

UE

NC

Y

0

200

400

600

800

MEAN = 0.238 106

STDEV = 0.182 106


(B) MONO @ 8295 eV

Intensity distribution depends strongly on photon energy!

Bingxin Yang



Effect of multi-shots integrationRELATIVE RMS ERROR OF MEASURED FLUX

(Q = 1 nC, E = 13.64 GeV, K = 3.5000)

PHOTON ENERGY (eV)8000 8100 8200 8300 8400

ST

AN

DA

RD

DE

VIA

TIO

N /

FL

UX

0.0

0.5

1.0

No Charge Normalization

With Charge Normalization

An acceptable spectrum needs integration of 256 – 1024shots, resulting scan time = 7 – 18 minutes @ 120 Hz.

ANGLE-INTEGRATED UNDULATOR SPECTRA

PHOTON ENERGY (eV)8150 8200 8250 8300 8350 8400

FL

UX

(10

6 P

HO

TO

NS

/nC

/0.0

1%B

W)

0.2

0.4

0.6

0.8

1.0

1.2

K = 3.5000E = 16.34 GeVN = 16 (shot)Time = 3.6 (min.)

Measured flux

Expected flux


PHOTON ENERGY (eV)

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

K = 3.5000E = 16.34 GeVN = 64 (shot)Time = 4.2 (min.)

Measured flux

Expected flux


PHOTON ENERGY (eV)

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

K = 3.5000E = 16.34 GeVN = 256 (shot)Time = 7 (min.)

Measured flux

Expected flux


PHOTON ENERGY (eV)

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

K = 3.5000E = 16.34 GeVN = 1024 (shot)Time = 18 (min.)

Measured flux

Expected flux

Bingxin Yang



Summary of One-Undulator Simulations

Intensity noise (jitter) at the spectrum edge is largely due to electron beam energy jitter.

With sufficient integration time, the measured spectrum is accurate enough to resolve effective K change at a level of K/K ~ 1.5 × 10-4.

Average will take longer if LINAC jitter has time structure.

A faster and more accurate technique is desirable.

Bingxin Yang



Electricity 101

V/V ~ 0.001, I/I ~ 0.001, R = 3.50xxx?

Compare two passive devices: (R-R0)/R ~ I

Bingxin Yang



Differential Measurements of Two Undulators

Insert only two segments in for the entire undulator.

Kick 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



Differential Measurements: Signal

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

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 = 16.34 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 (0.5 sec.)

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



Simulation II Recap Use one perfect reference undulator to test another perfect undulator (two Perfect Periodic Undulators)Set monochromator energy at the spectral edgeAccumulate difference count from the two undulators for ~64 bunches (0.5 second).



-4 -2 0 2 4

FR

EQ

UE

NC

Y0

500

1000

1500

K = 3.49999


N_avg = 64 (bunches)

K = 3.50001

K/K = 3 10-

6

The signal is statistically significant in resolving undulators with

Is it still meaningful?Can we detect minor radiation damage?

Bingxin Yang



Key Component: Reference Undulator

Last segment in the undulator

Period length and B-field same as other segments

Zero cant angle

Field characterized with high accuracy

Upstream corrector capable of 400 rad kicks.

Bingxin Yang



Key Component: Monochromator

Large acceptance aperture (30 mm 15 mm)

Wide bandwidth (E/E = 0.1%)

Asymmetrically cut Ge(111) crystals (2 – 8 keV) Multilayer reflectors (0.8 – 2.5 keV)

Low power only

Large dynamic range detector(s)

Low noise amplifier and 16-bit digitizers

Bingxin Yang



Asymmetrically Cut Ge(111)

sin

sinasym sym

E E

E E

ENERGY RESOLUTION OF ASYMMETRICALLY CUT Ge(111)

PHOTON ENERGY (eV)

3000 4000 5000 6000 7000 8000

E/E

0.0000

0.0005

0.0010

0.0015

0.0020

= 0 (DEG)

= 21.5° = 15°

= 12.5° = 18° = 26.5°

Bingxin Yang



Final RemarksWe proposed a differential measurement technique for effective K. It is based on comparison of angle-integrated flux intensity from a test undulator with that from a reference undulator. Within the perfect undulator approximation, its potential resolution, K/K = 3 10-6 or better, is sufficient for LCLS applications. It is essential to have remotely controlled roll away undulators for this technique to be practical.For not so perfect undulators, we need to extend the definition of Keff, or define a new figure of merit. The limitation of this proposed technique will need to be re-examined in that context.

Documents

Bingxin Yang High resolution effective K [email protected] September 22-23, 2004 High-Resolution Effective K Measurements Using Spontaneous