high-resolution effective k measurements using spontaneous undulator radiation
DESCRIPTION
High-Resolution Effective K Measurements Using Spontaneous Undulator Radiation. Bingxin Yang Advanced Photon Source Argonne National Lab. Two Essential Elements for Far-Field Measurements. (Adapted from x-ray diagnostics planning meeting, Feb. 2004, SLAC) Roll away undulators - PowerPoint PPT PresentationTRANSCRIPT
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
EXPECTED COUNTS = 1.226 106
(C) MONO @ 8210eV
PHOTON COUNTS AT SPECTRUM EDGE (8265.7 eV)
COUNTS (106 PER BUNCH)
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
EXPECTED COUNTS = 0.644 106
(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
EXPECTED COUNTS = 0.644 106
(A) MONO @ 8265.7 eV
PHOTON COUNTS AT SPECTRUM EDGE (8295 eV)
COUNTS (106 PER BUNCH)
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
EXPECTED COUNTS = 0.186 106
(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
EXPECTED COUNTS = 0.186 106
(B) MONO @ 8295 eV
Intensity distribution depends strongly on photon energy!
Bingxin Yang
High resolution effective K measurements [email protected]
September 22-23, 2004
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
ANGLE-INTEGRATED UNDULATOR SPECTRA
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
ANGLE-INTEGRATED UNDULATOR SPECTRA
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
ANGLE-INTEGRATED UNDULATOR SPECTRA
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
Electricity 101
V/V ~ 0.001, I/I ~ 0.001, R = 3.50xxx?
Compare two passive devices: (R-R0)/R ~ I
Bingxin Yang
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
HISTOGRAM OF DIFFERENCE COUNTS
DIFFERENCE COUNTS (103 PER BUNCH)
-100 -50 0 50 100
FR
EQ
UE
NC
Y
0
500
1000
1500
K = 3.4995
PHOTON ENERGY = 8265.7 eVTOAL COUNTS = 0.644 106
N_avg = 1 (bunch)
K = 3.5005
K/K = 1.5 10-
4
Bingxin Yang
High resolution effective K measurements [email protected]
September 22-23, 2004
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.
HISTOGRAM OF DIFFERENCE COUNTS
DIFFERENCE COUNTS (103 PER BUNCH)
-8 -6 -4 -2 0 2 4 6 8
FR
EQ
UE
NC
Y
0
500
1000
1500
K = 3.499965
PHOTON ENERGY = 8265.7 eVTOAL COUNTS = 0.644 106
N_avg = 1 (bunch)
K = 3.500035
HISTOGRAM OF DIFFERENCE COUNTS
DIFFERENCE COUNTS (103 PER BUNCH)
-8 -6 -4 -2 0 2 4 6 8
FR
EQ
UE
NC
Y
0
500
1000
1500
K = 3.499965
PHOTON ENERGY = 8265.7 eVTOAL COUNTS = 0.644 106
N_avg = 64 (bunches)
K = 3.500035
Example: Average improves resolution for K/K = 10-5
Bingxin Yang
High resolution effective K measurements [email protected]
September 22-23, 2004
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).
HISTOGRAM OF DIFFERENCE COUNTS
DIFFERENCE COUNTS (103 PER BUNCH)
-4 -2 0 2 4
FR
EQ
UE
NC
Y0
500
1000
1500
K = 3.49999
PHOTON ENERGY = 8265.7 eVTOAL COUNTS = 0.644 106
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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
High resolution effective K measurements [email protected]
September 22-23, 2004
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.