Undulator Effective-K Measurements
Using Angle-Integrated Spontaneous Radiation
Bingxin Yang and Roger Dejus
Advanced Photon Source
Argonne National Lab
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Some History of the Conceptual Development
1998 - 2002: APS Diagnostics Undulator e-beam energy measurement
– Using angle-integrated undulator radiation measure stored e-beam energy change
Jan. 20, 2004:
UCLA Commissioning workshop
– Galayda wish list for spontaneous radiation measurements
Feb. 10, 2004: X-ray diagnostics planning meeting (John Arthur)
– Roman: Not possible to measure Keff with required accuracy DK/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 mm
• Regular observation can monitor systematic changes in undulators
– Jim Welch:
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Hope for this workshop
Form a consensus
– Spontaneous spectral measurements can be used to measure Keff
with required accuracy (DK/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
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Outline
Features of the spontaneous spectrum and effect of beam
quality: numerical calculations
Average properties: e-beam divergence (sx’, sy’), x-ray beam
divergence (sw), and energy spread (sg)
Aperture geometry: width and height, center offset, and undulator
distances
Magnetic field errors
Effects of e-beam jitter: simulated experiments
Beamline Option 1: crystal monochromator with charge, energy and
trajectory angle readout
Beamline Option 2: crystal monochromator with differential
undulator setup
High-resolution experiment: locating magnetic mid-plane of the
undulator. Dependence on beam centroid position (x, y)
Summary
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Spontaneous Radiation Spectrum
ANGLE-INTEGRATED PHTON FLUX
FLUX
100 mrad
30 mrad
20 mrad
10 mrad
7800
8000
8200
8400
8600
+ ... ... =
PHOTON ENERGY (eV)
RADIATION SPECTRUM IN CM FRAME
FLUX
10 mrad
+
w0/N
0
FLUX
FLUX
w0
PHOTON ENERGY
7800
8000
8200
8400
PHOTON ENERGY (eV)
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
8600
Angle-integrated? How large is the aperture!
Pinhole (sinc) < 1 g N << Angle-integrated (numeric)
BXY: Large enough for the edge feature to be stable
UNDULATOR SPECTRA THRU SQUARE WINDOW
FLUX (106 PHOTONS/nC/0.01%BW)
C
1.6
1.4
A
B
K = 3.5000
E = 13.64 GeV
APERTURE = 140 mrad
(5mm@35m)
1.2
1.0
0.8
30 mrad
(5mm@167m)
0.6
160 mrad
25 mrad
0.4
20 mrad
15 mrad
0.2
8000
8050
8100
8150
10 mrad
8200
8250
8300
PHOTON ENERGY (eV)
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
8350
8400
Related publications
Momentum compaction measurements
B.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.
Dw
w
1 DF
1 DF

2N F
200 F
Resolution 
1
N
Energy spread measurements
B.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
DK/K simulations
B. X. Yang, “High-resolution undulator
measurements Using angle-integrated
spontaneous radiation,” PAC’05
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
How large is the aperture! FEL-relevant
UNDULATOR SPECTRA THRU SQUARE WINDOW
C
1.6
1.4
A
B
K = 3.5000
E = 13.64 GeV
APERTURE = 140 mrad
(5mm@35m)
1.2
RMS cone-radius 
sx
1.0
0.8
6
PHOTONS/nC/0.01%BW)
FLUX (10
LG
37 m m
 7.4 m rad
5m
30 mrad
(5mm@167m)
0.6
160 mrad
25 mrad
0.4
20 mrad
15 mrad
0.2
8000
8050
8100
8150
10 mrad
8200
8250
8300
PHOTON ENERGY (eV)
Capture the radiation cone: 2.35 – 5 rms radius  17 – 37 mrad
Measured radiation spectrum is more important that calculated
from field data!
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
8350
8400
6
FLUX (10 PHOTONS/nC/0.01%BW)
Marking the FEATURES
locationOFofLCLS
a spectral
UNDULATORedge
SPECTRUM (n = 1)
1.6
1.4
Peak Flux
1.2
 = 3.5000
 = 13.64 GeV
w1 = 8265.7 eV
1.0
0.8
0.6
0.4
HALF PEAK ENERGY
(8267.2 eV)
0.2
Peak Energy
We will watch
0.0
8000
8100
8200
8300
8400
how the following
PHOTON ENERGY (eV)
property changes:
HALF PEAK PHOTON ENERGY
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
8500
Effects of Aperture Change (Size and Center)
UNDULATOR SPECTRA THRU SQUARE WINDOW
C
1.6
1.4
A
B
K = 3.5000
E = 13.64 GeV
APERTURE = 140 mrad
(5mm@35m)
1.2
1.0
0.8
30 mrad
(5mm@167m)
6
PHOTONS/nC/0.01%BW)
FLUX (10
0.6
160 mrad
25 mrad
0.4
X-RAY SPECTRAL FEATURE OBSERVED
(OBSERVED THROUGH A SQUARE APERTURE)
8272
HALF-PEAK ENERGY (eV)
Plot the half-peak photon
energy vs. aperture size
Edge position stable for 25
– 140 mrad  100 mrad
best operation point
Independent of aperture
size  Independent of
aperture center position
DK/K = 2.4 x 10-4
8270
DK/K = 2.4 x 10-5
8268
8266
8264
20 mrad
15 mrad
0.2
10 mrad
0
8000
8050
8100
8150
8200
8250
8300
8350
8400
PHOTON ENERGY (eV)
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
50
100
150
APERTURE (mrad)
Bingxin Yang
bxyang@aps.anl.gov
200
Effects of Aperture Change (Source distance)
X-RAY SPECTRAL FEATURE OBSERVED
THROUGH A RECTANGULAR APERTURE
HALF-PEAK ENERGY (eV)
8267.4
Calculate flux through an
aperture satisfying:
DK/K ~ 2.4 x 10-5
≤ 100 mrad
≤ allowed by chamber ID
8267.2
Plot half-peak photon energy
Rectangular aperture reduces
variation
8267.0
K = 3.5000, E = 13.64 GeV, w1 = 8265.7 eV
Maximum vertical aperture = 4.8 mm
Maximum horizontal aperture = 8 mm
Maximum angle aperture = 100 mrad SQ
8266.8
8266.6
40
60
80
100
120
140
160
UNDULATOR TO APERTURE DISTANCE (M)
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Effects of Finite Energy Resolution
Four factors contribute to photon energy resolution
Electron beam energy spread (0.03% RMS  X-ray energy
width = 11.7 eV FWHM)
Monochromator resolution (DwM/w ~ 0.1% or 8 eV)
Photon beam divergence Dw~2.35/gN1/2 ~8mrad
Electron beam divergence sy’ ~1.2mrad
 DwTotal   2.35s g   DwM 
2
 2.35  s 2  D 2 

2



cot


 
B 
y'
w

 


g   w 
 w  
2
2
2
g
w

Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Effect of Finite Energy Resolution
X-RAY SPECTRAL
FEATURE OBSERVED
Edge position moves
with increasing
energy spread
(THROUGH 100 mrad SQUARE APERTURE)
HALF-PEAK ENERGY (eV)
8272
DK/K = 2.4 x 10-4
8270
8268
DK/K = 2.4 x 10-5
8266
8264
0
10
20
30
40
50
PHOTON ENERGY BOXCAR WIDTH (eV)
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Effects of Undulator Field Errors
Electron beam
parameters
E = 13.640 GeV
sx = 37 mm
sx’ = 1.2 mrad
sg/g = 0.03%
Detector
Aperture
80 mrad (H)
48 mrad (V)
Monte Carlo integration for 10 K particle histories.
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Comparison of Perfect and Real Undulator Spectra
Filename: LCL02272.ver; scaled by 0.968441 to make Keff = 3.4996
First harmonic spectrum changes little at the edge.
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
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.
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Summary of calculations so far
The following beam qualities are not problems for
measuring spectrum edge:
e-beam divergence (sx’, sy’),
x-ray beam divergence (Dw),
energy spread (sg) and monochromator resolution,
aperture width and height, center offset, and
undulator distances
Magnetic field errors
Preliminary 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.
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Jitters and Fluctuations
Bunch charge jitter
X-ray intensity is proportional to electron bunch charge (0.05%
fluctuation).
Electron energy jitter
Location of the spectrum edge is very sensitive to e-beam energy change
(10-5 noise): Dw/w = 2·Dg/g
2g 2w u
hc
w1 ( , ) 
,
w

u
K2
u
2 2
1
g 
2
Electron trajectory angle jitter
Trajectory angle (0.24 mrad jitter) directly changes grazing incidence
angle of the crystal monochromator
Damaging effect! Use simulation to assess impact.
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Beamline Option 1: Poor man’s solution
Operation procedure for setting Keff
C
1.6
1.4
A
B
K = 3.5000
E = 13.64 GeV
APERTURE = 140 mrad
(5mm@35m)
1.2
1.0
0.8
6
PHOTONS/nC/0.01%BW)
FLUX (10
One reference undulator
One flat crystal monochromator
(asymmetrically cut preferred)
One flux intensity detector
One hard x-ray imaging detector
Beamline slits (get close to 100 mrad)
UNDULATOR SPECTRA THRU SQUARE WINDOW
30 mrad
(5mm@167m)
0.6
160 mrad
25 mrad
0.4
20 mrad
15 mrad
0.2
8000
8050
8100
8150
10 mrad
8200
8250
8300
8350
PHOTON ENERGY (eV)
Pick one reference undulator (U33) and measure a full spectrum by
scanning the crystal angle (angle aperture ~ 100 mrad)
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 mrad 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
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
8400
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)
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
One Segment Simulation: Approach
ELECTRON BUNCH CHARGE BY SHOT
ELECTRON BUNCH CHARGE HISTOGRAM
2.0
MEAN = 1.001 nC
STDEV = 0.201 nC
400
1.5
FREQUENCY
BUNCH CHARGE (nC)
500
1.0
300
200
0.5
100
0.0
100
200
300
400
0
0.0
500
0.5
BUNCH NUMBER
ELECTRON BUNCH ENERGY CENTROID
1.5
2.0
ELECTRON BUNCH ENERGY HISTOGRAM
500
13.58
13.60
MEAN = 13.640 GeV
STDEV = 0.0137 GeV
400
FREQUENCY
13.62
13.64
13.66
13.68
300
200
100
13.70
0
100
200
300
400
500
13.58
13.60
A
500
B
1.4
FREQUENCY
1.0
0.8
0.6
0.2
13.66
13.68
13.70
MEAN = 8265.3 eV
STDEV = 16.6 eV
400
1.2
0.4
13.64
NOMINAL PHOTON ENERGY HISTOGRAM
MODEL UNDULATOR SPECTRA
C
13.62
BUNCH ENERGY (GeV)
BUNCH NUMBER
FLUX (106 PHOTONS/nC/0.01%BW)
BUNCH ENERGY (nC)
1.0
BUNCH CHARGE (nC)
8100
8200
200
100
K = 3.5000
E = 13.64 GeV
WINDOW > 50 mrad
8000
300
8300
8400
0
8200
8220
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
8240
8260
8280
8300
NOMINAL PHOTON ENERGY (eV)
PHOTON ENERGY (eV)
Bingxin Yang
bxyang@aps.anl.gov
8320
RAW COUNTS (K = 3.5000)
PHOTON COUNTS PER SHOT
Effect of electron energy “correlation”
1.2e+6
1.0e+6
8.0e+5
6.0e+5
4.0e+5
2.0e+5
0.0
8100
8200
8300
8400
PHOTON ENERGY (eV)
CHARGE NORMALIZE COUNTS (K = 3.5000)
Dg/g
PHOTON COUNTS PER SHOT
1e+6
Define “Correlated Electron-Photon Energy”
 2  y  y0 

 cot   D 
D


6e+5
4e+5
2e+5
0
8100
8200
8300
8400
PHOTON ENERGY (eV)
wCORR  w  w1 
NORMALIZE & CORRECTED COUNTS (K = 3.5000)
1e+6
PHOTON COUNTS PER SHOT
RMS error from simulation
8e+5
8e+5
6e+5
4e+5
2e+5
0
8100
8200
8300
CORRECTED PHOTON ENERGY (eV)
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
8400
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 instrument
No buffer for “unknown-unknowns”
Non-Gaussian beam energy distribution ???
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Beamline Option 2: Ultra-high Resolution
Reference Undulator (U33)
Period length and B-field same as other segments
Zero cant angle
Field characterized with high accuracy
Upstream corrector capable of 200 mrad steering (may be
reduced if needed).
Broadband monochromator (DE/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)
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Operation Procedures for setting Keff (BL2)
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
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
UNDULATOR SPECTRA THRU SQUARE WINDOW
C
1.6
1.4
A
B
K = 3.5000
E = 13.64 GeV
APERTURE = 140 mrad
(5mm@35m)
1.2
1.0
0.8
6
PHOTONS/nC/0.01%BW)
FLUX (10
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 mrad)
Position the crystal angle at the mid-edge
Roll in other undulator one at a time (test
undulator).
30 mrad
(5mm@167m)
0.6
160 mrad
25 mrad
0.4
20 mrad
15 mrad
0.2
8000
8050
8100
8150
10 mrad
8200
8250
8300
PHOTON ENERGY (eV)
Bingxin Yang
bxyang@aps.anl.gov
8350
8400
Differential Measurements of Two Undulators
Insert only two segments in for the entire
undulator.
Steer the e-beam to separate the x-rays
Use one mono to pick the
same x-ray energy
Use two detectors to detect
the x-ray flux separately
Use differential electronics
to get the difference in flux
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Signal of Differential Measurements
MODEL UNDULATOR SPECTRA
HISTOGRAM OF DIFFERENCE COUNTS
DIFFERENCE COUNTS (K = 3.5005)
A
PHOTON ENERGY = 8265.7 eV
TOAL COUNTS = 0.644  106
N_avg = 1 (bunch)
B
1.4
3
1.2
1.0
0.8
0.6
1500
-20
K = 3.5005
FREQUENCY
C
COUNTS (10 PER BUNCH)
FLUX (106 PHOTONS/nC/0.01%BW)
0
-40
500
-60
K = 3.5005
E = 13.64 GeV
Q = 1.0 nC
0.2
0
-100
-80
100
0.4
200
300
400
500
8000
8100
8200
1500
PHOTON ENERGY (eV)
100
PHOTON ENERGY = 8265.7 eV
6
TOAL COUNTS = 0.644  10
N_avg = 1 (bunch)
K = 3.4995
FREQUENCY
K = 3.5005
Select x-ray energy at the edge (Point A).
Record difference in flux from two undulators.
Make histogram to analyze signal quality
Signals are statistically significant when
peaks are distinctly resolved
Large aperture spectrum measurements
50
HISTOGRAM OF DIFFERENCE COUNTS
8400
Beam-based undulator measurement workshop, Nov. 14, 2005
0
3
DK/K =  1.5  10-4
8300
-50
DIFFERENCE COUNTS (10 PER BUNCH)
BUNCH NUMBER
K = 3.5000
E = 13.64 GeV
WINDOW > 50 mrad
1000
1000
500
0
-100
-50
0
50
3
DIFFERENCE COUNTS (10 PER BUNCH)
Bingxin Yang
bxyang@aps.anl.gov
100
Summing multi-shots improves resolution
Summing difference signals over 64 bunches
Distinct peaks make it possible to calculate the
difference DK at the level of 10-5.
HISTOGRAM OF DIFFERENCE COUNTS
HISTOGRAM OF DIFFERENCE COUNTS
PHOTON ENERGY = 8265.7 eV
6
TOAL COUNTS = 0.644  10
N_avg = 1 (bunch)
PHOTON ENERGY = 8265.7 eV
6
TOAL COUNTS = 0.644  10
N_avg = 64 (bunches)
1500
K = 3.499965
K = 3.500035
FREQUENCY
FREQUENCY
1500
K = 3.499965
K = 3.500035
1000
500
1000
500
0
0
-8
-6
-4
-2
0
2
4
6
8
3
DIFFERENCE COUNTS (10 PER BUNCH)
-8
-6
-4
-2
0
2
4
6
8
3
DIFFERENCE COUNTS (10 PER BUNCH)
Example: Average improves resolution for DK/K =  10-5
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Differential Measurement Recap
Use one reference undulator to test another undulator
simulataneously
Set monochromator energy at the spectral edge
Measure the difference of the two undulator intensity
Simulation gives approximately:
HISTOGRAM OF DIFFERENCE COUNTS
PHOTON ENERGY = 8265.7 eV
6
TOAL COUNTS = 0.644  10
N_avg = 64 (bunches)
1500
K = 3.49999
FREQUENCY
K = 3.50001
1000
• To get RMS error DK/K <
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?
0.710-4,
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
500
0
-4
-2
0
2
3
4
DIFFERENCE COUNTS (10 PER BUNCH)
Bingxin Yang
bxyang@aps.anl.gov
Other application of the techniques:
Search for the neutral magnetic plane
C
A
B
1.4
1.2
1.0
0.8
0.6
6
FLUX (10 PHOTONS/nC/0.01%BW)
MODEL UNDULATOR SPECTRA
0.4
0.2
K = 3.5000
E = 16.34 GeV
WINDOW > 50 mrad
8000
8100
8200
8300
PHOTON ENERGY (eV)
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.
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
8400
Simulation of undulator vertical scan
K  y   K  0 1  y 
    105 106
K  0
2 u 
Charge normalization only: ~ 20K shots / point
Charge-normalized and electron-energy corrected: ~ 512 shots / point
Differential measurements (two undulators): ~ 16 shots /point gives us
RMS error ~ 1.0 mm ?!
2
UNDULATOR VERTICAL SCAN (512 x 0.2 nC)/PT
UNDULATOR VERTICAL SCAN (20K x 0.2 nC)/PT
0.410
0.405
0.400
0.01
428000
DIFFERENCE SIGNAL
ELECTRON ENERGY CORRECTED
FLUX (106 PHOTONS/nC)
UNDULATOR VERTICAL SCAN (16 x 0.2 nC)/PT
430000
0.415
426000
424000
422000
420000
418000
0.00
-0.01
-0.02
416000
0.395
-50
-40
-30
-20
-10
0
10
20
30
40
50
-50
VETICAL POSITION
-40
-30
-20
-10
0
10
20
30
VETICAL POSITION
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
40
50
-0.03
-50
-40
-30
-20
-10
0
10
20
VETICAL POSITION
Bingxin Yang
bxyang@aps.anl.gov
30
40
50
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 ebeam 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
K apparent ( x, y )  K eff (0, 0)
K eff (0, 0)
an
y0 2  s y2
2
u
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
K eff
 K eff


x0  bn 
sx 
x
 x

Bingxin Yang
bxyang@aps.anl.gov
2
Summary (The Main Idea)
We propose to use angle-integrated spectra (through a
large aperture, but radius < 1/g) 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
DK/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, DK/K =  3  10-6 or better. It is sufficient for XFEL applications.
It can also be used for routinely logging magnet degradation.
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
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 mm in theory for now, hope
to get ~ 10 mm 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 field
Longitudinal wake field effect,
Experimental test in the APS 35ID
More?
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov
Monochromator Recommendation
A dedicated monochromator for undulator measurement
(low cost and robust, permanently installed).
Use it for DK/K measurements
Use it for regular vertical alignment check
Use 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 damage
Look for most damaged undulator segments for service for next
shutdown
Location of the monochromator
Front end  easy to service. Too crowded?
In tunnel OK.
Differential measurement strongly recommended
But 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.
Beam-based undulator measurement workshop, Nov. 14, 2005
Large aperture spectrum measurements
Bingxin Yang
bxyang@aps.anl.gov