Undulator Effective-K Measurements Using Angle-Integrated Spontaneous Radiation

1
Undulator Effective-K MeasurementsUsing
Angle-Integrated Spontaneous Radiation

• Bingxin Yang and Roger Dejus
• Advanced Photon Source
• Argonne National Lab

2
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/K1.510-4
• 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

3
Hope for this workshop

• Form a consensus
• Spontaneous spectral measurements can be used to
  measure Keff with required accuracy
  (DK/K1.510-4)
• 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

4
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

5
Spontaneous Radiation Spectrum
6
Angle-integrated? How large is the aperture!

• Pinhole (sinc) lt ltlt
  Angle-integrated (numeric)
• BXY Large enough for the edge feature to be
  stable

7
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,
  BIW00, Boston, May 2000, AIP Proc. 546, p. 234.
• Energy spread measurements
• B.X. Yang, and J. Xu, Measurement of the APS
  Storage Ring Electron Beam Energy Spread Using
  Undulator Spectra, PAC01, 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, PAC05
• DK/K simulations
• B. X. Yang, High-resolution undulator
  measurements Using angle-integrated spontaneous
  radiation, PAC05

8
How large is the aperture! FEL-relevant

• Capture the radiation cone 2.35 5 rms radius ?
  17 37 mrad
• Measured radiation spectrum is more important
  that calculated from field data!

9
Marking the location of a spectral edge

• We will watch
• how the following
• property changes
• HALF PEAK PHOTON ENERGY

10
Effects of Aperture Change (Size and Center)

• 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

11
Effects of Aperture Change (Source distance)

• Calculate flux through an aperture satisfying
• 100 mrad
• allowed by chamber ID
• Plot half-peak photon energy
• Rectangular aperture reduces variation

12
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 Dqw 2.35/gN1/2 8 mrad
• Electron beam divergence sy 1.2 mrad

13
Effect of Finite Energy Resolution

• Edge position moves with increasing energy spread

14
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.

15
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.

16
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.

17
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 (Dqw ),
• 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.

18
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
  2Dg/g
• 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.
19
Beamline Option 1 Poor mans solution

• 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)

Operation procedure for setting Keff

• 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

20
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)

21
One Segment Simulation Approach
22
Effect of electron energy correlation

• Define Correlated Electron-Photon Energy

RMS error from simulation
23
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 ???

24
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)

25
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 mrad)
• 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 lt threshold).
• Use the measured electron beam angle data in
  real-time to correct for angle jitters if
  necessary

26
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

27
Signal of Differential Measurements
DK/K ? 1.5 ? 10-4

• 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

28
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.

Example Average improves resolution for DK/K ?
10-5
29
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

• To get RMS error DK/K lt 0.7?10-4, 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?

30
Other application of the techniquesSearch 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.

31
Simulation of undulator vertical scan

• 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 ?!

32
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

33
Summary (The Main Idea)

• We propose to use angle-integrated spectra
  (through a large aperture, but radius lt 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 lt ? 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.

34
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).

Whats 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?

35
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.