1
Pinhole Measurement Approach to K Measurements
using Spontaneous Radiation

• November 14, 2005
• J. Welch, R. Bionta, S. Reiche

2
Basic Layout
Basic Scheme
Slit width must be small to get clean signal. 2
mm shown.
Useg 1 is worst case
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Fundamental Measurements

• Relative energy deviation of 1st harmonic
  photons
• Relative energy deviation of electron beam

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Derived Quantities

• Electron beam angles x, y
• ?K / K the relative difference between a given
  segment K and that of a reference segment

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Experimental Procedure to Measure K

1. All segments out, flatten orbit to a few times
   BBA quality. Need orbit angles less than 10
   micro-radians to avoid scraping 1st harmonic SR
   on vacuum chamber.
2. Insert one segment, adjust slit width for
   constant angular size, scan slit position to
   minimize apparent ? K/K , energy jitter
   correction on.
3. Remove segment, repeat with different segment.
   The difference in K is calculated from the
   difference in measured ? K/K for the two segments.

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Simulation Procedure

1. Set nominal values for reference and test
   segments and detector (Ks, detector geometry,
   machine parameters)
2. Add random energy and beam orbit jitter
3. Calculate expected 1st harmonic photon energy
   averaged over detector geometry
4. Add random photon statistics noise, machine
   energy, and beam angle.
5. Calculate ?K/K based on the noisy values. This
   becomes the measured value of ? K/K.
6. Repeat one shot at a time.

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Flux Spectrum in Simulation

• Shifted interference function at constant flux
• Valid for 1st harmonic photons over /- 10
  micro-radian range

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Spectrum Verification Reiche/Ott Calculation

• Essentially same agreement result for off axis
  radiation and radiation produced by detuned
  segments

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Spectrum Verification line outs

• Reich/Ott photons from 8000-8500 eV, from -1 mm
  to 1 mm at 145 m from source. Y line out is very
  similar.

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Geometry Effects

• Effect of finite detector size and offset

• u1(0) is the theoretical on-axis resonant photon
  energy.

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?K/K Calculation

• ?K/K beam energy term photon energy term
  geometry term

Minimize
Measure
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Aligning the Pinhole
Scan range / - 1 mm X and Y
Actual beam Axis 0.5, 0.5

• Simple 2D scan, one shot per data point, 0.1 mm
  steps, no multi-shot averaging
• Error is added to geometry term.

Measured Beam axis 0.33, 0.34
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Photon statistics

• Variance of mean photon energy due to photon
  statistics
• Need 104 counts for 10-4 relative error in mean.
• At minimum charge, there are at least 2 x 106
  photons incident on 0.1 x 1 mm detector.
• Error is added to ?ltugt/ltugt term.

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Simulated K Measurement
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Simulation values used

• Detector Model
• Efficiency 1
• Energy Sensitivity 1 eV / 8.275 keV
• Size 0.1mm x 1.0 mm
• Beam Model
• Orbit jitter 25 sigma, position and angle
• Energy jitter, 0.1 energy uncertainty 3x10-5.
• Beam size, 36 micron sigma, beta 30 m.
• Minimum charge, 0.2 nC.
• Segment Model
• Design values for K and positions, 113 periods

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Detector Requirements

• ?ltugt/ltugt sensitivity 1 x 10-4
• Energy window 8000 - 8500 eV enough to include
  the 1st harmonic bandwidth and beam energy jitter
  effect.
• Precisely movable slits with adjustable width.
• Scan range of a few mm, x,y. Slit width range 0
  to a few mm.
• Efficiency (counts per photon) 1 or better.

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Global Alignment Tool?

• ?? can be measured to better than 1 micro-radian
  with pinhole scan, globally!
• x, y can then be integrated from slope, similar
  to method of autocollimator measurement for
  straightness.