Transcript "Pinhole Measurement" Approach to K Measurements using Spontaneous Radiation

“Pinhole Measurement”
Approach to K Measurements
using Spontaneous Radiation
November 14, 2005
J. Welch, R. Bionta, S. Reiche
Basic Layout
Basic
Scheme
Slit width must be
small to get clean
signal. 2 mm shown.
Useg #1 is worst case
Fundamental Measurements
• Relative energy
deviation of 1st
harmonic photons
• Relative energy
deviation of
electron beam
Derived Quantities
• Electron beam angles x´, y´
• ∆K / K: the relative difference between a
given segment K and that of a reference
segment
Experimental Procedure to
Measure K
1.
2.
3.
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.
Insert one segment, adjust slit width for constant angular
size, scan slit position to minimize apparent ∆ K/K ,
energy jitter correction on.
Remove segment, repeat with different segment. The
difference in K is calculated from the difference in
measured ∆ K/K for the two segments.
Simulation Procedure
1.
2.
3.
4.
5.
6.
Set nominal values for reference and test segments and
detector: (K’s, detector geometry, machine parameters)
Add random energy and beam orbit jitter
Calculate expected 1st harmonic photon energy averaged
over detector geometry
Add random photon statistics noise, machine energy, and
beam angle.
Calculate ∆K/K based on the noisy values. This becomes
the “measured” value of ∆ K/K.
Repeat one shot at a time.
Flux Spectrum in Simulation
• Shifted interference function at constant flux
• Valid for 1st harmonic photons over + /- 10 micro-radian
range
sin[ N(u  u1 ( ) /u1 ( )] 
F(u, )  A

 N(u  u1 ( ) /u1 ( ) 
where dependence on K,  is implicit and
2
A = A( ,K) only.

Spectrum Verification: Reiche/Ott Calculation
•
Essentially same
agreement result
for off axis
radiation and
radiation
produced by
detuned segments
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.

Geometry Effects
• Effect of finite detector size and offset
dduF(u, )u

u

 dduF(u, )
,u
where integration is over detector solid angle
and only the first harmonic photon energy range.
 2  2

2
2
2
2
u ,u  u1(0)1
3 X 0   X /4  3 Y 0   Y /4 

2
 3 1 K /2

where  ,  are the angular offset, angular size of the
detector wrt beam angle.
• u1(0) is the theoretical on-axis resonant photon energy.
∆K/K Calculation
• ∆K/K = beam energy term + photon energy
term + geometry term
Minimize
Measure
K 1 K 2 2  u  2  2


g


2
2
K
K  
u  3 K
where g = 3   /4     /4
2
x0
2
x
2
y0
2
y
for an assumed rectangular aperture of width
 x,(y ) and transverse location  x 0,(y 0) .
Aligning the Pinhole
• Simple 2D scan, one shot per
data point, 0.1 mm steps, no
multi-shot averaging
• Error is added to geometry
term.
Scan range
+ / - 1 mm
X and Y
Actual beam
Axis 0.5, 0.5
“Measured”
Beam axis
0.33, 0.34
Photon statistics
 u /u0 
1
N periods N counts
• 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 ∆<u>/<u> term.
Simulated K Measurement
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
Detector Requirements
• ∆<u>/<u> 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.
Global Alignment Tool?
• ∆ can be measured to better than 1 microradian with pinhole scan, globally!
• x, y can then be integrated from slope,
similar to method of autocollimator
measurement for straightness.