1. Slope measurements from test-beam irradiations
Crystal Detector Performance Group
Christopher Rogan
California Institute of Technology

2. Test-beam Irradiations
Normalized laser and electron responses
Each xtal irradiated for ~10 hours
120 & 90 GeV electrons
nominally
~50k events / 60 s ~15 rad/hour
Ratio of electron (S(t)) and laser response (APD/PN R(t)) parameterized by
Xtal response depends on radiation dose-rate and individual xtal characteristics
SM22 - xtal 168
120 GeV e-
6k events / 60 s
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

3. Christopher Rogan - Crystal Detector Performance Group 18-09-07
2006 Irradiation data sets
Goals:
Understand transparency change dynamics
Look at distribution of xtal alpha values with more statistics
Study alpha extraction systematics
6 different xtals irradiated
SM GeV e-
Xtal 168
Tighter beam-spot for single xtal alpha extraction
SM GeV e-
Xtals 88, 128, 148, 552, 672
Wider beam-spot allows for study of transparency change in groups of xtals (extracting neighbor xtal alpha values)
Issues:
Data quality - DAQ issues, lower than optimal rate (~6k / 60 s)
Minimal transparency change vs. APD/PN stability
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

4. Extracting ‘alpha’ values
Previous strategy: use ‘correlation plot’
‘alpha’ corresponds to the slope of the ratio of the electron and interpolated laser responses
4 mm x 4 mm hodoscope cut around point of maximum response
‘electron’ and ‘laser’ response values taken from distribution fit
Requires many events at one level of xtal transparency (in situ?)
Relative electron response
SM22 - xtal 168
120 GeV e-
Relative laser response
Events
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

5. Extracting ‘alpha’ values
Fitted Sigma as function of Alpha
RMS as function of Alpha
Sigma / mean
Sigma / mean
New strategy: minimize xtal energy resolution with respect to alpha value
Transparency changes affect electron responses - degrades energy resolution. Laser monitoring system (and optimal choice of alpha) is designed to minimize resolution
Fitted (gaussian) sigma is not a smooth function of alpha
Instead, use RMS of energy distribution with selected events - smooth function
Problem become one dimensional minimization (for single xtal)
E9 resolutions
SM22 - xtal 168
120 GeV e-
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

6. Energy resolution minimization
Alpha vs. iteration
Use iterative method to minimize energy resolution as a function of alpha
For one xtal can, for example, use a parabolic interpolation minimization (Brent’s method)
Algorithm converges quickly
For selected events one can extract alpha with arbitrary precision
Resolution vs. iteration
SM22 - xtal 168
120 GeV e-
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

7. Systematic error of the slope extraction
Selects events within a ‘sigma window’ for fitted raw data
Alpha value appears independent of ‘window’ size
Small spread in alpha value distribution from different sets of events
.008
.58%
Alpha
SM22 - xtal 168
120 GeV e-
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

8. ‘Correlation plot’ vs. ‘resolution minimization’ methods
25 independent 4 mm x 4 mm hodo bins
One can look at xtal response for events incident on different parts of xtal face
Statistics limited in non-central bins
Plot is just an illustration (axis scales are different, etc.)
Just an illustration
SM22 - xtal 168
120 GeV e-
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

9. ‘Correlation plot’ vs. ‘resolution minimization’ methods
Using ‘correlation plot’ method:
‘correlation plot’ method suffers in low statistics bins
Error on alpha from linear fit doesn’t coincide with actual spread
Still statistics limited in outer bins
Alpha
Mean 1.373
RMS
SM22 - xtal 168
120 GeV e-
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

10. ‘Correlation plot’ vs. ‘resolution minimization’ methods
Using ‘resolution minimization’ method:
25 independent samples corresponding to 4 mm x 4 mm hodo bins
‘resolution minimization’ statistically consistent with ‘correlation plot’
Spread in alpha distribution improved by a factor of 10
‘correlation plot’:
Mean 1.373
Sigma ~11%
‘resolution minimization’:
Mean 1.384
Sigma ~1%
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

11. E1 resolution minimization
25 independent samples corresponding to 2 mm x 2 mm hodo bins
Algorithm minimizes the energy resolution of single xtal
Does not require information from surrounding xtals
Assumes relative xtal response over face of xtal is maintained during transparency change (containment correction)
~.7% percent spread
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

12. E25 resolution minimization
Algorithm minimizes the energy resolution of E25 object
Requires information from surrounding xtals but no containment correction
Slightly sensitive to surrounding xtal alpha values (fixed for this algorithm)
Result consistent with E1 minimization
25 independent samples corresponding to 2 mm x 2 mm hodo bins
~.8% percent spread E1
Mean: 1.367
RMS: .0098
E25
Mean: 1.355
RMS: .011
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

13. Magnitude of transparency change
The spread in alpha distributions reflects how much the object (E1, E25) resolution depends on alpha
~1%
As a result, more transparency change yields a better resolution on the parameter -- seen for xtals 168 and 128
~3%
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

14. Resolution minimization
Minimization algorithms work for xtals with less transparency change
Spread in alpha value greater for less transparency change
Here: 25 independent event samples corresponding to mm x 2 mm hodo bins
E1 and E25 minimizations consistent
E1 minimization:
Mean 1.572
Sigma ~2%
E25 minimization:
Mean 1.589
Sigma ~2.5%
SM06 - xtal 128
90 GeV e-
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

15. Resolution minimization
~.2%
.05% APD/PN instability
‘correlation plot’
SM06 - xtal 148
90 GeV e-
Difficulties with xtal 148 result from lack of transparency change
Regardless, resolution minimization yields (qualified) alpha vale
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

16. Resolution minimization
E1 method: Mean 1.541
Sigma ~9.5%
E25 method: Mean 1.356
Sigma ~16%
Appreciable spread in alpha; E1 and E25 minimizations still consistent
E25 method further degrade due to transparency changes in neighbors with unknow alpha values
Important to remember: Regardless of resolution of alpha parameter, the energy resolution is still minimized wrt alpha; spread reflects that energy resolution is relatively insensitive to alpha value
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

17. Christopher Rogan - Crystal Detector Performance Group 18-09-07
‘Neighbor’ xtals
SM22 - xtal 167
120 GeV e-
For ‘neighbor’ xtals in irradiation there is no hodoscope data to construct containment correction for E1 resolution minimization => can use E25 approach
One can extract alpha value even without enough statistics for ‘correlation plot’ approach
~.8% change in xtal 167 laser response
E25: Mean 1.186
Sigma ~5%
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

18. Resolution minimization summary
Resolution of alpha parameter is closely related to magnitude of transparency change - should be taken into consideration for future irradiations
Appreciable spread in alpha values between xtals - must calculate alpha in situ
Dispersion of  for 35 BTCP crystals
2002
# Crystals
2003
mean = 1.538
/mean  6%
2004 (fall)
2004 (spring)
2006 (center)
 alpha vs % transparency change
2006 (neighbor) 
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

19. Christopher Rogan - Crystal Detector Performance Group 18-09-07
Outlook
‘Resolution minimization’ approach appears more robust and powerful than ‘correlation plot’ method
E1 & E25 minimization approaches can be used in situ to extract alpha values (in fact, in situ data is better suited for this approach than TB irradiation data)
E25 minimization does not require containment correction - requires inter-calibration constants. Inter-calibration constants require xtal alpha values => Two sets of constants could be calculated simultaneously. Iterative resolution minimization algorithms are adaptable to all existing inter-calibration schemes
Development of toy Monte Carlo in progress to demonstrate this scheme
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

20. Christopher Rogan - Crystal Detector Performance Group 18-09-07
EXTRA SLIDES
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

21. R-plot from previous studies
SM06 xtal 552
R-plot from previous studies
~.6% change in xtal 552 laser response
R-plot shows that a range of alpha values could be quoted depending only on which subset of data points is used -- error on the fit parameter certainly doesn’t reflect this fact
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

22. Christopher Rogan - Crystal Detector Performance Group 18-09-07
SM06 xtal 552
E1 method:
Mean 1.567
Sigma ~3%
E25 method:
Mean 1.491
Sigma ~7%
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

23. Christopher Rogan - Crystal Detector Performance Group 18-09-07
Neighbor xtals: SM06 108
E25: Mean 1.186
Sigma ~17%
E25 weighted: Mean 1.515
Sigma ~16%
~.6% change in xtal 108 laser response (comparable to level of APD/PN stability). Weighting done with number of events in sample bin.
Resolution on central xtal (128) alpha not as good as for 167. E25 for neighbors is quite sensitive to central xtal alpha!
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

24. Christopher Rogan - Crystal Detector Performance Group 18-09-07
Neighbor xtals: SM22 169
E25: Mean 1.786
Sigma ~18%
E25 weighted: Mean 1.826
Sigma ~18%
~.3% change in xtal 169 laser response (comparable to level of APD/PN stability). Weighting done with number of events in sample bin.
4/26/2019
Christopher Rogan - Crystal Detector Performance Group

25. Alpha value distribution
Using these minimization approaches to calculating alpha values has been yielding values consistent with previous picture
It is extremely important that we understand the distribution of alpha values
Dispersion of  for 35 BTCP crystals
2002
# Crystals
2003
mean = 1.538
/mean  6%
2004 (fall)
2004 (spring)
2006 (center)
2006 TB alpha
2006 (neighbor)
Central
Neighbor 
4/26/2019
Christopher Rogan - Crystal Detector Performance Group