Principle and physics opportunities of gamma ray tracking detector Part I

1
Principle and physics opportunities of gamma ray
tracking detector(Part I)

• I-Yang Lee
• Lawrence Berkeley National Laboratory
• 5th international Balkan School in Nuclear
  physics
• Brasov, Romania, 7-14 September, 2006

2
Outline

• Introduction
• Principle of tracking detector
• Ge detector
• Signal decomposition
• Tracking
• Data acquisition
• Mechanical
• Physics opportunities
• Future perspectives
• Summary

3
Advantages of g-ray tracking
Compton suppression

• Efficiency Proper summing of scattered gamma
  rays, no solid lost to suppressors
• Peak-to-background Reject Compton events
• Doppler correction - Position of 1st interaction
• Polarization Angular distribution of the 1st
  scattering
• Counting rate - Many segments

Tracking
4
Performance of g-ray detectors
100 year history of gamma-ray detector development
5
Technical Challenges

• Advances in Ge detector production
• Segmentation size 2 cm ? 30-40 segment/crystal
• Closely pack irregular tapered hexagon shape
• Fast electronics
• ADC with 10 nsec sampling rate, gt 12 bit
  resolution
• Efficient algorithms
• Signal analysis position resolution 2 mm
• Tracking multiple gamma rays
• Computing power
• Cluster with 200 computer to process 20,000 ?/sec

6
Germanium detector
Energy resolution
electrons
n
p
holes
signal
HV
Number of e-h pairs for 1 MeV, N 106 / 3 3
?105
7
Segmented detector array
currently operational
6 seg 3 xtal
1 seg 7 xtal
32 seg 1 xtal
MINIBALL
RISING
SeGA
9 seg 2 xtal
4 seg 4 xtal
EXOGAM
GRAPE
8
Segmented detector array
under construction
32 seg 2 xtal
8 seg 4 xtal
ANL
TIGRESS (2009)
36 seg 4 xtal
36 seg 3 xtal
AGATA Demo (2008)
GRETINA (2010)
9
GRETINA Design

• 7 modules of 4 crystals each
• Covers 1p steradian solid angle (to cover 4p
  will take 30 modules - GRETA).
• Modules can be placed at 31.7º (5 positions),
  58.3º (4), 90º (8), and 121,7 º (4).
• On-line processing gives g-ray energy and
  position.

10
Tracking

• Outline
• Introduction
• Tracking principle
• Tracking issues and algorithms
• Status and results
• Future improvments

11
Interaction of g-ray with Matter

• ? Photo electric
• ? Compton scattering
• ? Pair production

12
Tracking introduction
Tracking - Use properties of g-ray interaction
with Ge to determine the g-ray scattering
sequence
Example 1.33 MeV 5 interactions 4 Compton, 1
photo Separation of interactions 0.5 5 cm
13
Tracking principleSource location and
interaction points are known

• Assume full energy is deposited
• 2) Start tracking from the source

source
Eg Ee1 Ee2 Ee3
Eg
Eg
For N! possible permutations, check each
interaction point for Compton scattering
conditions
N5
Select the sequence with the minimum ?2 lt ?2
max ? correct scattering sequence ? rejects
partial energy event ? reject gamma rays with
wrong direction
14
Tracking issues

• Computing time ? N!. Cut off large N events, or
  better algorithm

4 ! 24 8 !
40,320 12! 479,001,600

• Finite position and energy resolutions.
  Trade-off efficiency vs. P/T
• depending on experimental requirements

15
Tracking algorithm

• multiple g-ray hitting the detector

• Group interaction into clusters
• Tracking each cluster

• Any two points with
• lt ?p are grouped
• into the same cluster

16
Tracking algorithm
INPUT Position and Energy of Interactions From
Signal Decomposition

• Split Clusters
• Use 3-D position of interactions
• Determine principle axes of
• cluster moment
• Split cluster perpendicular to
• the axes

Cluster Identification Based on Angular Separation
Tracking Clusters Using Compton and
Pair-production Formulae
Principle axis
Split
Good
Add
Split
Bad
Split-Add
Add
OUTPUT Gamma Rays Reconstructed Energy,
Interaction Points, and Scattering Sequence
17
Tracking results
Mg 25, a 10?
Eg 1.33 MeV, Dr 1 mm
18
Tracking success rate
Eg 1.33 MeV, Mg 25, Dr 0 mm
Success Rate Good 100 Add 96 Split
44 Split-add 67
Ideal
Current algorithm
19
Tracking processing time
Eg 1.33 MeV, a 10?, Dr 1 mm
75 MHz SUN Sparcstation
Time distribution For Mg
25 Cluster creation 10 Initial tracking
20 Add, tracking 30 Split, tracking
35 Split-add tracking 5
For 25,000 g rays Need 100 75 MHz processors
10 modern processors
20
Tracking improvements

• Improve ?2
• Speed up tracking
• Improve cluster creation and splitting
• Coupling with signal decomposition
• Correct for range of electrons
• Other tracking methods
• e.g. Back tracking (AGATA)

21
Tracking improvements
Improve sensitivity of ?2 using additional
physics constrains

• Use angular distribution information
• Use absorption length information

However, These are probabilistic formulae
22
Tracking improvements
Speed up tracking

• Skip bad sequences (implemented)

If ?2 gt ?2 max after the first scattering
2 3 1 4 5 2 3 1 5 4 2 3 4 1 5 2 3 4 5 1 2 3 5 1
4 2 3 5 4 1 2 4 1 3 5
Skip all permutations with the same sequence

• Calculate ?2 using points lt total number
• of interactions (implemented)
• Time is reduced by a factor N(N-1)(N-2)..(N-M)/
  N!

23
Tracking improvements
Speed up tracking

• Physics based permutation sequence
• Order interactions by energy
• Permute low energy points first
• Examine fewer permutations than N!

1.33 MeV, N7 7!5040 Permu. Event
5 33 10 50 15 62 20
65
Another possible parameter radial position of
interactions
24
Tracking improvements
Speed up tracking

• Adaptive permutation sequence
• Track energy ordered events (learning mode)
• Arrange permutation by frequency
• Track with learned order of
• permutation (production mode)

1.33 MeV, N 7 7! 5040 Permu.
Event 3.4 50 5.0 59 7.0
64 8.4 65
25
Signal decomposition

• Outline
• Introduction
• Sensitivity of signals to the position of
  interaction point.
• Why is it difficult to determine positions from
  signals?
• Decomposition algorithms
• Signal calculation
• Chanllenges

26
Signal Decomposition - Introduction

• Gamma-ray tracking requires positions and
  energies of all gamma interactions.
• Digital pulse processing of segment data
• Uses data from both hit segments and image
  charges
• Extracts multiple interaction positions
  energies
• Must allow for at least two interactions per hit
  segment
• Uses a library of (calculated?) basis pulse
  shapes
• Can be done on a per-crystal basis
• Ideally suited to parallel processing
• Requires about 90 of total CPU cycles
• - The major processing bottleneck
• - Baseline GRETINA design allows only
• 4 ms/crystal/CPU for decomposition

27
Coincidence scans setup
Position sensitivity Measure pulse shape of a
single interaction using a prompt coincidence
requirement between GRETINA prototype III and
Clover(s)
1mCi 137Cs source Vertical and slit collimators
to define 90 deg scattering 500nsec
overlap Coincidence trigger 200 events/day
28
GRETINA three-crystal prototype
Received June 4, 2004

• Tapered hexagon shape
• Highly segmented 6 ? 6 36
• Close packing of 3 crystals
• 111 channels of signal

• Tests performed
• Mechanical dimension
• Temperature and LN holding time
• Energy resolution
• Singles scan
• Coincidence scan
• In-beam measurements

29
Coincidence scans
A
Clover 2 crystals
EcloverEA 662keV
30
Pulse Shapes from coincidence scan
200 events
Dx 5mm
31
Multiple interactions
GEANT simulations 1 MeV gamma into GRETA Most
hit crystals have one or two hit segments Most
hit segments have one or two interactions
32
Separation of two interaction points
33
Why is it hard?
Determine position and energy of several
interaction points form signals which are the
sum of the contributions from the individual
interaction points
Large parameter space to search Average segment
6000 mm3 so for 1 mm position sensitivity -
two interactions in one segment 1.8 x 106
positions - two interactions in each of two
segments 3 x 1012 positions - two interactions
in each of three segments 6 x 1018
positions PLUS energy fractionation, time-zero,
Underconstrained fits (especially with gt 1
interaction/segment) For one segment, have
only 9 x 40 360 nontrivial numbers Strongly-va
rying, nonlinear sensitivity - dc2/d(?z) much
larger near segment boundaries
34
Decomposition Algorithms

• Algorithms selected for detailed study (GRETINA)
• Adaptive Grid Search
• Constrained Least-Squares /
• Sequential Quadratic Programming
• Singular Value Decomposition
• Other algorithms (AGATA)
• Genetic algorithm
• Neural networks
• Wavelet transformations

http//fsunuc.physics.fsu.edu/gretina/Signal_Deco
mp_Workshop_FSU_June05/Program.htm
35
Signal Decomposition AGS
Match measured signal with basis signal on a grid

• Adaptive Grid Search algorithm
• Start on a course grid, to roughly localize the
  interactions

36
Signal Decomposition AGS
Match measured signal with basis signal on a grid

• Adaptive Grid Search algorithm
• Start on a course grid, to roughly localize the
  interactions
• Then refine the grid close to the identified
  interaction points.

37
Signal Decomposition AGS
Adaptive Grid Search algorithm Start on a
course grid, to roughly localize the
interactions, then refine the grid close by.
Computing time t number of interactions
38
AGS performance

• Current Adaptive Grid Search algorithm
• AGS, followed by constrained least-squares
• 1 or 2 interactions per hit segment
• Grid search in position only energy fractions
  are L-S fitted
• Coarse grid is 2x2x2 mm (front) or 3x3x3 mm
  (rear)
• - Gives N lt 600 coarse grid points per segment.
• - For two interactions in one segment, have
  N(N-1)/2 lt 1.8 x 105 pairs of points for grid
  search.
• - This takes 3 ms/cpu to run through.
• Works very well for both 1- and 2-segment events
• Reproduces positions of simulated events to ½
  mm
• Very fast 3-8 ms/event/CPU for 1 seg
• 15-25 ms/event/CPU for 2 seg. (2GHz P4)

39
AGS SQP Results
Adaptive Grid Search constrained least-squares
Example events Blue measured Red fitted
40
Signal Decomposition SVD
Represent the signal decomposition as a matrix
inversion problem
We measure or calculate signal shapes for
interaction points on a grid. ? Matrix A
A
To determine the energy at all grid points from
the measured composite signals, we need A-1
A-1
Computing time number of interaction points
41
Signal Decomposition SVD
Singular Value Decomposition algorithm

• Very roughly
• Full matrix is underdetermined (singular).
• But it can be decomposed into the product of
  three
• matrices, one of which contains the
  correlations
• (eigenvalues). By neglecting the small
  eigenvalues, the
• product can be inverted.
• Then an approximate fit can be obtained with
  very little
• computational effort, using a precalculated
  SVD inverse.
• The more eigenvalues kept, the higher the
  quality of the fit.

42
SVD matrix decomposition
A UWVT
Singular values are non-negative
Decomposition is unique up to the interchange of
entire rows or columns
U, V are column orthonormal UTUVTVI
Tech-X Corp
43
SVD dimension reduction
If the singular value spectrum decays quickly, A
can be approximated well by only a few singular
values eg. M lt 104, N lt 103, n 50
44
SVD Status

• Collaboration with Tech-X Corp.
• Funded under DOE SBIR grant to investigate
• alternative algorithms
• Started with Singular Value Decomposition
• Using signal basis developed for AGS
• Developed two-step SVD
• 2 mm grid (50 eigenvalues) to localize
  interaction region,
• followed by 1 mm grid (200 e.v.) over reduced
  space
• Works perfectly for single interaction
• Currently tested for up to 3x2 interactions
• Results certainly good enough as input to SQP
• CPU time linear in number of interactions
• lt 6 ms/segment/CPU (2GHz G5)

45
SVD Results

• CPU lt 6 ms/segment/CPU (2GHz G5)
• Results certainly good enough as input to SQP

2D projections of SVD amplitudes Interaction
sites at (13,9,11) and (8,11,11)
46
Signal Calculation

• Detector geometry
• Impurity concentration
• HV

• Detector geometry
• Drift velocity
• Neutron damage

• Electric field
• Weighting potential (tabulated on a 1 mm grid)

Field Calculation (FEM)
Signal calculation
(Maxwell 3D)

• Interaction position
• Electronics response

• Calculations are carried out for a grid of
  interaction points in crystals
• Pulse shape from the 36 outer contacts are
  calculated
• Pulse shape from the central contact is obtained
  by summing the signals from the outer contacts

47
Field and weighting potential

• Electric field

Boundary condition applied bias voltage

• Weighting potential for segment k

Boundary condition 1 V on the segment k
0 V on all other segments
48
Maxwell 3D
Real potential
Weighting potential
(1)
(2)

• Weighting potential is calculated by applying 1
  V on the segment collecting the charge and 0 V to
  all the others (Ramos Theorem).
• It measures the electrostatic coupling (induced
  charge) between the moving charge and the sensing
  contact.

49
Trajectory and signal

• Trajectory for electrons and holes

anisotropic

• Induced charge (S. Romo, Proc. IRE 27(1939)584)
• If a charge q moves from position x1 to position
  x2,
• then the induced charge on electrode k is

50
Drift velocity
Function of E-filed
Anisotropic in magnitude
Anisotropic in direction
51
Example of calculated signal
Prototype III (x,y,z) (-9, 20, 30)
52
Status of drift velocity
53
Challenges of signal calculation

• Improve model of drift velocity
• Physical model NS/OE measurements for holes
• Knowledge of impurity concentration
• Neutron damage
• Understand charge collection at segment
• lines and end of crystal
• Determine electronics response
• Match time of experimental signal with time
  of base signal (t0)

54
Time-zero alignment
Raw signals t0-aligned signals
55

• End of Part I