# Presentation: 655552

## 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***

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## Outline

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

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## Advantages of -ray tracking

**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

**Compton suppression**

**Tracking**

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## Performance of -ray detectors

- 100 year history of gamma-ray detector development

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## 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, > 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 ****γ****/sec**

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## Germanium detector

* **Number of e-h pairs for 1 MeV,   N* = 106 / 3 = 3 105

**Energy resolution**

- + HV

- signal

- p

- n

**electrons**

**holes**

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## Segmented detector array

- RISING

- EXOGAM

- MINIBALL

- SeGA

- GRAPE

**9 seg ****×2 xtal**

**1 seg × 7 xtal**

**4 seg ****× 4 xtal**

**6 seg ****× 3 xtal**

**32 seg ****× 1 xtal**

**currently operational**

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## Segmented detector array 

- GRETINA (2010)

- TIGRESS (2009)

- AGATA Demo (2008)

- ANL

**36 seg ****× 4 xtal**

**8 seg ****× 4 xtal**

**36 seg ****× 3 xtal**

**32 seg ****× 2 xtal**

**under construction**

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## GRETINA Design

***GRETINA Design***

- 7 modules of 4 crystals each
- Covers ≈ 1π steradian solid angle (to cover 4π 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 -ray energy and position.

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## Tracking

**Outline**
- Introduction
- Tracking principle
- Tracking issues and algorithms
- Status and results
- Future improvments

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##  Interaction of -ray with Matter

****** ****Photo electric**
****** ****Compton scattering**
****** ****Pair production**

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## Tracking introduction

**Example**; 1.33 MeV
- 5 interactions: 4 Compton, 1 photo
- Separation of interactions: 0.5 – 5 cm

| x (cm) | y (cm) | z (cm) | E (MeV) |
| --- | --- | --- | --- |
| 9.82 | -8.07 | -8.69 | 1.0184 |
| 10.07 | -7.68 | -8.56 | 0.0418 |
| 10.11 | -7.65 | -8.59 | 0.0044 |
| 13.58 | -5.27 | -9.01 | 0.1202 |
| 13.57 | -5.55 | -8.91 | 0.1452 |

**Tracking - Use properties of ********-ray interaction with Ge **
**to determine the ********-ray scattering sequence**

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## Tracking principleSource location and interaction points are known

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

- E = Ee1 + Ee2 + Ee3

- For N! possible permutations, check each interaction point for Compton scattering conditions

- Select the sequence with the minimum 2 < 2 max
-  **correct scattering sequence**
-  **rejects partial energy event**
**** **reject  gamma rays with wrong direction**

**N=5**

**source**

***E*********

***E’*********

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## Tracking issues

** ****Computing time ******** N!.**  Cut off large N events, or better algorithm

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

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

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## Tracking algorithm

- Any two points with
-  < p are grouped
- into the same cluster

- Group interaction into clusters
- Tracking each cluster

**  ****multiple  ********-ray hitting the detector **

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## Tracking algorithm

- INPUT
- Position and Energy of Interactions From Signal Decomposition

- Cluster Identification
- Based on Angular Separation

- Tracking Clusters
- Using Compton and Pair-production Formulae

- Good

- Add

- Split

- Bad

- OUTPUT
- Gamma Rays Reconstructed
- Energy, Interaction Points, and Scattering Sequence

- Split-Add

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

- Principle axis

- Split

- Add

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## Tracking results

**M******** = 25, ********=10******

**E******** = 1.33 MeV, ********r = 1 mm**

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## Tracking success rate

**Ideal**

**Current algorithm**

**Success Rate**
**Good****	****  100%**
**Add****	****    96%**
**Split****	****    44%**
**Split-add   67%**

**E******** = 1.33 MeV, M******** = 25, ********r = 0 mm**

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## Tracking processing time

**75 MHz SUN Sparcstation**

-      **Time distribution**
-             **For M******** = 25**
- Cluster creation    10%
- Initial tracking       20%
- Add, tracking        30% Split, tracking        35%
- Split-add tracking    5%

***For 25,000 ************  rays***
***Need 100 75 MHz processors***
***= 10 modern processors***

**E******** = 1.33 MeV,  ******** = 10********,  ********r = 1 mm**

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## 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)

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## Tracking improvements

**Use angular distribution information**
**Use absorption length information**

**However, These are probabilistic formulae**

**Improve sensitivity of ********2  ****using additional physics constrains**

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## Tracking improvements

**Skip bad sequences (implemented)**

- 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

- If 2 > 2 max after the first scattering

- Skip all permutations with the same sequence

** ****Calculate ********2 ****using points < total number **
**        ****of interactions** **(implemented)**
- 	Time is reduced by a factor = N(N-1)(N-2)..(N-M)/N!

**Speed up tracking**

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## Tracking improvements

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

- 1.33 MeV, N=7
-      7!=5040
**Permu.       Event**
-    5%	     33%
-  10%	     50%
-  15%	     62%
-  20%	     65%

- Another possible parameter — radial position of interactions

**Speed up tracking**

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## Tracking improvements

- 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%

| 1  2  3  5  6  7  4 |
| --- |
| 1  2  3  7  5  6  4 |
| 1  2  3  5  7  6  4 |
| 1  3  2  5  6  7  4 |
| 1  2  3  6  5  7  4 |
| 1  2  4  5  7  6  3 |
| 1  2  6  5  7  4  3 |
| 1  2  5  4  6  7  3 |
| 1  2  6  4  5  7  3 |
| 1  2  5  7  4  6  3 |

**Speed up tracking**

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## 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

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## 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

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## Coincidence scans setup

***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

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## GRETINA three-crystal prototype

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

** ****Tapered hexagon shape**
** ****Highly segmented****	****6 ******** 6 = 36**
** ****Close packing of 3 crystals**
** ****111 channels of signal**

**Received June 4, 2004**

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## Coincidence scans 

**A**

**Clover **
**2 crystals**

- Eclover+EA= 662keV

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## Pulse Shapes from coincidence scan

***Pulse Shapes from coincidence scan***

******x =5mm**

**~ 200 events**

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## 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

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## Separation of two interaction points

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## Why is it hard?

**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 > 1 interaction/segment)
-      For one segment, have only ~ 9 x 40 = 360 nontrivial numbers
**Strongly-varying, nonlinear sensitivity**
- 2/(z) much larger near segment boundaries

- Determine position and energy of several interaction
- points form signals which are the sum of the
- contributions from the individual interaction points

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## 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_Decomp_Workshop_FSU_June05/Program.htm

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## Signal Decomposition: AGS

**Adaptive Grid Search algorithm:**
-  Start on a course grid, to roughly localize the interactions

- Match measured signal with basis signal on a grid

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## Signal Decomposition: AGS

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

- Match measured signal with basis signal on a grid

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## 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

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## 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 < 600 coarse grid points per segment.
- - For two interactions in one segment, have 			N(N-1)/2 < 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 ~ 1⁄2 mm
-  Very fast;  ~ 3-8 ms/event/CPU for 1 seg;
- 	      ~ 15-25 ms/event/CPU for 2 seg. (2GHz P4)

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## AGS + SQP Results

- Example events
- Blue: measured
- Red:  fitted

**Adaptive Grid Search**
**+**
**constrained least-squares**

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## 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

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## 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.

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## SVD matrix decomposition

- Singular values are non-negative

- A = UWVT

- Decomposition is unique up to the interchange of entire rows or columns

- U, V are column orthonormal:            UTU=VTV=I

**Tech-X Corp**

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## SVD – dimension reduction

- If the singular value spectrum decays quickly, A can be approximated well by only a few singular values
- eg.  M < 104,  N < 103, n ~50

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## 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:
- 	**< 6 ms/segment/CPU**  (2GHz G5)

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

- Results certainly good enough as input to SQP

***SVD Results***

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

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## Signal Calculation

-  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

**Signal **
**calculation**

**Field **
**Calculation**
**(FEM)**

-  Interaction position
-  Electronics response

-  Detector geometry
-  Drift velocity
-  Neutron damage

-  Detector geometry
-  Impurity concentration
-  HV

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

_*(Maxwell 3D)*_

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## 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** *

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## Maxwell 3D

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

- (1)

- (2)

- Real potential

- Weighting potential

***Maxwell 3D***

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## Trajectory and signal

**Trajectory : ****for electrons and holes**

-   **Induced charge ****(S. Romo, Proc. IRE 27(1939)584)**
- 	If a charge *q* moves from position *x**1* to position *x**2*,
- 	then the induced charge on electrode *k* is

- anisotropic

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## Drift velocity

**Anisotropic in magnitude**

**Anisotropic in direction**

**Function of E-filed**

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## Example of calculated signal

**Prototype III   (x,y,z) = (-9, 20, 30)**

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## Status of drift velocity

|  | Velocity | Measurements | Theory/model |
| --- | --- | --- | --- |
| electron | magnitude | yes | physics |
|  | direction | some | physics |
| hole | magnitude | yes | interpolation |
|  | direction | few | empirical |

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## 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 (t****0****)**

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## Time-zero alignment

- Raw signals			    t0-aligned
-  					    signals

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***End of Part I***

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