Tracking Team. started at the Global Level Processing meeting (15-16/05/2003 in Legnaro)

Transcription

1 Gamma-ray Tracking 1 Team 2 Aim of tracking 3 - Physical processes in Ge 4 Problems related to physics 5 Problems coming from preamp/preprocessing/psa 6 Tracking algorithms cluster method (forward, probabilistic, fuzzy) backtracking method 7- Performances 8 Status of team work 9 Shopping list

2 Tracking Team started at the Global Level Processing meeting (15-16/05/2003 in Legnaro) Members: England: York France: Strasbourg, Orsay Italy: Legnaro, Padova, Milano Poland: Krakow Roumania: Bucharest Sweden: Stockholm + anybody else who would like to work on tracking Team leader: A. Lopez-Martens

3 Aim of tracking - Read for each event the list of deposited energies and positions of all the interactions points in AGATA e 1, x 1, y 1,z 1 e 2, x 2, y 2,z 2.. e n, x n, y n,z n - Disentangle the interaction points i.e reconstruct individual photon trajectories and write out photon energies, incident and scattering directions E 1, (θ,φ) inc,1,(θ,φ) sc,1 E 2, (θ,φ) inc,2,(θ,φ) sc,2 E i, (θ,φ) inc,i,(θ,φ) sc,i Doppler correction Polarization measurement OPTIMIZATION= ε ph x P/T

4 Physical Processes in Ge for photons Compton Photon range : λ(e) = M A /(N av.ρ). 1/Σσ E λ(10 kev) ~ 55 µm λ(100 kev) ~ 0.3 cm λ(200 kev) ~ 1.1 cm λ(500 kev) ~ 2.3 cm λ(1 MeV) ~ 3.3 cm

5 Compton Scattering source 0 E γ 0 1 e 1 E γ 1 θ 1 2 e 2 E γ 2 3 e 3 θ 2 assuming that the e - is at rest, from conservation of energy & momentum: incident energy at i cos(θ i ) = 1 m e c 2 (1/E γ i 1/E γ(i-1) ) scattered energy at i = E γ( i-1)-e i

6 Is track order = ? Compton Scattering Rules Original photon energy: E γ 0 = e 1 + e 2 + e 3 (if totally absorbed!!) 1) from source + interaction positions : cosθ 1 = E γ1,pos from energy deposition + incident energy: E γ 1 = E γ e 1 2) cosθ 2 = Track order = Permutation with best χ 2 = E γ2,pos E γ 2 = E γ1 e 2 2 n=1 E γn E γn,pos E γ(n-1) 2

7 Some complications! Electron momentum profile => change in scattering direction! Interaction position position of energy deposition γ inc γ sc σ ion /σ Brem ~ E e- (MeV) /21.8 γ e -! Rayleigh scattering => change in incident direction (@ low energy & end of track)

8 Additional Complications From PSA: uncertainty in position of interaction: (position & energy dependent) x x position resolution xx From preamp: energy threshold x x x From preprocessing: energy resolution

9 1- Cluster method G. Schmid et al. Tracking Algorithms forward peaking of the Compton scattering cross-section α = E γ /m e c 2 θ clusterisation in (θ,φ) space of interaction points belonging to the same track => interaction points with an angular distance θ 0 between each other (Link algorithm) or with respect to a given point (Leader algorithm) constitute a cluster

10 -Forward tracking mgt code by D. Bazzacco 1. Create cluster pool => for each cluster, E γ0 = cluster depositions 2. Test mechanism -do the interaction points satisfy the Compton scattering rules? χ 2 N-1 = n=1 W n E γn E γn,pos 2 E γ(n-1) -does the interaction satisfy photoelectric conditions (e 1,depth,distance to other points)? -do the interaction points correspond to a pair production event? E 1st =E γ 2 m e c 2

11 Example of reconstruction in an ideal 4π Ge shell E γ = 1.33 MeV M γ = 30 good bad 27 gammas detected in photopeak 16 reconstructed in photopeak

12 - probabilistic tracking (identical cubic pixels) G. Duchêne, I. Piqueras 1. Pixel clustering according to proximity criteria (distance + angle between segments with energy deposition) E γ0 = segment energies 2. Identification of 1 st hit in cluster based on e i /E γ0 fraction 3. Photopeak event selection 2 interactions 2 segments unique relation between 1 st scattering angle and e 1 /E γ0 when E γ0 corresponds to a fully absorbed photon energy photopeak E1/Etotal photopeak E1/Etotal => selection via contours of θ 1 vs e 1 /E γ0 for various E γ0 energy bins Compton E1/Etotal Compton E1/Etotal

13 - Fuzzy tracking C. Rossi Alvarez 0. Fuzzification/ Implementation of Linguistic rules 1. Identification of the 1 st hit interaction For each i,j deposition pair having medium-big scattering angle OR medium big energy deposition fraction e i /E γ apply fuzzy rules to find out if i can be 1st ( cannot be 2 nd ) 2. Fuzzy IterativeSelfOrganizingDataAnalysisTechniquesAlgorithm cluster creation around 1 st hit Pattern recognition method based on physical distances 3. Missed 1 st hits: small angle AND small energy deposition recovery procedure 4. Fuzzy Cluster Validation selection criteria : energy balance f(e γ E fuzzy cluster )

14 2- Backtracking method J. Van der Marel et al. 83% 87% photoelectric energy deposition is ~ independent of incident energy + peaked around kev => interaction points within a given deposited energy interval (e min < e i < e max ) will be considered as the last interaction of a fully absorbed photon track

15 - backtracking B. Cederwall, L. Milechina, A. Lopez-Martens 1. Create photoelectric interaction pool: e min < e i < e max 2. Find closest interaction j to photoelectric interaction i prob. for photoelectric interaction > P phot,min distance between interaction points < limit E inc = e i + e j, E sc = e i 3. Find incident direction from incident + scattered energies cosθ =1 m e c 2 (1/E sc 1/E inc ) 4. Find previous interaction k or source along direction cosθ(energies) - cosθ(positions) < limit prob. for Compton interaction > P comp,min distance between interaction points < limit E inc = e i +e j +e k E sc = e i +e j

16 Relative performances Very difficult to compare Simulations in a Spherical Ideal Shell MeV photons multiplicity cm inner and 24 cm outer radius: ε ph = 70%, P/T =77% Compton-Photoelectric-Pair production interactions secondary particle tracking packing of interaction points if distance < 0.5 cm smearing of the center of gravity of the packed interaction points as a fn of deposited energy (FWHM ~0.5 cm at 100 kev, ~ 0.16 cm at 1 MeV) energy threshold 5 kev Reconstruction P/T efficiency Forward tracking Fuzzy tracking (no single hit gammas) Backtracking (no single hit gammas)

17 Peak Efficiency and P/T at E γ = 1 MeV (Forward tracking algorithm) AGATA Crystals: 9 cm long, 8 cm diameter (at the back); arranged in triple-clusters; balanced volumes. Number of crystals Ω (%) Resp. funct. M γ 1 M γ 10 M γ 20 M γ (Ball, cm) no dead materials Eff. (%) P/T (%) 180 (Ball, cm) with capsules and cryostats (Ball, cm) + inner Al shell 2mm thick (Ball, cm) no dead materials (Ball, cm) with capsules and cryostats

18 Status of Team work 1. Development + testing of algorithms 2. Detailed comparison of forward + back tracking using the same simulated data: ideal spherical shell MeV multiplicity 30 BT FT ε ph ε ph (1 st int. ok) P/T Σpeak/photopeak % backtracked photopeak events are not (~15%) or badly (~6%) reconstructed by FT!!

19 Shopping list Continue comparing (similar and different) algorithms Find and try out new algorithms Combine the good features of existing algorithms Try out algorithms on simulated AGATA data (with all physical/kinematic effects, all dead material (reaction chamber, capsules, cryostats, ancillary detectors,.) Produce data for data analysis working group On line implementation (speed, CPU, ) And anything else you can think of..