1. Wednesday, May 9 th 2007Torsten Beck Fast Pulse Shape Analysis for AGATA-Germanium- Detectors Torsten BeckWednesday, 9. Mai 2007 Student seminar Wednesday, 9. Mai. 2007

2. Wednesday, May 9 th 2007Torsten Beck outline   -spectroscopy with relativistic beams (RISING )  Segmented Ge-detectors (AGATA)  New concept for pulse shape analysis  Wavelet transformation  Fast data base search (Hamming distance)  Results for single interactions  Complex interactions  Outlook

3. Wednesday, May 9 th 2007Torsten Beck Gamma spectroscopy with relativistic beams Doppler shift ( factor of 1.5 for  40% ) Doppler broadening detector size ~7cm (diameter, length) distance to target ~70cm  lab [deg]  E  /E  0 [%] Detector opening angle  =3° Doppler broadening  =0.11  =0.43  =0.57   1  1 Doppler shift of  -rays Lorentz boost of  -rays gain in geometrical efficiency at forward angles in lab. system ( factor of 2 for  40% )

4. Wednesday, May 9 th 2007Torsten Beck Coulomb excitation of the 84 Kr-beam E  [keV] Counts E  [keV] Counts 882 84 Kr 2 +  0 + FWHM ~ 1.5 % without Doppler correction Particle identification before and after the target Forward scattering angle selection Fixed  39.6%  value ( no energy spread) Event by event Doppler correction 84 Kr (113 AMeV) + Au (0.4 g/cm 2)

5. Wednesday, May 9 th 2007Torsten Beck The Ge-Cluster detector array RISING RingAngle [deg] Distance [mm] Resolution [%] Efficiency [%] 115.97001.00 233.07001.820.91 336.07001.93 0.89 Total:1.56 2.81 15 EUROBALL Cluster detectors 105 Ge crystals

6. Wednesday, May 9 th 2007Torsten Beck too many detectors are needed to avoid summing effects Combination of: segmented detectors digital electronics pulse processing tracking the  -rays EUROBALL Ge Tracking Array  ~ 3º  ~ 1º Idea of  -ray tracking

7. Wednesday, May 9 th 2007Torsten Beck AGATA Design and characteristics 4   -array for Nuclear Physics Experiments at European accelerators providing radioactive and high-intensity stable beams Principal design features of AGATA Efficiency: 40% (M  =1) 25% (M  =30) today’s arrays ~10% (gain ~4) 5% (gain ~1000) Peak/Total: 55% (M  =1) 45% (M  =30) today~55% 40% Angular Resolution: ~1º  FWHM (1 MeV, v/c=50%) ~ 6 keV !!! today~40 keV Rates: 3 MHz (M  =1) 300 kHz (M  =30) today 1 MHz 20 kHz

8. Wednesday, May 9 th 2007Torsten Beck AGATA Detector Module 1 three 36-fold segmented Ge detectors 2 preamplifier 3 frame support 4 digital pulse processing electronics 5 fiber-optics read-out 6 LN 2 – dewar 7 target position Ge-crystals: 10 cm long, 8 cm diameter tapered, hexagonal/pentagonal shape encapsulated

9. Wednesday, May 9 th 2007Torsten Beck AGATA performance in FAIR experiments RISING AGATA-15(45) (2004/5) ~2010 Efficiency : 1-3% 10.5% (~15%) FWHM: 20 keV ~7 keV at v/c~0.5, multiplicity: 1-5, target-detector distance: 15 cm Much increased sensitivity Angular distribution and polarisation measurements,  -coincidence measurements, g-factors background suppression through determination of source

10. Wednesday, May 9 th 2007Torsten Beck Exogam, Miniball, SeGa: optimized for Doppler correction at low  -multiplicitiy   up to 20% Tracking Arrays based on Position Sensitive Ge Detectors Large Gamma Arrays based on Compton Suppressed Spectrometers   40 — 20 % ( M  =1 — M  =30)   10 — 5 % ( M  =1 — M  =30) GAMMASPHEREEUROBALLGRETAAGATA Idea of  -ray tracking

11. Wednesday, May 9 th 2007Torsten Beck Pulse Shape Analysis Mirror charges in segments what is puls shape analysis doing: it trays to find the interaction position from a  -ray with the Ge-crystall

12. Wednesday, May 9 th 2007Torsten Beck 0o0o A1A1 B1B1 C1C1 D1D1 E1E1 F1F1 Core F3F3 F2F2 F1F1 F1F1 F2F2 F3F3 F4F4 F5F5 F6F6 Image charges : azimuthal detector sensitivity Detector characterization

13. Wednesday, May 9 th 2007Torsten Beck Ingredients of  -ray Tracking Pulse Shape Analysis to decompose recorded waves Highly segmented HPGe detectors · · · · Identified interaction points (x,y,z,E,t) i Reconstruction of tracks e.g. by evaluation of permutations of interaction points Digital electronics to record and process segment signals  1 2 3 4 reconstructed  -rays

14. Wednesday, May 9 th 2007Torsten Beck Radius:S3 signal rise time Azimuthal angle:S4-S2/(S4+S2) Asymmetry Segmented detector signals S4 S3 S2 S1 pulse shape analysis induced charge

15. Wednesday, May 9 th 2007Torsten Beck ~ 100 keV ~1 MeV ~ 10 MeV  -ray energy Isolated hits Angle/Energy Pattern of Hits Photoelectric Compton Scattering Pair Production Probability of E 1st = E  – 2 mc 2 interaction depth Three main interaction mechanisms

16. Wednesday, May 9 th 2007Torsten Beck requirements for pulse shape analysis  the algorithm needs to analyse the data online (~30  s per event), so that not the hole set of data has to be saved.  the position of interaction needs to be calculated as precise as possible.

17. Wednesday, May 9 th 2007Torsten Beck concept of pulse shape analysis pulse shape wavelet transformation wavelet transformation database of binary signals from simulated and wavelet transformed puls shapes database of binary signals from simulated and wavelet transformed puls shapes calculation of hamming distance between seeked position and database calculation of hamming distance between seeked position and database selection of positions with smallest hamming distance selection of positions with smallest hamming distance calculation center of gravity calculation center of gravity binarisation =3 element from database number of flipped bits binary signal 01001 00111 xor wavelet coefficients binary signal creation of the binary array, by transforming positive coefficients to 1 and negative to 0 01001 7-5-35 wavelet-coeffizienten binäre representation hamming cloud at seek position x = 10; y = 10; z = 55 selected interaction hamming distance found interaction position x = 15; y = 15; z = 55 found interaction position x = 15; y = 15; z = 55 output of interaction position mother-wavelet convolution By using the wavelet transform the signal will be fragmented in to a time- frequency representation signal

18. Wednesday, May 9 th 2007Torsten Beck What is a wavelet transformation and how can we use it? Wavelet transformation wavelet wavelet transformation is basically a convolution between the signal to analyse and the wavelet function. data The wavelet transformation is a relatively new concept (about 10 years old). It provides a time-frequency representation:  = time shift s = time scaling

19. Wednesday, May 9 th 2007Torsten Beck Haar wavelet what is the wavelet transformation doing?  = time shift s = time scaling

20. Wednesday, May 9 th 2007Torsten Beck wavelet transform

21. Wednesday, May 9 th 2007Torsten Beck Low- (LP) and high pass (HP) analysis but the transform needs to be faster information about different time intervals

22. Wednesday, May 9 th 2007Torsten Beck HP LP implementation the Haar wavelet coefficients give the average slope of the recent time windows

23. Wednesday, May 9 th 2007Torsten Beck test of wavelet transform Euclidean distance Wavelet distance vs. limit of acceptance

24. Wednesday, May 9 th 2007Torsten Beck binarisation of wavelet coefficients example of binarisation: wavelet coefficient5.34-4.35-5.981.34 binary coefficient1001 procedure is still to slow and needs to be speeded up, to solve this it is just taken the direction of the slope.

25. Wednesday, May 9 th 2007Torsten Beck Hamming distance In information theory, the Hamming distance between two binary strings of equal length is given by the number of positions for which the corresponding symbols are different. 101010 110010 011000 hamming distance = xor measured interaction in binary representation binary interaction from database

26. Wednesday, May 9 th 2007Torsten Beck test of Hamming distance Euclidean distance Hamming distance vs. limit of acceptance

27. Wednesday, May 9 th 2007Torsten Beck test of the method mean variance = 1 mm 2 elements found mean variance = 0 mm 5 elements found mean variance = 8 mm 3 elements found mean variance = 1 mm 1 element found speed of the algorithem ~ 100  s per event mean accuracy  ±1 mm

28. Wednesday, May 9 th 2007Torsten Beck Complex interactions

29. Wednesday, May 9 th 2007Torsten Beck Complex interactions hamming limit at 65 now there are two problems accuring

30. Wednesday, May 9 th 2007Torsten Beck Complex interactions it is necessary to handle two interactions in one data set

31. Wednesday, May 9 th 2007Torsten Beck not all combinations of wavelet coefficients can be truly converted in to a binary representation Complex interactions + +

32. Wednesday, May 9 th 2007Torsten Beck Complex interactions

33. Wednesday, May 9 th 2007Torsten Becksummary  AGATA yields an enormous amount of data  Wavelet transformation + binarisation allows a fast determination of the interaction position ~100  s per event (pentium m 1.7GHz) ~ 1 mm in accuracy  online Doppler shift corrections are possible  for complex  -interactions the pulse shape analysis is improvable

34. Wednesday, May 9 th 2007Torsten Beck alternative application of the binary search a fast text search can be implemented by using the wavelet transformation combined with the binary representation. a text can be transformed in to a wavelet- and a binary representation, like this, we can search a text as shown for the  -interactions in a Ge-Detector.

35. Wednesday, May 9 th 2007Torsten Beck the end thank you very much