1. Towards a Pulseshape Simulation / Analysis Kevin Kröninger, MPI für Physik GERDA Collaboration Meeting, DUBNA, 06/27 – 06/29/2005

2. Outline Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005

3. SIMULATION

4. Simulation Overview I Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005

5. Simulation Overview II Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 What happens inside the crystal? Local energy depositions translate into the creation of electron-hole pairs with E dep : deposited enery E eh : 2.95 eV at 80 K in Ge E gap = 0.73 eV at 80 K ¾ of energy loss to phonons Corresponds to approximatly 600,000 e/h-pairs at 2 MeV Due to bias voltage electrons and holes drift towards electrodes (direction depends on charge and detector type) Charge carriers induce mirror charges at the electrodes while drifting = E dep / E eh SIGNAL

6. Drifting Field / Bias Voltage I Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 In order to move charge carriers an electric field is needed Calculate field numerically: 3-D grid with spatial resolution of 0.5 mm Define Dirichlet boundary conditions (voltage, ground) depend on geometry (true coxial? non-true coxial? etc.) So far: no depletion regions, zero charge density inside crystal, no trapping Solve Poisson equation φ = 0 inside crystal using a Gauss-Seidel method with simultaneous overrelaxiation Need approximatly 1000 iterations to get stable field Electric field calculated as gradient of potential

7. Drifting Field / Bias Voltage II Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005

8. Drifting Field / Bias Voltage III Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Example: non-true coaxial n-type detector

9. Drifting Process Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005

10. Mirror Charges – Ramos Theorem Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Ramos Theorem: Induced charge Q on electrode by point-like charge q is given by Calculation of weighting field: Set all space charges to zero potential Set electrode under investigation to unit potential Ground all other electrodes Solve Poisson equation for this setup (use numerical method explained) Q = - q · φ 0 (x) Q : induced charge q : moving pointlike charge φ 0 : weighting potential

11. Weighting Fields I Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 x

12. Weighting Fields II Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Example: true coaxial detector with 6 φ- and 3 z-segments (Slices in φ showing ρ-z plane) φ = 0°φ = 90° φ = 180° φ = 270° y x z

13. Preamp / DAQ Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Drift and mirror charges yield charge as function of time Preamp decreases accumulated charge exponentially, fold in gaussian transfer function with 35 ns width DAQ samples with 75 MHz time window 13.3 ns Example: (signal after drift, preamp and DAQ)(signal after drift)

14. Setups / Geometries / Eventdisplays I Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Full simulation of non-true coaxial detector electrode core Charge Time Charge Current

15. Setups / Geometries / Eventdisplays II Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005

16. Setups / Geometries / Eventdisplays III Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Full simulation of true-coxial 18-fold segmented detector Time Charge core electrodes

17. Analysis Approach

18. Pulseshape Analysis in MC: Spatial Resolution I Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Is it possible to obtain spatial information of hits from pulseshapes? In principal YES! Risetime of signal (10% - 90% amplitude) is correlated with radius of hit due to different drift times of electrons and holes Relative amplitude of neighboring segments is correlated to angle Events with more than one hit in detector give ambiguities Studied in Monte Carlo with 2-D 6-fold segment detector, no DAQ, no sampling

19. Pulseshape Analysis in MC: Spatial Resolution II Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Spatial information of radius and angle

20. Pulseshape Analysis: SSE/MSE Discrimination I Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Do 0νββ signals differ from background signals? Background mainly photons that Compton-scatter: multiple hits in crystal Multisite events (MSE) Signal due to electrons with small mean free path: localized energy deposition Singlesite events (SSE) Expect two shoulders at most from SSE and more from MSE Count number of shoulders in current Apply mexican hat filter with integral 0 and different widths (IGEX method) Count number of shoulders: 2 : SSE >2 : MSE

21. Pulseshape Analysis: SSE/MSE Discrimination II Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005

22. Pulseshape Analysis: SSE/MSE Discrimination III Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Fraction of SSE and MSE for different filter widths Separation of SSE/MSE in principle possible, combine with information from neighboring segments Identified as SSE Identified as MSE SSE MSE Filter width Fraction of Events

23. Data to Monte Carlo Comparison

24. Data to Monte Carlo Comparison I Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Data from teststand (see X. Liu) Later on used for SSE selection Source

25. Data to Monte Carlo Comparison II Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Teststand data vs. Monte Carlo Energy [MeV] General agreement No finetuning yet Next: pulseshapes without any additional selection criteria

26. Data to Monte Carlo Comparison III Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Comparison of pulseshapes Charge Data Monte Carlo

27. Data to Monte Carlo Comparison IV Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Comparison of pulseshapes Current Data Monte Carlo

28. Data to Monte Carlo Comparison V Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Comparison of pulseshapes Current Charge

29. Data to Monte Carlo Comparison VI Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Comparison of pulseshapes Charge amplitude Current amplitude

30. Data to Monte Carlo Comparison VII Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 Comparison of pulseshapes Risetime [ns]

31. Conclusion Kevin Kröninger, MPI München GERDA Collaboration MeetingDUBNA, 06/27 – 06/29/2005 First approach towards a simulation of pulseshapes Different geometries / fields available Package available and linked to MaGe Pulseshape analysis to further reduce background via SSE/MSE identification is feasible need sampling rate as large as possible (1 GHz 1 ns possible?) Data to Monte Carlo comparison using teststand data yields coarse agreement finetune parameters of simulation