1. A High-Rate TPC for PANDA
Christian Höppner
Technische Universität München
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

2. PANDA-TPC TPC JAMBOREE Aachen March 2007
Outline
The PANDA Experiment
The PANDA TPC
Space Charge Effects
Tracking of Cosmic Myons with a small GEM-TPC
Pattern Recognition
A Generic Kalman Filter Implementation for Global Tracking in PANDA
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

3. PANDA: Antiproton Annihilations at Darmstadt
Facility for Antiproton and Ion Research (FAIR), GSI, Darmstadt
High Energy Storage Ring: 1 – 15 GeV antiproton-beam
Continuous beam
Internal p-target
Hadron-physics: charm-spektroscopy, gluonic excitations, hypernuclei, ….
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

4. The PANDA Spectrometer
2 x events / s
~ 3 tracks / Event
4π - spectrometer: 2T solenoid-field
Antiproton Beam
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

5. The PANDA Spectrometer
Central Tracker
Momentum measurement: dp/p ~ 1%
Material budget < 1% X0
PID via dE/dx
Proposal: Highrate-TPC with continuous readout Also proposed: STT
Decision for PANDA TDR 2009
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

6. PANDA-TPC TPC JAMBOREE Aachen March 2007
Geometry:
Radius: cm, Length: 1.5 m
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

7. PANDA-TPC TPC JAMBOREE Aachen March 2007
Electron drifttime ~ 50 μs (at 107 Events / s)
Event Mixing (500 Events happen per e--Drifttime)
Although ion backflow is suppressed: Some ions make it to the drift volume → Accumulation of space charge
Geometry:
Radius: cm, Length: 1.5 m
Challanges for high-rate TPC
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

8. Simulation of Space Charge
Realistic GEANT Simulation
Ion-backflow ε=1 (1 ion from amplification per incoming primary electron) realistic values 1 < ε < 10
Ion-backdrift: 1.7 cm/ms Equilibrium reached after 100 ms
QUESTION: What’s the effect of this space charge on the reconstruction of tracks?
Two Contributions:
Primary ionization & ions from amplicfication
Electron drift
Amplification & Readout
Beam
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

9. Track Distortions due to Space Charge
Displacement of several mm possible
Mean: ε = mm ε = mm
Has to be corrected for in reconstruction (as done e.g. in ALEPH)
Difference of reconstructed and generated electron starting point
ΔR [cm]
R [cm]
z [cm]
Also, slightly imperfect solenoid field has been taken into account
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

10. PANDA-TPC TPC JAMBOREE Aachen March 2007
GEM – TPC Test Chamber
cosmic myon
Scintillator PMT
Triple GEM - + + -
80 mm + - - + + -
Ar/CO2 + -
Elektronics: ALICE TPC – Inverter/PASA/ALTRO (noise ~ 1900 e-)
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

11. PANDA-TPC TPC JAMBOREE Aachen March 2007
GEM – TPC Test Chamber
Elektronics: ALICE TPC – Inverter/PASA/ALTRO (noise ~ 1900 e-)
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

12. PANDA-TPC TPC JAMBOREE Aachen March 2007
Event Topology z
primary electron clusters
Investigate tracks which are rather perpendicular to readout plane
→ important topology for PANDA y x
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

13. PANDA-TPC TPC JAMBOREE Aachen March 2007
Event Topology z y x
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

14. PANDA-TPC TPC JAMBOREE Aachen March 2007
Event Topology
Per Pad: puls finding
(MultiFit) z A y t0 x
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

15. PANDA-TPC TPC JAMBOREE Aachen March 2007
Event Topology z y x
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

16. PANDA-TPC TPC JAMBOREE Aachen March 2007
Event Topology z y
With samples (t0,A):
Clustering in x-y x
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

17. PANDA-TPC TPC JAMBOREE Aachen March 2007
Event Display
Schematic Data z y x
pattern recognition: hough transform fit: chi2-minimization
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

18. PANDA-TPC TPC JAMBOREE Aachen March 2007
Event Display
Schematic Data z y x
pattern recognition: hough transform fit: chi2-minimization
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

19. Pattern Recognition – Hough Tranform
Straight Lines: E.g. in yz-plane: y = a z + b each point (yi, zi) becomes a straight line in the parameter space (a,b) b = (-zi) a + yi the lines in (a,b) space of collinear points intersect in a point
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

20. Pattern Recognition – Hough Tranform
Straight Lines: E.g. in yz-plane: y = a z + b each point (yi, zi) becomes a straight line in the parameter space (a,b) b = (-zi) a + yi the lines in (a,b) space of collinear points intersect in a point
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

21. Pattern Recognition – Hough Tranform
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

22. Pattern Recognition – Hough Tranform
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

23. Pattern Recognition – Hough Tranform
Also applicable to helical tracks (if they intersect the origin [x,y]=[0,0] )
Pattern recognition is done completely in x,y plane R is distance of center of circle θ is azimuthal angle of track in origin In image space (R, θ) for each point (xi,yi) a curve is drawn: The curves from points on the same helix (R,θ) intersect in one point.
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

24. Large PANDA-TPC prototype
A prototype with 50 cm drift length and 30 cm diameter will be built before the PANDA TDR in 2009
Detector will be used in FOPI
Study materials for construction of final detector
mechanical stability
gas purity
HV insulation
Study HV supply to field cage
insulation
resistor chain
stability
Study mechanical properties of field cage and readout plane
Study integration of front-end electronics
Study performance with close-to-final front-end electronics
Study distortions, calibration, corrections
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

25. Large PANDA-TPC prototype
Electronics: N-XYTER asic looks promising (GSI detector lab for CBM)
analog zero suppression
Testing pending
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

26. A Generic Kalman Filter Implementation
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

27. Objective: seperate algorithm from parametrizations
Kalman filter algorithm
Pure linear algebra
Parametrizations
Hits: examples:
TPC (r, φ, z)
STT (x,y,dr)
PixelMVD (x,y,z)
Tracks: examples:
Barrel Spectrometer: some helix-representation
Forward Spectrometer: e.g. local straight line parametrization
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

28. Class Structure of Generic Kalman Filter
User implements:
concreteHit
concreteTrackRep
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

29. Kalman Filter Ingredients
As formulated in Frühwirth et al. “Data Analysis techniques …“
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

30. Distribution of Responsibilities
All information of hits up k-1 is already in the state vector and the covariance matrix xk-1 and Ck-1
→ Process Hit k
Kalman
Kalman Gain
Update
Track propagation / prediction
TrackRep
Calculation of residuals
Hit
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

31. Distribution of Responsibilities
Kalman
Kalman Gain
Update
Track propagation / prediction
TrackRep
Calculation of residuals
extrapolate to where?
Hit
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

32. Distribution of Responsibilities
Kalman
Kalman Gain
Update
Track propagation / prediction
TrackRep
Calculation of residuals
Hit
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

33. Distribution of Responsibilities
Voila!
Updated state and covariance!
Next iteration could without any problem use hit from different detector that measures very different coordinates
Kalman
Kalman Gain
Update
Track propagation / prediction
TrackRep
Calculation of residuals
Hit
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

34. Example Straight Line Fit
trackRep
Free parameter: z
State vector: xk=(ax,bx,ay,by)T
Extrapolation (trivial)
HIT (some pixel detector)
Free Parameter: z
Hit coordinates mk = (x, y)T
H Matrix:
Residual
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

35. PANDA-TPC TPC JAMBOREE Aachen March 2007
Example: Helix Fit
trackRep
Free parameter: r
State vector: xk=(Φk,zk,λ,C,D)T
Extrapolation
Covariance matrix prediction: Calculation of Jacobian matrix numerically or analytically
HIT (e.g. TPC)
Free Parameter: r
Hit coordinates mk = (rΦ, z)T
H Matrix:
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

36. PANDA-TPC TPC JAMBOREE Aachen March 2007
Example: Helix Fit
Circles: hits red dashed: start value for fitter green: result of fit
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

37. PANDA-TPC TPC JAMBOREE Aachen March 2007
Example: Helix Fit
Off-diagonal elements of covariance matrix a very large for representation
→ we need a better suited track representation
xk=(Φk,zk,λ,C,D)T
Circles: hits red dashed: start value for fitter green: result of fit
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

38. Example: Local Straight Line Fit
trackRep
6th order Runge-Kutta solver for propagation in arbitrary magnetic field
Numerical jacobi matrix calculation for error propagation
Solenoid
Dipole z
xk = (xk,yk,xk‘,yk‘,q/p)
Circles: hits red dashed: start value for fitter green: result of fit
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

39. Idea: Generic Kalman with GEANE
trackRep
Free parameter (length along track) and track representation (state vector) defined in GEANE way
Extrapolation of track and error propagation including multiple scattering and energy loss done by GEANE
HIT (for each detector kind)
User provides H-Matrix for transformation from hit coordinates to GEANE track parameter space
That’s it!
Code is basically ready to be used with GEANE
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

40. PANDA-TPC TPC JAMBOREE Aachen March 2007
Global Track Fit in PANDA
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

41. Challanges for the PANDA TPC Project
Space Charge
Event Mixing
Primary reactions at 107 / s with ~ 3 tracks / event
Electron drift time is ~ 50 μm → tracks of 500 events are in the chamber at a given time
Continuous operation → tracks can a priori only be reconstructed with unknown offset in z
Finding an absolute time for event a track belongs to: - endcap penetration or target pointing can help - final z-pinning with hits from other detectors (vertex tracker)
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

42. Concepts for continuous readout at high rates
What could it look like?
Raw data from ADC cards: 500 GB / s (times and amplitudes)
To computer farm: ~ factor 10 less (clustering, tracklet recognition, ..)
Some online track fitting in computer farm
Matching with other detectors or other means of finding an absolute time for the event
Construction of events
Physics selection (trigger)
- Simulations are being done on hardware clustering implementation
- Track reconstruction algorithms are being developed
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

43. Conclusion and Outlook
GEM-based TPC proposed as central tracker for PANDA
Space charge effects will distort tracks in order of mm → has to be corrected for in reconstruction
8 cm test-chamber is running nicely – ALICE electronics seems to be under control → study time structure of signals and spatial resolution
(of perpendicular tracks)
First experiences with Hough transform has been gained with test chamber → implement cylindrical tracks for PANDA software
A generic implementation of the Kalman Filter has been used for first track fits in the PANDA software framework → searching for best track representations ??
A large prototype will be built before the PANDA TDR in 2009 – this detector will be used for a new physics program at FOPI
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007

44. PANDA-TPC TPC JAMBOREE Aachen March 2007
Fit Results
C. Höppner (TUM E18)
PANDA-TPC TPC JAMBOREE Aachen March 2007