1. EAS Time Measurements P.K.Mohanty (On behalf of the GRAPES-3 Collaboration) 5 th Workshop on AstroParticle Physics, 14 – 16 December 2010 at CRL, Ooty

2. θ Δθ = c Δt / (D 21 cos θ) t 2 – t 1 = D 21 sinθ /c D 21 inter detector separation, c is velocity of light Measured parameter: Arrival times w.r.t. the array trigger

3. Factors contributes to Δt ● Fluctuation of arrival times of particles in the shower front ~ nano seconds ● Detector response ~ nano seconds ● Digitization accuracy of TDC ~ sub nano second Will be discussed in the TDC calibration in the first part ● Time offsets (TDC0) due to propagation delay of signal in the cable and electronics which is seen to change with time Determination of Time Offsets to an accuracy better than half nano second with a completely new, but simple technique will be discussed in the second part of the talk

4. TDCs in the GRAPES-3 experiment Four types of TDC used in the GRAPES-3 experiment Type Dynamic Range Resolution PHILLIPS 800 ns 200 ps HOSHIN 1 000 ns 285 ps TDC32 50 000 ns 512 ps HPTDC 50 000 ns 195 ps Calibration performed about twice in a year to determine and monitor the resolution of TDC. (Detailed Talk already given by Ajai yesterday)

5. Calibration of a PHILLIPS channel using a 40 MHz crystal oscillator Y = p0 + p1 X X = Time delays, Y = TDC counts Data Deviation from fit Linear Fit

6. Fit with a quadratic polynomial: y = p0 + p1 x + p2 x 2 RMS ~ 70 ps

7. A HOSHIN Channel Linear Fit A quadratic polynomial fit RMS ~40 ps

8. GRAPES-3 TDC-32 Linear Fit RMS ~ 70 ps Excepted Value of p1 = 1.92 counts/ns Our Value = 1.91993 counts/ns Diff = 7x10 -5 counts/ns or 0.036ps

9. GRAPES-3 HPTDC RMS ~ 40 ps

10. Calibration with 40MHz, 32MHz, 25MHz, 20MHz, 16MHz and 10 MHz Clocks

11. Combined Fit of the 6 clocks

12. Long term variation of calibration of a PHILLIPS module TDC (ns) = T (tdc=3000 counts) – T (tdc=500 counts) T calculated using the fit parameters p0, p1 and p2 and tdc 1ns Individual channel variation ~ 40 ps

13. Long term variation of another PHILLIPS module

14. Long term variation of a HOSHIN module 18ns Individual channel variation ~ 100 ps

15. Long term variation of a TDC32 Module 20ps

16. Summary of the TDC calibration ● PHILLIPS and HOSHIN TDCs show non linearity. ● The GRAPES-3 TDC-32 and HPTDC shows excellent linearity and the calibration values are closer to the expected values. ● The long term calibration plot shows some PHILLIPS channels have significant variation. HOSHIN modules are more stable. ● The variation of calibration values among the channels for GRAPES-3 TDC32 and HPTDC is less than 20ps and also the long term variation is within 20 ps. ● We have planned to replace all the PHILIPS and HOSHIN TDCs with HPTDC very soon.

17. A.B Muon Trigger ShowerTrigger OR START STOP TDC ADC Time Offsets t cal = t det – t pad Muon telescope is the common reference for all detectors

18. Question: Can we determine Time Offsets from shower data itself which is available 24 hours? Answer: Yes

19. Time Offsets from shower data Take the measured time difference between two neighbouring detectors △ t shower by shower △ t = t 2 measured – t 1 measured = (t 2 sh + t 2 offset ) – (t 1 sh + t 1 offset ) = (t 2 sh – t 1 sh ) + (t 2 offset – t 1 offset ) Angular dist.Fixed value GRAPES-3 scintillator array

20. (t 2 offset – t 1 offset ) Sigma = 11.4 ns mainly due to the angular effect Error in peak = 0.2 ns For D2 – D1 Condition: both detectors should have tdc signal

21. D200 – D199 D599 – D518

22. Time Offsets of D1 w.r.t. its 6 neighbours

23. Time Offset Variation

24. The relative time offsets can be determined between any two neighbouring detectors in the GRAPES-3 array better than a half nano second. This is probably not new. However, in the shower analysis we need to correct the time offsets w.r.t. one common reference. Question: How to determine the time offsets with respect to one common reference? We didn’t have concrete answer until now due to the reason as follow.

25. For example, We would like to determine the time offset D100 w.r.t. D1 Then starting from D1, choose a nearest detector in the direction of D100 and then from this detector to it's nearest and so on till we reach D100 and then add △ t for each combination △ t 100-1 = △ t 2-1 + △ t 19-2 +.....................................+ △ t 100 - 99 There are many possible paths. For sake of simplicity, let's choose the shortest path. We will have the following problem (1) We have to manually track the path and do a book keeping (2) If any detector is off on the path or abnormal then in trouble.

27. The New Method: Random Walk Let the computer solve the problem Starting from a reference detector, go to a destination detector following a random path using random numbers For example we start from D1 and want to go to D100 Method: Start from D1 and select one of the six nearest neighbours using random number. From this detectors again select it’s neighbour using random. Keep doing this till you reach D100. Now we got one path. Start again from D1 and get other possible paths.

28. Random Path (Starting D1, Dest. D50)

30. The New Method: Random Walk △ t 100-1 = △ t 5-1 + △ t 16-5 +.....................................+ △ t 100 - 98 Let’s for the path is from D1 to D5, D5 to D16, …. D98 to D100 Known Repeat this many times to get a distribution of the time offsets

31. △ t distribution from Random Walk D100 - D1

32. △ t distribution from Random Walk D200-D1 Only in 15 seconds, the time offsets of all the detectors w.r.t the reference detector is solved D300-D1

33. Checking the correctness of the method From direct method the relative offset is known from shower data between the nearest neighbours with a good accuracy. Let’s compare the output from Random Walk with the direct method. Example: from direct method we know the offset between D99 and D100 but not with respect to D1 From Random walk method we obtained between D1 and D100 Also D1 and D99. Then (D100 – D99) Random = (D100 – D1) - (D99 – D1) Δ = (D100 – D99) Random - (D100 – D99) Direct

34. Random Walk and Direct method comparison

35. Time Offset Variation with Time For D2 w.r.t. D1

36. For D17 w.r.t. D1

37. For D47 w.r.t. D1

38. For D503 w.r.t. D1

39. Summary ● The new method simple and inexpensive to determine the time offsets ● Expecting to get better angular resolution using this new method. This work is in progress. ● The new method will give better accuracy if the detector separation is not too large.

40. THANKS