2. Can the charge resolution and/or time resolution. be improved by changing the RC time of the integration circuit in the frontend

Transcription

1 Simulation of the PMT-TOT System R. W. Ellsworth February 2, 21 1 Questions to be Addressed 1. Can the charge resolution and/or time resolution be improved by changing the RC time of the integration circuit in the frontend board? 2. Can the charge resolution and/or time resolution be improved by using RG6 rather than RG59 cables. 3. What is the sensitivity to the length of the cables?

2 2 Simulation of Components 1. Simulate PMT output pulse. 2. Propagate pulse down cable. 3. Propagate through DC blocking capacitor and terminating resistor. 4. Integrate output of frontend board transconductance amplifier. 5. Determine T start, T stop, and TOT. item Repeat for many pulses. 3 Details 1. PMT pulse simulation. Andy wrote Awk script to extract photoelectron production times from HAWC Monte Carlo gamma showers. Make cuts on primary energy, number of PMT s. Write file of many pe times for specific n pe. 2

3 2. Assume a model of a single-pe pulse: V (t) = const t e t/τ where τ = 2.5ns. The pulse looks like this: e-9 1e-8 1.5e-8 2e-8 time, sec 3. With time steps of.2 ns add in a singlepe pulse at each time on the list of times, for each n pe -event. Signal has 248 values. Some output pulses for 1 pe events: 3

4 .25 5 different 1 pe signals.2.15 signal.1.5 5e-9 1e-8 1.5e-8 2e-8 2.5e-8 3e-8 time, sec 4. Propagate signal down cable. Use previously developed code which (a) Computes discrete Fourier transform of signal. (b) Computes each frequency component after a length L of cable. Take into account the speed and attenuation of each component. (c) reassembles the signal via the inverse FFT. 4

5 This method is a variation of that developed by Wigington and Nahman. (R. L. Wigington and N. S. Nahman, Proc. IRE, 45, 166 (1957).) (This paper was referenced in the Lawrence Radiation Laboratory Counting Note Pulse Response of Coaxial Cables, by Q. Kerns et al., 1966.) Cable input needed: capacitance/ft, nominal propagation speed, attenuation in db/1 ft at 1.E8 Hz. Memo on this at: http : //umdgrb.umd.edu/ ellswort/totsim /lossy.pdf 5. Aside: here is a demonstration; a pulse input to 468 ft RG 58. 5

6 The blue points are the delayed pulse measurments, the green the prediction. 6. Simulation of cable termination. At the end of the cable, we have: V in V out C R 6

7 Here R is 75 Ω, C = 1.E 8F (estimated). Approximation: neglect reflected signal. We know V in (t),r, C. Compute V out (t) numerically. 7. Signal is then input to transconductance amplifier: the input voltage signal turns into output current signal. The circuit is: i i 2 i C 1 R V Again, compute output voltage numerically. 7

8 A special case: square input current pulse. result The peak occurs when the input current stops. 8. Example of entire process: 1-pe signal, 73 ft RG 59. 8

9 Modeled PMT output signal fort.5 1e-7 2e-7 3e-7 4e-7 5e-7 time, sec Signal out from cable RG59 fort.12 1e-7 2e-7 3e-7 4e-7 5e-7 time, sec 9

10 Signal after cable termination RG59 fort.37 1e-7 2e-7 3e-7 4e-7 5e-7 time, sec 1

11 12 1 ToT integrator output RG59 fort e-7 2e-7 3e-7 4e-7 5e-7 time, sec 9. Finding TOT. The vertical scale of integrated output signal is calibrated with a single-pe signal, for the low-threshold amplifier. The peak value is divided by 4 to find the T start and T stop voltage thresholds. For the high-threshold simulation, a 5-pe signal, with no timing fluctuations, is used. For each event, T start, T stop, and TOT = T stop T start are found. 11

12 4 Some Results 4.1 TOT Distributions, Low Threshold For RG59, Integrator RC = 85 ns (standard), n pe = 2, 3, 6: ft RG59, 1/4 pe threshold tot2pedf.dat tot3pedf.dat tot6pedf.dat TOT, ns The fluctuations are due only to pe start times. 12

13 Now try reducing the RC by 4x (2xforR,C) ft RG59, 1/4 pe threshold TOT, ns The peaks are shifted downward, widths change little. Fractional widths increase. 4.2 Gain Fluctuations Use resolution data from S.J. Brice et al., NIM 562, 26 on Mini- BooNE R5912 PMT s. Peak of single pe resolution distribution corresponds to σ q q =.39 For n pe the uncertainty in total charge, Q is σ Q Q =.39 npe 13

14 The code normalizes the PMT output signal integral to the total charge for Gain = , and adds in a deviation chosen from a Gaussian with the above σ. Then the signal, dq is multiplied by dt 75Ω to make a voltage pulse. With these fluctuations the TOT distributions for 2, 3, 6 pe s, for standard RC, look like: ft RG59, 1/4 pe threshold tot2pe.dat tot3pe.dat tot6pe.dat TOT, ns 14

15 4.3 T start Distributions For 1 pe signals, with charge fluctuations, 73 ft RG59, the T start distribution is: 12 1 Tstart Distribution RG 59 fort time, sec 15

16 Now replace the 73 ft RG59 with 73 ft RG6, and recalibrate: Tstart Distribution RG fort time, sec 16

17 The time spread has been reduced. (σ from 3.3 to 2.3 ns) 4.4 TOT vs. true Charge For 73 ft RG59, plots of actual (fluctuated) charge, vs. TOT: Qtotal, Coul 3.5e-12 3e e-12 2e e-12 1e-12 5e-13 Actual Charge vs. ToT, Npe = ToT, ns Qtotal, Coul 6e-12 5e-12 4e-12 3e-12 2e-12 1e-12 Actual Charge vs. ToT, Npe = ToT, ns 17

18 The spread is caused by the pe time jitter. The next graph has no-jitter data included: True charge, Coulomb Actual Charge vs. ToT, Npe =3 9e-12 8e-12 7e-12 6e-12 5e-12 4e-12 3e-12 2e-12 1e TOT, ns 1.6e-11 Actual Charge vs. ToT, Npe =6 1.4e-11 Qtotal, Coul 1.2e-11 1e-11 8e-12 6e-12 4e ToT, ns 18

19 Can the situation be improved with a shorter or different cable? Set the cable length =, and recalibrate. Result is, for 3 pe, True charge, Coulomb Actual Charge vs. ToT, Npe =3 9e-12 8e-12 7e-12 6e-12 5e-12 4e-12 3e-12 2e-12 1e TOT, ns 19