TPC Results tpc1c

 

How to Do Analysis
List of Runs

General
minSignal = 3.0
gas VGEM VDrift drift-field VD (cm/ns) CD (trans) CD (long) Nt for 6 mm
ArCO2 (90:10) 2620 7120 300 2.32E-3 0.222 0.264 57
ArCO2 (80:20) 2930 8555 375 1.34E-3 0.156 0.181 56
P10 2750 4820 138 5.49E-3 0.564 0.374 55

Timing
Histogram of drift time in time bins. Full region and blow up of the end points.
gas T-bin
@ DD=0		 T-bin
@ DD=15		 VD(cm/ns) Magboltz plot
ArCO2 (R:97-110) 1400 2700 (2.31+-0.03)E-3 2.32E-3 eps
ArCO2 (R:406-409) 200 2460 (1.33+-0.03)E-3 1.34E-3 eps
P10 (R:204-225) 220 790 (5.3+-0.2)E-3 5.49E-3 eps

Pad response function and amplitude error
The error on the amplitude has 3 components:
constant, statistical prop.to sqrt(A) and systematic prop.to A. However, to be flexible it is described by a (high order) polynomial.

NEW: (6/10/2004) The error is the quadratic sum of the polynomial and minSignal. I.e. there is a constant term + a polynomial (systematic error).
gas P0 P1 plot
ArCO2 (90:10) (R:97-111) 0. 0.225 eps
ArCO2 (80:20) (R:406-409) 0. 0.225 eps
P10 (R:204-207) 2.8664 0.20196 eps

The parameters of the pad response function:
gas FWHM2 del a b plot
ArCO2 (90:10) (R:97-110) 8.68+0.3782*z 11.9 -0.3 0 ps
ArCO2 (80:20) (R:406-409) 8.97+0.240*z 11.9 -0.3 0 ps
P10 (R:204-207) 9.358+2.0524*z 11.42+0.1228*z 0 0 ps

Bias
gas plot
ArCO2 (90:10) (R:97-110) ps
ArCO2 (80:20) (R:406-412) ps
P10 (R:204-211) all ; cuts

Amplitude vs drift distance
The amplitude in a row is determined from the fit of the PRF to the charge distribution in the row. The maximum of the PRF is taken as the amplitude in the row. This maximum depends on the drift distance due to diffusion. In the data the amplitude of one channel (apart from late pulses from dispersion only) is determined as the average ADC over the 15 bins before and 15 bins after the maximum, i.e. 30*5ns where the maximum of the ADC distribution is in the middle of the range.
gas plot parametrisation
ArCO2 (90:10) (R:101-110) ps 84.77 - 0.1042*Z/mm
ArCO2 (80:20) (R:413-451) ps 85.99 - 0.3499*Z/mm
P10 (R:212-225) ps 47.46 - 0.1366*Z/mm
Simulation eps for ArCO2 (90:10) and ArCO2 (80:20)

Simulation for ArCO2 (90:10) and ArCO2 (80:20) without rebinning (sampling ? ns); drop of amplitude is similar for both gasses, difference ~ 5%; for ArCO2 (80:20) with rebinning (sampling 30*5ns). The 60% drop observed in ArCO2 (80:20) can not be explained with this simulation (~20%) even accounting for an additional 20% as observed in the gain measurement. The drop of 18.4% observed in ArCO2 (90:10) is in reasonable agreement with the simulation. The treatment of rebinning is different in data and simulation.

Resolution
gas remaining bias resolution CD vs electrons Mean 1/N s0 CD Magboltz comment
ArCO2 (R:101-110) ps eps cd 0.0238 0.072 0.25 +- 0.04 0.22
ArCO2 (R:413-451) ps eps cd 0.0234 0.073 0.238+-0.005 0.156 assuming amplitude drop only due to diffusion
cd N/A 0.073 ~ 0.2 amplitude drop as for ArCO2 (90:10) + 20%
cd N/A 0.073 ~ 0.17 correcting amplitude drop as for ArCO2 (90:10)
P10 (R:212-225) all ; cuts eps cd 0.0251 0.134 0.50 +- 0.01 0.56 from tpc1b data: 0.43


Since N for ArCO2 (80:20) depends on z (unless the full drop of amplitude is corrected) a mean 1/N is meaningless. For the fits in 6 amplitude regions N is more-or-less constant due to the cuts. The value for CD is an eye-fit from the plot of CD vs electrons.

Statistics
This is a test which value of N has to be used for the extraction of the diffusion constant CD. (figure)
The number of electrons (amplitude) n is distributed like a Landau distribution with mean N. The resolution for a given number of electrons n is proportional to 1/sqrt(n), i.e. the residuals are distributed like a Gaussian with width ~1/sqrt(n).

In this test the binned amplitude distribtion of the ArCO2 (90:10) data is used, shown in the first plot. The plot below shows the sum of Gaussians where the width is ~n. For each bin of the amplitude distribution a Gaussian with the corresponding width and a maximum proportional to the number of entries was added.

However, for the residuals the width of the Gaussians are proportional to 1/sqrt(n), which is shown in the last plot. By chance this distribution is more or less Gaussian itself (the RMS and the sigma are similar). The sigma 0.148 is closer to the mean on the distribution 1/sqrt(n) (second plot) than to 1/sqrt(mean(n)) = 0.131.
Therefore the mean NT should not be used to estimate the resolution.

Last update:
20/9/2004, Kirsten

 

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