Wire map

Figure8.13shows the wire map of chamber 2 for different thresholds. For low thresh-olds there is an excess of hits in channels 512–760. This excess almost vanishes with a threshold of 3.0 or higher. As shown in Section6.3.3, some Helix chips showed a smaller amplification than most of the others. We adapted the data of these chips to the same

8.4 Threshold estimation 115

Threshold [ADC-units]

2 4 6 8 10

0 5 10 15 20 25

(a)Multiplicity versus threshold

Threshold [ADC-units]

2 4 6 8 10

0 0.2 0.4 0.6 0.8 1

(b)Efficiency versus threshold

Figure 8.12: The hit multiplicity and the efficiency of chamber 1 in dependence of the threshold allows us to estimate an optimal threshold (≈².5 ADC-units).

level of amplification, before everything was combined to entire chamber data objects.

One ADC-unit of the adjusted channels was larger than one ADC-unit of the remaining channels. Hence these channels had a larger digitalization noise. To suppress this noise, the threshold as estimated in Section 8.4.1had to be further increased to about 3.25 or 3.50 ADC-units.

8.4.3 Charge distribution

Because the dynamical range of our analog readout chain was not large enough for the biggest hits found, the peak distributions (see Figure8.14) show an accumulation of hits with a peak height of 125. All hits with higher peaks end up in this cut-off region, which is smeared out due to different offsets and baseline jumping (see 6.3). The sharp rise in these distribution below 4 ADC-units (see Figure 8.14(a) and 8.14(b)) indicates that there are still some noise hits in our sample using a threshold of 3 ADC-units. Increasing the threshold to 4 ADC-units results in the distributions given in Figure 8.15and8.16.

Although a threshold of 4 ADC-units is a factor of four above the noise level (see Fig-ure8.4(b)), the charge distributions in Figure8.15do not resemble clean Landau distribu-tions, because the Landau peak is not very well separated from the noise (Figure8.15(b)) or not separated at all (8.15(a)and8.15(c)). The charge distributions of some single chan-nels of the group plotted in Figure 8.15 are shown in Figure 8.16. Nine of the sixteen channels feature very clean Landau distributions (like the ones in 8.16(a)and 8.16(b)), five show a somewhat distorted one and the remaining two are distorted by a large peak

Channel

Figure 8.13: The wire maps of chamber 2 for different thresholds show an excess of hits in the two upper Helix chips (channels 512 to 760).

at small hit sizes (see Figure 8.16(c)). We conclude, that only a small part of the chan-nels plotted as group in Figure8.15(b) produced the distortion of the summed Landau distributions.

8.5 Efficiency 117

Landau-Scale = 1241 Landau-Mean = 10.29 Landau-σ = 7.27 Landau-Scale = 1241 Landau-Mean = 10.29

700 Landau-Scale = 3564

Landau-Mean = 4.574 Landau-σ = 1.798 Landau-Scale = 3564 Landau-Mean = 4.574 Landau-σ = 1.798

(c)Chamber 2

Figure 8.14: Peak distributions of a group of 16 channels around anode 344

Charge [ADC-units]

700 Landau-Scale = 2635

Landau-Mean = 29.03 Landau-σ = 14.92 Landau-Scale = 2635 Landau-Mean = 29.03

600 Landau-Scale = 1891

Landau-Mean = 41.66 Landau-σ = 18.15 Landau-Scale = 1891 Landau-Mean = 41.66

1000 Landau-Scale = 5412

Landau-Mean = 9.58 Landau-σ = 4.323 Landau-Scale = 5412 Landau-Mean = 9.58 Landau-σ = 4.323

(c)Chamber 2

Figure 8.15: Charge distributions of a group of 16 channels around anode 344.

8.5 Efficiency

For reasons described in Section8.3we could only determine a pseudo efficiency using two instead of three chambers. To eliminate using faked or noisy hits as reference, a selected reference hit had to be at least 20 ADC-units high. The expected hit coordinate was calculated using Formula8.4to project the reference into the second chamber.

If a hit was found around the expected position (±40 channels), the channel at the ex-pected position was considered efficient (6= the channel were it was found!). Therefore a dead region does not clearly stand out but is smeared out due to the uncertainty in the position determination (see Figure8.17(a)around channel 280). However a dead re-gion in the reference chamber, like channel 275 to 290 in chamber 1, reflects itself in the analyzed chamber (see Figure8.17(b)chamber 2 channel 293 to 307).

For the plots of the efficiency versus the threshold (Figure8.18) we used only the correctly operating regions. For these “good” regions, every chamber is functioning properly, dead channels and regions, where the chambers did not overlap due to the beam divergence were eliminated. In this “good” region the efficiency is 92% for chamber 1 and 73% for chamber 2 using a threshold of 3.5 ADC-units. For chamber 1 the efficiency reaches a

Charge [ADC-units]

25 Landau-Scale = 130.4

Landau-Mean = 37.73 Landau-σ = 16.95 Landau-Scale = 130.4 Landau-Mean = 37.73 Landau-σ = 16.95

(a)Chamber 1 – Channel 341

Charge [ADC-units]

(b)Chamber 1 – Channel 342

Charge [ADC-units]

250 Landau-Scale = 145.7

Landau-Mean = 29.44 Landau-⇐ = 17.78 Landau-Scale = 145.7 Landau-Mean = 29.44 Landau-⇐ = 17.78

(c)Chamber 1 – Channel 343

Charge [ADC-units]

70 Landau-Scale = 514.9

Landau-Mean = 8.201 Landau-σ = 3.955 Landau-Scale = 514.9 Landau-Mean = 8.201 Landau-σ = 3.955

(d)Chamber 2 – Channel 344

Figure 8.16: Charge distributions of some single channels belonging to the group in Figure8.15.

plateau between 2.5 and 6.5 ADC-units. The efficiency curve of chamber 2 steeply de-creases with increasing thresholds. This indicates that the gain of chamber 2 was too low and it was operated at insufficiently high voltage.

8.6 Homogeneity

One of our main goals was to measure the homogeneity over all the chambers. A good measure for gain homogeneity is the mean charge of the hits found. There are two ways to determine it:

• One can simply calculate the statistical mean of the charge. However, this method is sensitive to the threshold chosen. A too high threshold leads to a loss of small hits and therefore to a too large mean value. In case of a too small threshold there are additional, small noise hits which lower the mean value.

8.6 Homogeneity 119

Figure 8.17: Efficiency for every single channel

Threshold [ADC-unit]

Figure 8.18: Efficiency versus threshold

• If one fits a Landau function to the charge distribution, the dependency on the threshold can be eliminated. One has to restrict the fit however to the region above the noise hits to tender the fitted peak position parameter a noise independent mea-sure of the gain. If the Landau peak is not clearly separated from the noise tail (e.g.

Figure8.15(a), (b) and8.16(c)) a reasonable fit is not possible at all and an automatic

fitting procedure partly delivers incorrect fitting parameters, especially wrong peak

Figure 8.19: The mean charge value for every single channel is plotted for chamber 1 and cham-ber 2.

Since the Landau peak for many channels is not well separated from the noise tail, espe-cially in chambers 0 and 2, we had to use the first method.