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Timing Techniques for Drift Chambers
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Nuclear Physics B (Proc. Suppl.) 248–250 (2014) 127–130 www.elsevier.com/locate/npbps
Cluster Counting/Timing Techniques for Drift Chambers M. Cascellaa,b , F. Grancagnolob , G. Tassiellib,c,d a Universit` a
del Salento, Lecce, Italia sezione di Lecce, Italia c Universit` a G. Marconi, Roma, Italia d Fermilab, Batavia, USA b INFN
Abstract We describe the advantages of the cluster counting techniques over the traditional ways of integrating the ionization charge for particle identification for the purpose of particle identification. We also discuss the improvement in the determination of the impact parameter resolution in a drift cell using cluster timing techniques instead of considering only the arrival time of the first electron. Finally, we illustrate a possible way to define a fast trigger/filter. Keywords: drift chambers, particle trackers
Introduction Cluster timing in drift chambers consists in recording the drift times of all individual ionization cluster due to the passage of an ionizing track in the active medium. With this information, space point resolution and particle identification can be radically improved. Cluster Counting/Timing techniques may be beneficial to a variety of particle physics experiments, from rare decays search, where high resolution at low momentum (50300 MeV) is of paramount importance, to flavor factories where accuracies of the order of a few percent in dE/dx are needed for particle identification and flavor tagging; future high energy lepton collider experiments would also greatly benefit from both these improvements.
1. Particle identification with cluster counting The time separation between consecutive clusters, at any impact parameter, for helium mixtures, goes from a few to a few tens of nanoseconds. Thus single electron counting can be performed with commercially available GSa/s flashADC. http://dx.doi.org/10.1016/j.nuclphysbps.2014.02.025 0920-5632/© 2014 Elsevier B.V. All rights reserved.
The time resolution can be set to exactly compensate the cluster splitting due to diffusion, making the electron counting a real primary ionization measurement. Figure 1 shows the digitized pulse shape for a cosmic muon and the reconstructed clusters; 1.1. The experimental setup Measurements of primary ionization in a 95/5 mixture of helium/isobutane have been performed in a beam test [1] with a 2.6 cm aluminum square drift cell with a 25 μm sense wire. The measurements were used to study the performance of cluster counting in particle identification; several events were grouped together to simulate a long track. The drift tube was instrumented with a fast risetime ( 160 ps), wide band ( 100 kHz to 1.7 GHz) preamplifier and the signal was acquired with a digital oscilloscope ( 1.1 GHz band- width, 8 bits ADC per channel and 2 Gsamples/s sampling rate). 1.2. Results Experimental results show a clear improvement of cluster counting over dE/dx currently limited by the cluster recognition performance.
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M. Cascella et al. / Nuclear Physics B (Proc. Suppl.) 248–250 (2014) 127–130
Figure 1: Digitized pulse shape for a cosmic ray in a 8mm drift tube with 90/10 He/Ib mixture; the red box shows the cluster reconstructed by the PeakFit software.
Figure 3: The three curves are dE/dx, dN/dX (experimental) and dN/dx (theoretical).
2. Spatial resolution and hit filtering with cluster timing The cluster distributions for a track with 100 hits are shown in Fig. 2, while Fig. 3 illustrates the π/μ separation with cluster counting as a function of the number of samples on experimental data compared to the results obtained with a 20% truncated mean integral of the collected charge. The net gain of cluster counting over charge integration (3.2σ versus 2.0σ) is of a factor 1.7 at least and can reach, in optimal condition a relative increment of a factor 2.5.
Figure 2: Experimental distribution of the separation power s for simulated tracks with 100 hits using the “20% truncated mean” (top) s2σ; the theoretical limit is s = 2.8σ abd “dN/dx” (bottom) s3.2σ; the theoretical limit is s = 5σ.
2.1. The simulation The results presented in the following sections have been obtained using a Garfield++ simulation of a periodic system of 7 mm square drift cells with 20 μm sense wires and 40 μm field wires (the sense:field wire ratio is 1:5), immersed in a 90/10 mixture of He/Ib. Positrons with energy E = 105.6 GeV/c2 with random direction (θ, the polar angle is uniformly distributed and φ, the angle between the track and zˆ, the sense wire direction, is always π/2) and random impact parameter (uniformly distributed) are generated; the clusters generated in the gas and collected by the anode wire are simulated and recorded. The effect of diffusion is simulated by adding to the cluster distance √ d a Gaussian contribution with μ = 0 and σ = 200μm d. The length of the track segment inside the cell ltrack , used to compute the mean free path λ is not computed from b but always taken from the simulation truth. 2.2. Spatial resolution In a conventional drift chamber only the time of the first cluster is used to estimate the track impact parameter, resulting in a systematic overestimation. Cluster timing techniques use the information provided by the later clusters to form a weighted average of the impact parameter estimates, provided by the different clusters. Cluster timing is particularly relevant for small impact parameters where the contribution from the ionization statistics is largest. Fig. 4 shows the transverse position resolution of the KLOE drift chamber and the three terms that contribute to it. At short impact parameters, the dominant effect is the ionization statistics; to improve the resolution in this zone we plan to extract additional information from the time of arrival of all the clusters.
M. Cascella et al. / Nuclear Physics B (Proc. Suppl.) 248–250 (2014) 127–130
Figure 4: Spatial resolution gets contributions from many different sources , data from the KLOE prototype test beam [2]. Cluster timing techniques aim at reducing the primary ionization contribution.
The impact parameter computed using the ith cluster distance is: ⎞ ⎞ ⎛⎛ d12 + di2 1 ⎜⎜⎜⎜⎜⎜ d12 + di2 ⎟⎟⎟ ⎟ 2 ⎟⎠ + (λi ) ⎟⎟⎟⎠ bi = − ⎜⎝⎜⎝ 2 4 λi
129
Figure 6: Distribution of the residuals for several estimators for b in the interval 0.8 < btrue < 1 mm. The estimators are, in order, d, b2 , b3 , b4 , and b5 .
and its variance is
⎞2 ⎛⎛ ⎞2 ⎟⎟ 1 1 ⎜⎜⎜⎜⎜⎜⎜ d12 + di2 ⎟⎟⎟ 2 ⎟⎠ − (λi ) ⎟⎟⎟⎟⎠ σ2λ σbi = 2 2 ⎜⎜⎝⎜⎝ λi 4λ bi 4
where λi = int(i/2)λ and the definition of di , λi , etc. is shown in Fig. 5. Figure 7: Performance comparison of the cluster timing method (bottom curve) vs. the classical method (top curve) for a drift cell of radius r = 5 mm.
method vs. the classical method for a drift cell of radius r = 5 mm. 3. Tracker based hit filter/trigger
Figure 5: An ionizing track together with the first five cluster depositions along its trajectory; di is the distance between the cluster generation point and the wire, λi is the projection of the distance along the track direction.
We have realized a simple Garfield++ based simulation of a 7 mm, 1:5, square drift cells, immersed in a 90/10 mixture of He/Ib. The distribution of the residuals (the quantity bi − btrue ) is shown in Fig. 6. We believe we can obtain a better impact parameter b by taking the weighted sum of several bi . Fig. 7 compares the theoretical performance of the cluster timing
Finally a preliminary study has been started to realize a tracker based trigger algorithm for the Mu2e detector. Its purpose is to determine t0 , the moment when a electron track enters the tracker so that it can be used by the pattern recognition program. The algorithm exploits the fact that the last ionization cluster should arrive at the sense wire about at the same time for all wires (after correcting for the cell width). A prototype classifier has been tested using the Mu2e analysis and Monte Carlo framework. We build an histogram of the arrival time of the last clusters tlast (Fig. 8 left) the two peaks corresponds to two different tracks. This information can be used to filter hits that do not belong to the track (select one peak) and to measure the track time t0 tlast (Fig. 8 right).
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M. Cascella et al. / Nuclear Physics B (Proc. Suppl.) 248–250 (2014) 127–130
Figure 8: Performance of a track based trigger: distribution of the arrival time of the last clusters in a typical Mu2e signal event (left); distribution of the difference between tlast (from a single track) and t0 the track time given by the Monte Carlo simulation (right).
4. Conclusions We are planning a campaign of measurements with single drift tubes and a prototype drift chamber to test cluster timing algorithms for the purpose of resolution improvement and on the field. References [1] G. Cataldi et “Cluster counting in helium based gas mixtures” NIM A 386 (1997) 458-469 [2] M. Adinolfi et al (KLOE Collaboration), “The KLOE drift chamber”, NIM A 461 (2001) 25-28
Nuclear Physics B (Proc. Suppl.) 248–250 (2014) 127–130 www.elsevier.com/locate/npbps
Cluster Counting/Timing Techniques for Drift Chambers M. Cascellaa,b , F. Grancagnolob , G. Tassiellib,c,d a Universit` a
del Salento, Lecce, Italia sezione di Lecce, Italia c Universit` a G. Marconi, Roma, Italia d Fermilab, Batavia, USA b INFN
Abstract We describe the advantages of the cluster counting techniques over the traditional ways of integrating the ionization charge for particle identification for the purpose of particle identification. We also discuss the improvement in the determination of the impact parameter resolution in a drift cell using cluster timing techniques instead of considering only the arrival time of the first electron. Finally, we illustrate a possible way to define a fast trigger/filter. Keywords: drift chambers, particle trackers
Introduction Cluster timing in drift chambers consists in recording the drift times of all individual ionization cluster due to the passage of an ionizing track in the active medium. With this information, space point resolution and particle identification can be radically improved. Cluster Counting/Timing techniques may be beneficial to a variety of particle physics experiments, from rare decays search, where high resolution at low momentum (50300 MeV) is of paramount importance, to flavor factories where accuracies of the order of a few percent in dE/dx are needed for particle identification and flavor tagging; future high energy lepton collider experiments would also greatly benefit from both these improvements.
1. Particle identification with cluster counting The time separation between consecutive clusters, at any impact parameter, for helium mixtures, goes from a few to a few tens of nanoseconds. Thus single electron counting can be performed with commercially available GSa/s flashADC. http://dx.doi.org/10.1016/j.nuclphysbps.2014.02.025 0920-5632/© 2014 Elsevier B.V. All rights reserved.
The time resolution can be set to exactly compensate the cluster splitting due to diffusion, making the electron counting a real primary ionization measurement. Figure 1 shows the digitized pulse shape for a cosmic muon and the reconstructed clusters; 1.1. The experimental setup Measurements of primary ionization in a 95/5 mixture of helium/isobutane have been performed in a beam test [1] with a 2.6 cm aluminum square drift cell with a 25 μm sense wire. The measurements were used to study the performance of cluster counting in particle identification; several events were grouped together to simulate a long track. The drift tube was instrumented with a fast risetime ( 160 ps), wide band ( 100 kHz to 1.7 GHz) preamplifier and the signal was acquired with a digital oscilloscope ( 1.1 GHz band- width, 8 bits ADC per channel and 2 Gsamples/s sampling rate). 1.2. Results Experimental results show a clear improvement of cluster counting over dE/dx currently limited by the cluster recognition performance.
128
M. Cascella et al. / Nuclear Physics B (Proc. Suppl.) 248–250 (2014) 127–130
Figure 1: Digitized pulse shape for a cosmic ray in a 8mm drift tube with 90/10 He/Ib mixture; the red box shows the cluster reconstructed by the PeakFit software.
Figure 3: The three curves are dE/dx, dN/dX (experimental) and dN/dx (theoretical).
2. Spatial resolution and hit filtering with cluster timing The cluster distributions for a track with 100 hits are shown in Fig. 2, while Fig. 3 illustrates the π/μ separation with cluster counting as a function of the number of samples on experimental data compared to the results obtained with a 20% truncated mean integral of the collected charge. The net gain of cluster counting over charge integration (3.2σ versus 2.0σ) is of a factor 1.7 at least and can reach, in optimal condition a relative increment of a factor 2.5.
Figure 2: Experimental distribution of the separation power s for simulated tracks with 100 hits using the “20% truncated mean” (top) s2σ; the theoretical limit is s = 2.8σ abd “dN/dx” (bottom) s3.2σ; the theoretical limit is s = 5σ.
2.1. The simulation The results presented in the following sections have been obtained using a Garfield++ simulation of a periodic system of 7 mm square drift cells with 20 μm sense wires and 40 μm field wires (the sense:field wire ratio is 1:5), immersed in a 90/10 mixture of He/Ib. Positrons with energy E = 105.6 GeV/c2 with random direction (θ, the polar angle is uniformly distributed and φ, the angle between the track and zˆ, the sense wire direction, is always π/2) and random impact parameter (uniformly distributed) are generated; the clusters generated in the gas and collected by the anode wire are simulated and recorded. The effect of diffusion is simulated by adding to the cluster distance √ d a Gaussian contribution with μ = 0 and σ = 200μm d. The length of the track segment inside the cell ltrack , used to compute the mean free path λ is not computed from b but always taken from the simulation truth. 2.2. Spatial resolution In a conventional drift chamber only the time of the first cluster is used to estimate the track impact parameter, resulting in a systematic overestimation. Cluster timing techniques use the information provided by the later clusters to form a weighted average of the impact parameter estimates, provided by the different clusters. Cluster timing is particularly relevant for small impact parameters where the contribution from the ionization statistics is largest. Fig. 4 shows the transverse position resolution of the KLOE drift chamber and the three terms that contribute to it. At short impact parameters, the dominant effect is the ionization statistics; to improve the resolution in this zone we plan to extract additional information from the time of arrival of all the clusters.
M. Cascella et al. / Nuclear Physics B (Proc. Suppl.) 248–250 (2014) 127–130
Figure 4: Spatial resolution gets contributions from many different sources , data from the KLOE prototype test beam [2]. Cluster timing techniques aim at reducing the primary ionization contribution.
The impact parameter computed using the ith cluster distance is: ⎞ ⎞ ⎛⎛ d12 + di2 1 ⎜⎜⎜⎜⎜⎜ d12 + di2 ⎟⎟⎟ ⎟ 2 ⎟⎠ + (λi ) ⎟⎟⎟⎠ bi = − ⎜⎝⎜⎝ 2 4 λi
129
Figure 6: Distribution of the residuals for several estimators for b in the interval 0.8 < btrue < 1 mm. The estimators are, in order, d, b2 , b3 , b4 , and b5 .
and its variance is
⎞2 ⎛⎛ ⎞2 ⎟⎟ 1 1 ⎜⎜⎜⎜⎜⎜⎜ d12 + di2 ⎟⎟⎟ 2 ⎟⎠ − (λi ) ⎟⎟⎟⎟⎠ σ2λ σbi = 2 2 ⎜⎜⎝⎜⎝ λi 4λ bi 4
where λi = int(i/2)λ and the definition of di , λi , etc. is shown in Fig. 5. Figure 7: Performance comparison of the cluster timing method (bottom curve) vs. the classical method (top curve) for a drift cell of radius r = 5 mm.
method vs. the classical method for a drift cell of radius r = 5 mm. 3. Tracker based hit filter/trigger
Figure 5: An ionizing track together with the first five cluster depositions along its trajectory; di is the distance between the cluster generation point and the wire, λi is the projection of the distance along the track direction.
We have realized a simple Garfield++ based simulation of a 7 mm, 1:5, square drift cells, immersed in a 90/10 mixture of He/Ib. The distribution of the residuals (the quantity bi − btrue ) is shown in Fig. 6. We believe we can obtain a better impact parameter b by taking the weighted sum of several bi . Fig. 7 compares the theoretical performance of the cluster timing
Finally a preliminary study has been started to realize a tracker based trigger algorithm for the Mu2e detector. Its purpose is to determine t0 , the moment when a electron track enters the tracker so that it can be used by the pattern recognition program. The algorithm exploits the fact that the last ionization cluster should arrive at the sense wire about at the same time for all wires (after correcting for the cell width). A prototype classifier has been tested using the Mu2e analysis and Monte Carlo framework. We build an histogram of the arrival time of the last clusters tlast (Fig. 8 left) the two peaks corresponds to two different tracks. This information can be used to filter hits that do not belong to the track (select one peak) and to measure the track time t0 tlast (Fig. 8 right).
130
M. Cascella et al. / Nuclear Physics B (Proc. Suppl.) 248–250 (2014) 127–130
Figure 8: Performance of a track based trigger: distribution of the arrival time of the last clusters in a typical Mu2e signal event (left); distribution of the difference between tlast (from a single track) and t0 the track time given by the Monte Carlo simulation (right).
4. Conclusions We are planning a campaign of measurements with single drift tubes and a prototype drift chamber to test cluster timing algorithms for the purpose of resolution improvement and on the field. References [1] G. Cataldi et “Cluster counting in helium based gas mixtures” NIM A 386 (1997) 458-469 [2] M. Adinolfi et al (KLOE Collaboration), “The KLOE drift chamber”, NIM A 461 (2001) 25-28