- Email: [email protected]
Drift properties of the ATLAS MDT chambers
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Nuclear Instruments and Methods in Physics Research A 568 (2006) 672–681 www.elsevier.com/locate/nima
Drift properties of the ATLAS MDT chambers R.M. Avramidoua,b,, E.N. Gazisb, R. Veenhofc a
Harrison M. Randall Laboratory, University of Michigan, Ann Arbor, MI, USA b National Technical University of Athens, Athens, Greece c Instituto Superior Tecnico IST, Lisboa, Portugal
Received 1 December 2004; received in revised form 16 June 2006; accepted 11 July 2006 Available online 5 September 2006
Abstract A cosmic ray setup has been assembled, in order to verify that the BIS-MDT chamber fulfils the requirements of the ATLAS Muon Spectrometer. We use measurements obtained with this setup to study the drift time spectra of the MDT tubes and explain its features, by comparing them with the predictions of Garfield, Magboltz and Heed simulation programs. The drift time spectra have a peculiarity of a double peak. The second peak is a clear evidence of the Ramsauer dip of the electron cross-section. r 2006 Elsevier B.V. All rights reserved. PACS: 07.05.Tp; 29.40.Cs; 29.40.Gx Keywords: MDT chamber; Garfield simulation; Drift time spectra; Ramsauer dip
1. Introduction The ATLAS detector for the Large Hadron Collider at CERN will study the products of proton–proton collisions at energies of up to 14 TeV at luminosities up to 1034 cm2 s1. High-precision muon momentum measurements (dp/p10% at pT ¼ 1 TeV/c) over large areas using monitored drift tube (MDT) chambers are important for the ATLAS experiment. The BIS-MDT chamber Module-0 [1,2] was used in a cosmic ray setup to verify that the requirements of the ATLAS Muon Spectrometer [3] are fulfilled [4]. The BISMDT chamber consists of two multilayers composed of four layers each. Each layer consists of 30 aluminium drift tubes 1700 mm long, 30 mm in diameter, with 400 mm wall thickness, and a 50 mm diameter central W-Re wire. The multilayers are separated by seven 6 mm thick aluminum strips. The BIS-MDT chamber is fully equipped with a gas system and relevant electronics [5,6]. There is a parallel gas supply for each tube and each multilayer; the gas flow is 35 NL/h (1 volume change per Corresponding author. CERN, PH Department, Gene`ve 23, CH-1211, Switzerland. Tel.: +41 22 767 1148; fax: +41 22 767 8350. E-mail address: [email protected] (R.M. Avramidou).
0168-9002/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2006.07.064
day). The gas is the nominal ATLAS MDT gas of Ar (93%)–CO2 (7%) at a pressure of 3 bar (absolute). A high voltage of 3080 V is applied, which corresponds to a gas gain of 2 104.
2. Individual tube time spectra The drift time spectrum (Fig. 1) is built for each muon drift tube using all the detected muons [7]. The muon drift time tmeasured, is given by the expression tmeasured ¼ tm+td+telectronicsttrigger, where tm is the time when the muon hits the tube, td is the time interval between the passage through the tube of the muon, which interacts with the gas atoms and the moment that the first ionization electrons reach the wire and the induced signal passes the threshold, telectronics is the propagation time of the signal along the wire and ttrigger is the time when the trigger signal provides the start pulse of the time to the digital converter (TDC) module connected to the tube. The drift time spectrum is fitted with functions described in Ref. [7]. The starting point t0 (half of the rise time of the leading edge) and the ending point t1 (half of the falling time of the trailing edge) define the physical time window. The value of t0 is related to
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6.5 6 5.5
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5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 89
Fig. 1. Typical time distribution of the muon hits for the first multilayer of the MDT chamber. The time distribution is essentially the same for both multilayers.
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2
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103
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Electric field [V/cm]
Fig. 3. Simulation of the electron drift velocity as a function of the electric field for the operation conditions of the muon drift chamber for Ar (93%)–CO2 (7%). 6.5 6
The following is to be noted for the various regions of the time spectrum:
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Fig. 2. Simulation of the electron drift velocity as a function of the drift path for the operation conditions of the muon drift chamber for Ar (93%)–CO2 (7%).
the gas properties like the ionization, the diffusion, the multiplication factor and the electron drift velocity which depend on the electric field, pressure and temperature. The quantity defined as tmax ¼ t1–t0 depends on the drift properties of the tubes, so it provides an indication of the uniform operational behaviour of the chamber.
The leading time is small due to the strong electric field close to the anode wire and the small cluster spacing, which results from the high pressure. The double peak in the time distribution is explained by the corresponding double peak in the electron drift velocity, since the number of events, dN, in the time interval dt, is proportional to the drift velocity uD (dN/dt ¼ dN/dx dx/dt ¼ c uD). In the following we shall try to give an explanation for the shape of the drift velocity graph (Figs. 2 and 3). The space–time relation for the Ar–CO2 mixture, in the domain where the electron mobility pis ffiffi constant (r45 mm), approximately follows a r / t law, since the electron mobility is more or less constant for Eo103 V/cm. Such p non-linear behaviour gives a time ffiffi distribution N / 1= t and it is verified by the drift velocity curve uDpE (Fig. 3). The non-linearity of the space–time relation plays an important role in case of space charge effects, where the field fluctuations result in significant variations of the drift time and thus changes in the r–t relation [8].
Studying the two plots (Figs. 2 and 3) for the drift velocity, as a function of the drift path and the electric field, respectively, based on Magboltz [9], Heed [10] and Garfield [11] simulation programs, we observe that the second peak occurs at a distance of 0.3 cm from the wire,
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r [cm] Fig. 4. Electric field in a drift tube as a function of the distance from the anode wire.
Fig. 6. Cross-section for electrons in CO2, as a function of their energy.
Fig. 5. Cross-section for electrons in Ar, as a function of their energy.
where the electric field is 1613 V/cm and the drift velocity 4.6 cm/ms. An additional smaller peak (not visible in drift time spectra) at about 4.6 cm/ms and at electric field of 104 V/cm is caused by the increased vibrational energy loss in CO2 at 4 eV [12] (Figs. 6 and 7). Fig. 4 shows the electric field as a function of the distance from the wire.
3. Cross-section The electron drift velocity is derived from the gas crosssections. We shall study it deeper in order to understand the behaviour of the electron drift velocity. The crosssections have a rich structure because typical drift electron energies are of the same order as the energies of molecular atomic levels. This is in particular the case for molecules. The cross-sections for Ar and CO2 are shown in Figs. 5 and 6 (Appendix) [12], respectively. The Magboltz
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Electron energy [eV] Fig. 7. Cross-sections for pure Ar (lowest curve), for pure CO2 (topmost curve) and for mixtures with 1%, 2%, 3%, 4%, 5%, 6%, 7%, 10%, 20%, 30%, 50% CO2.
1.5 1.4 1.3 Energy distribution [normalised]
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1 Electron energy [eV]
Fig. 8. Electron energy of the cross-section minimum as a function of CO2 fraction. The minimum shifts to higher energies when more CO2 is added.
Fig. 9. Energy distribution of electrons in Ar (93%)–CO2 (7%). The distributions correspond, from left to right, to electric fields of 800, 1000, 1600, 2000, 3200 V/cm.
program [9] uses them to compute the electron drift velocity, the diffusion tensor as well as the Townsend and attachment coefficients. Magboltz solves the Boltzmann transport
equations for electrons in gas mixtures under the influence of electric and magnetic fields (using Monte Carlo techniques [13]).
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Fig. 10. The mean electron energy as a function of CO2 fraction for the energy distributions of the previous figure. The addition of CO2 to pure Ar, causes a decrease of the mean electron energy. x103
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The cross-sections for Ar, CO2 and their mixtures are shown in Fig. 7. The cross-section of the mixture changes substantially with the addition of small quantities of CO2.
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Fig. 11. The energy distribution shifts to lower energies with the addition of CO2 to pure Ar, for a constant electric field of 1000 V/cm. The distributions correspond, from right to left at high electron energies, to 0%, 0.1%, 0.5%, 1%, 2%, 5%, 7%, 50% and 100% of CO2.
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1 Electron energy [eV]
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Fig. 12. The transverse diffusion coefficient for pure Ar (topmost curve) and for mixtures of 7%, 10%, 20%, 100% CO2 (from top to bottom).
More specifically the addition of CO2 increases the crosssection, while its minimum shifts to higher energies (Fig. 8). The cross-section of CO2 is typically one order of magnitude larger than the cross-section of Ar at electron energies up to 1 eV. Moreover their behaviour differs
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Fig. 13. The transverse diffusion coefficient as a function of the CO2 percentage and of the electric field.
Fig. 15. Influence of the addition of CO2 in the drift velocity as a function of the electric field. The lowest, almost flat, curve is for pure Argon, while the following are for 0.5%, 1%, 1.5%, 2%, 2.5%, 3%, 4%, 5%, 6%, 7%, 8%, 9% and 10% CO2.
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significantly. The cross-section of CO2 falls steadily with energy up to 2 eV with a minimum at 1.7 eV, the one of Ar has a Ramsauer minimum at 0.24 eV, while the crosssection of the mixture Ar (93%)–CO2 (7%) has a Ramsauer dip at 0.45 eV.
2
1
Fig. 14. Influence of the addition of CO2 on the drift velocity as a function of the drift path. The lowest, almost flat, curve is for pure Argon, while the following are for 0.5%, 1%, 1.5%, 2%, 2.5%, 3%, 4%, 5%, 6%, 7%, 8%, 9% and 10% CO2.
CO2 fraction [%]
Fig. 16. Maximum drift velocity as a function of the CO2 percentage.
The Ramsauer minimum in the Ar cross-section corresponds to the energy at which incoming electrons undergo an S-wave phase shift by an angle of p, while traversing the strongly attractive field around the Ar nucleus. At the minimum, the S-wave cross-section therefore vanishes. P-wave scattering does not yet have high
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Fig. 17. The electric field at which the drift velocity in Ar–CO2 mixtures, reaches its maximum increase almost linearly with the CO2.
Fig. 19. Influence of the addition of water on the drift velocity as a function of the electric field. The curves correspond from left to right to pure Ar (93%)–CO2 (7%) and water addition of 0.5%, 1%, 1.5% and 2%.
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Electron drift velocity [cm/µsec]
5.5 5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 2
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103 104 Electric field [V/cm]
Fig. 18. Maximum drift time as a function of the CO2 percentage.
Fig. 20. Influence of the addition of nitrogen in the drift velocity as a function of the electric field. The curves correspond from bottom to top to pure Ar (93%)–CO2 (7%), and nitrogen addition of 0.5%, 1%, 1.5%, 2%, 2.5% and 3%.
amplitude at these energies so the total cross-section is small and the mean free path is large. This effect is responsible for the second peak that we observe and it is very interesting as it was one of the early
pure quantum effects to be observed [14–18]. Since the electron goes through the attractive field of nucleus with inverted phase, without any further interactions, it gains energy from the electric field and increases its drift velocity.
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Fig. 21. Influence of the water addition on the double peak, which gradually disappears as the water quantity increases. The time spectra correspond from bottom to top to pure Ar (93%)–CO2 (7%) (lowest), and water addition of 0.5% and 1%.
Fig. 22. Influence of the nitrogen addition on the double peak, which gradually disappears as the nitrogen quantity increases. The time spectra correspond from bottom to top to pure Ar (93%)–CO2 (7%) (lowest), and nitrogen addition of 0.5% and 1%.
The electron drift velocity is related to the cross-sections via the energy distribution function which is determined by the electric field and the cross-sections (elastic, vibration, excitation, ionization, attachment, etc.) as well as the energy loss by electrons during collisions with gas molecules. Fig. 9 shows that the electron energy
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distribution in the Ramsauer dip (0.35–0.60 eV) is largest for E ¼ 1613 V/cm. The value of 1613 V/cm corresponds to the value of the electric field, at which the second peak of the drift velocity is observed (Fig. 3). So the explanation of the appearance of the double peak at the drift time spectra is related to the Ramsauer dip of the electron cross-section, which causes the second maximum of the drift velocity. Although pure Ar has a Ramsauer dip, the drift velocity of electrons does not show a second peak (see Section 4). The reason for this observation is that in pure Ar, electrons with energy at the Ramsauer minimum have a very long mean free path and thereby acquire rapidly energies far above the minimum. Fig. 10 shows that the average electron energy in pure Ar is 4 eV and only few electrons have energies near the Ramsauer minimum (Fig. 11). The electrons therefore have a tendency to move fast but not forward, they are scattered in all directions and the transverse diffusion coefficient is high. The addition of CO2 reduces the transverse diffusion significantly and increases the drift velocity. Figs. 12 and 13 show the effect on the transverse diffusion coefficient of the addition of different percentages of CO2 in pure Ar. 4. Drift velocity Pure noble gases have low drift velocities, especially at low electric fields and they are too slow for use at the MDT chambers as they do not satisfy the detector dead-time constraints. Adding CO2 to Argon increases dramatically the electron drift velocity. In addition CO2 acts as quencher and reduces diffusion. Moreover it does not cause ageing effects. Figs. 14 and 15 show the influence of the addition of CO2 on the drift velocity for various fractions of CO2 as a function of the distance from the anode wire and as a function of the electric field, respectively. These figures can be compared with the measurements of Zhao et al. [19]. The good agreement is not surprising since the CO2 cross-sections used in Magboltz are in part based on these measurements. Figs. 14 and 16 show that the peak velocity increases with the addition of a higher percentage of CO2. Moreover, the maximum of the velocity shifts to higher electric fields when increasing the CO2 fraction (Figs. 15 and 17). The effects of the behaviour of the drift velocity are related to the peculiarities of the electron cross-section for these components. The cross-section increases with the addition of CO2, while it shows a minimum (Ramsauer dip), which shifts to higher energies, as already mentioned above. This tendency explains the shift of the velocity maximum to higher electric fields for higher fractions of CO2. The increase of the minimum value of the crosssection and the consequent decrease of the mean free path would be expected to cause a lower peak velocity contrary to the trend which is observed. The explanation is that there is an increase in the mean electron energy due to the higher electric field strength, which dominates over the decrease due to the shorter mean free path.
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Fig. 23. Detailed cross-sections for electrons in CO2, as a function of their energy.
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Another quantity which is directly related to the electron drift velocity is the drift time. The maximum drift time decreases up to 3% of CO2 and then increases (Fig. 18). The reason for the decrease is that pure Ar is very slow and it starts to become faster with small additions of CO2. The steep decrease up to 1% of CO2 can be explained by the cross-section (Ramsauer dip) and the significant reduction of the transverse diffusion. The plot is in good agreement with the expected results from the integration of the velocity curves of Fig. 14. Moreover, the mean electron energy is high, so the drift velocity is increased and the drift time is reduced. This effect is still dominant up to 2% of CO2. For higher percentages of CO2 the cross-section goes up, the mean free path goes down and consequently the drift time increases, as this effect starts now to become dominant.
Acknowledgements
5. Applications
[1] The First Precision Drift Tube Chambers for the ATLAS Muon Spectrometer ATL-MUON-2001–2004. (MPI-PhE/2001–2003), (ATL-COM-MUON-2001–2015), F. Bauer et al., 28 Feb 2001, Paper Contributed to the Ninth Vienna Conference on Instrumentation, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 478, No. 1–2, 1 February 2002, pp. 153–157. [2] Th. Alexopoulos, et al., IEEE Trans. Nucl. Sci. NS-49(5) (2002) 2484. [3] ATLAS, Muon Spectrometer, Technical Design Report, CERN/ LHCC/97-22, ATLAS TDR, 10, 31 May 1997. [4] Th. Alexopoulos, et al., IEEE Trans. Nucl. Sci. NS-50(6) (2003) 2420. [5] Fifth Workshop on Electronics for LHC experiments, CERN 99-09, CERN/LHCC/99-33, October 1999. [6] Seventh Workshop on Electronics for LHC experiments, CERN 2001–2005, CERN/LHCC/21–34, October 2001. [7] Automatic Synchronization of Drift-Time Spectra and Maximum Drift-Time Measurement of an MDT, O. Kortner, F. Rauscher, ATL-MUON-2005–012, Geneva, CERN, 08 Mar 2002, available in the web address: http://documents.cern.ch/cgi-bin/setlink?base= atlnot&categ=Note&id=muon-2005-012S. [8] M. Aleksa, M. Deile, N. P. Hessey, W. Riegler, MDT Performance in a High Rate Background Environment, ATL-MUON-98-258, Geneva, CERN, 22 October 1998, available in the web address: /http://preprints.cern.ch/cgi-bin/setlink?base=atlnot &categ=Note&id=muon-98-258S. [9] S. Biagi, MAGBOLTZ: Transport of electrons in gas mixtures, CERN Program Library. [10] I. Smirnov, HEED: Interactions of particles with gases, CERN Program Library W5060. [11] R. Veenhof, GARFIELD—Simulation of gaseous detectors, CERN Program Library W5050. [12] S. Biagi, Private communication. [13] S.F. Biagi, Monte Carlo simulation of electron drift and diffusion in counting gases under the influence of electric and magnetic fields, Nucl Instr. and Meth. A 421 (1999) 234. [14] Carl Ramsauer, Ann. der Phys.(Leipzig) 64 or 65 (1921) 513. [15] Carl Ramsauer, Ann. der Phys. (Leipzig) 66 (1921) 513. [16] J.S. Townsend, V.A. Bailey, Phil. Mag. 43 (1922) 593. [17] W. Blum, L. Rolandi, Particle Detection with Drift Chambers, Springer, Berlin, 1993. [18] R. Veenhof, Choosing a gas mixture for the Alice TPC, ALICE-INT2003–2029, February 13, 2003. [19] T. Zhao, Y. Chen, S. Han, J. Hersch, A study of electron drift velocity in Ar–CO2 and Ar–CO2–CF4 gas mixtures, Nucl. Instr. and Meth. A 340 (3) (1994) 485.
As already shown in Ref. [19] the second peak is sensitive to % level contaminations by water (H2O) and nitrogen (N2). Therefore, the second peak can be used as a monitoring tool for such contaminations (Figs. 19 and 20). Additional 2% of water makes the second peak vanish, while the drift velocity is reduced substantially for drift distances larger than 2 mm, while at drift distances of 5–6 mm the drift velocity is reduced by a factor of 4 (Figs. 4 and 19). The addition of nitrogen makes a second peak appear at higher fields and therefore at smaller times, as can be seen in Fig. 20. Figs. 21 and 22 show the influence of water and nitrogen addition on the drift time spectra. The detection of a global change in the gas mixture requires about 20 K events (the higher the statistics the clearer the effect). At the level of one multiplayer, the time needed to collect sufficient statistics is of the order of 1 h. This time depends on the chamber position, since the muon rate varies for the different parts of the muon spectrometer. Moreover investigating this at the level of the distribution line, we could take into account more than one multilayers, which are fed by the same line, and increase the statistics. 6. Conclusions The drift time spectra of the MDT (Monitored Drift Tube) chambers of the ATLAS Muon Spectrometer, which use a gas mixture of Ar (93%)–CO2 (7%) under a pressure of 3 bar, has a peculiarity of a double peak that is directly related to the electron drift velocity. The second peak appears at an electric field of 1613 V/cm. The origin is a dip in the cross-section for electron energies of 0.35–0.60 eV which is related to the Ramsauer effect. This effect allows the electron to increase its energy and its velocity, as the total cross-section is small and the mean free path is long.
We would like to express our thanks to Stephen Biagi, author of Magboltz program for providing us the crosssection plots and his important remarks on the content of this paper. This work has been partially supported by the project ‘‘PYTHAGORAS I’’, which is co-funded by the European Social Fund (75%) and National Resources (25%). Appendix The plots in Fig. 23 show in detail the CO2 crosssections [12]. References
Nuclear Instruments and Methods in Physics Research A 568 (2006) 672–681 www.elsevier.com/locate/nima
Drift properties of the ATLAS MDT chambers R.M. Avramidoua,b,, E.N. Gazisb, R. Veenhofc a
Harrison M. Randall Laboratory, University of Michigan, Ann Arbor, MI, USA b National Technical University of Athens, Athens, Greece c Instituto Superior Tecnico IST, Lisboa, Portugal
Received 1 December 2004; received in revised form 16 June 2006; accepted 11 July 2006 Available online 5 September 2006
Abstract A cosmic ray setup has been assembled, in order to verify that the BIS-MDT chamber fulfils the requirements of the ATLAS Muon Spectrometer. We use measurements obtained with this setup to study the drift time spectra of the MDT tubes and explain its features, by comparing them with the predictions of Garfield, Magboltz and Heed simulation programs. The drift time spectra have a peculiarity of a double peak. The second peak is a clear evidence of the Ramsauer dip of the electron cross-section. r 2006 Elsevier B.V. All rights reserved. PACS: 07.05.Tp; 29.40.Cs; 29.40.Gx Keywords: MDT chamber; Garfield simulation; Drift time spectra; Ramsauer dip
1. Introduction The ATLAS detector for the Large Hadron Collider at CERN will study the products of proton–proton collisions at energies of up to 14 TeV at luminosities up to 1034 cm2 s1. High-precision muon momentum measurements (dp/p10% at pT ¼ 1 TeV/c) over large areas using monitored drift tube (MDT) chambers are important for the ATLAS experiment. The BIS-MDT chamber Module-0 [1,2] was used in a cosmic ray setup to verify that the requirements of the ATLAS Muon Spectrometer [3] are fulfilled [4]. The BISMDT chamber consists of two multilayers composed of four layers each. Each layer consists of 30 aluminium drift tubes 1700 mm long, 30 mm in diameter, with 400 mm wall thickness, and a 50 mm diameter central W-Re wire. The multilayers are separated by seven 6 mm thick aluminum strips. The BIS-MDT chamber is fully equipped with a gas system and relevant electronics [5,6]. There is a parallel gas supply for each tube and each multilayer; the gas flow is 35 NL/h (1 volume change per Corresponding author. CERN, PH Department, Gene`ve 23, CH-1211, Switzerland. Tel.: +41 22 767 1148; fax: +41 22 767 8350. E-mail address: [email protected] (R.M. Avramidou).
0168-9002/$ - see front matter r 2006 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2006.07.064
day). The gas is the nominal ATLAS MDT gas of Ar (93%)–CO2 (7%) at a pressure of 3 bar (absolute). A high voltage of 3080 V is applied, which corresponds to a gas gain of 2 104.
2. Individual tube time spectra The drift time spectrum (Fig. 1) is built for each muon drift tube using all the detected muons [7]. The muon drift time tmeasured, is given by the expression tmeasured ¼ tm+td+telectronicsttrigger, where tm is the time when the muon hits the tube, td is the time interval between the passage through the tube of the muon, which interacts with the gas atoms and the moment that the first ionization electrons reach the wire and the induced signal passes the threshold, telectronics is the propagation time of the signal along the wire and ttrigger is the time when the trigger signal provides the start pulse of the time to the digital converter (TDC) module connected to the tube. The drift time spectrum is fitted with functions described in Ref. [7]. The starting point t0 (half of the rise time of the leading edge) and the ending point t1 (half of the falling time of the trailing edge) define the physical time window. The value of t0 is related to
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6.5 6 5.5
Drift velocity [cm/µsec]
5 4.5 4 3.5 3 2.5 2 1.5 1 0.5 0 89
Fig. 1. Typical time distribution of the muon hits for the first multilayer of the MDT chamber. The time distribution is essentially the same for both multilayers.
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103
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Fig. 3. Simulation of the electron drift velocity as a function of the electric field for the operation conditions of the muon drift chamber for Ar (93%)–CO2 (7%). 6.5 6
The following is to be noted for the various regions of the time spectrum:
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r [cm]
Fig. 2. Simulation of the electron drift velocity as a function of the drift path for the operation conditions of the muon drift chamber for Ar (93%)–CO2 (7%).
the gas properties like the ionization, the diffusion, the multiplication factor and the electron drift velocity which depend on the electric field, pressure and temperature. The quantity defined as tmax ¼ t1–t0 depends on the drift properties of the tubes, so it provides an indication of the uniform operational behaviour of the chamber.
The leading time is small due to the strong electric field close to the anode wire and the small cluster spacing, which results from the high pressure. The double peak in the time distribution is explained by the corresponding double peak in the electron drift velocity, since the number of events, dN, in the time interval dt, is proportional to the drift velocity uD (dN/dt ¼ dN/dx dx/dt ¼ c uD). In the following we shall try to give an explanation for the shape of the drift velocity graph (Figs. 2 and 3). The space–time relation for the Ar–CO2 mixture, in the domain where the electron mobility pis ffiffi constant (r45 mm), approximately follows a r / t law, since the electron mobility is more or less constant for Eo103 V/cm. Such p non-linear behaviour gives a time ffiffi distribution N / 1= t and it is verified by the drift velocity curve uDpE (Fig. 3). The non-linearity of the space–time relation plays an important role in case of space charge effects, where the field fluctuations result in significant variations of the drift time and thus changes in the r–t relation [8].
Studying the two plots (Figs. 2 and 3) for the drift velocity, as a function of the drift path and the electric field, respectively, based on Magboltz [9], Heed [10] and Garfield [11] simulation programs, we observe that the second peak occurs at a distance of 0.3 cm from the wire,
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r [cm] Fig. 4. Electric field in a drift tube as a function of the distance from the anode wire.
Fig. 6. Cross-section for electrons in CO2, as a function of their energy.
Fig. 5. Cross-section for electrons in Ar, as a function of their energy.
where the electric field is 1613 V/cm and the drift velocity 4.6 cm/ms. An additional smaller peak (not visible in drift time spectra) at about 4.6 cm/ms and at electric field of 104 V/cm is caused by the increased vibrational energy loss in CO2 at 4 eV [12] (Figs. 6 and 7). Fig. 4 shows the electric field as a function of the distance from the wire.
3. Cross-section The electron drift velocity is derived from the gas crosssections. We shall study it deeper in order to understand the behaviour of the electron drift velocity. The crosssections have a rich structure because typical drift electron energies are of the same order as the energies of molecular atomic levels. This is in particular the case for molecules. The cross-sections for Ar and CO2 are shown in Figs. 5 and 6 (Appendix) [12], respectively. The Magboltz
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Electron energy [eV] Fig. 7. Cross-sections for pure Ar (lowest curve), for pure CO2 (topmost curve) and for mixtures with 1%, 2%, 3%, 4%, 5%, 6%, 7%, 10%, 20%, 30%, 50% CO2.
1.5 1.4 1.3 Energy distribution [normalised]
1.2 1.1 1 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 2
3
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1 Electron energy [eV]
Fig. 8. Electron energy of the cross-section minimum as a function of CO2 fraction. The minimum shifts to higher energies when more CO2 is added.
Fig. 9. Energy distribution of electrons in Ar (93%)–CO2 (7%). The distributions correspond, from left to right, to electric fields of 800, 1000, 1600, 2000, 3200 V/cm.
program [9] uses them to compute the electron drift velocity, the diffusion tensor as well as the Townsend and attachment coefficients. Magboltz solves the Boltzmann transport
equations for electrons in gas mixtures under the influence of electric and magnetic fields (using Monte Carlo techniques [13]).
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Fig. 10. The mean electron energy as a function of CO2 fraction for the energy distributions of the previous figure. The addition of CO2 to pure Ar, causes a decrease of the mean electron energy. x103
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The cross-sections for Ar, CO2 and their mixtures are shown in Fig. 7. The cross-section of the mixture changes substantially with the addition of small quantities of CO2.
0.6
Fig. 11. The energy distribution shifts to lower energies with the addition of CO2 to pure Ar, for a constant electric field of 1000 V/cm. The distributions correspond, from right to left at high electron energies, to 0%, 0.1%, 0.5%, 1%, 2%, 5%, 7%, 50% and 100% of CO2.
0.4
1 Electron energy [eV]
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Fig. 12. The transverse diffusion coefficient for pure Ar (topmost curve) and for mixtures of 7%, 10%, 20%, 100% CO2 (from top to bottom).
More specifically the addition of CO2 increases the crosssection, while its minimum shifts to higher energies (Fig. 8). The cross-section of CO2 is typically one order of magnitude larger than the cross-section of Ar at electron energies up to 1 eV. Moreover their behaviour differs
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Fig. 13. The transverse diffusion coefficient as a function of the CO2 percentage and of the electric field.
Fig. 15. Influence of the addition of CO2 in the drift velocity as a function of the electric field. The lowest, almost flat, curve is for pure Argon, while the following are for 0.5%, 1%, 1.5%, 2%, 2.5%, 3%, 4%, 5%, 6%, 7%, 8%, 9% and 10% CO2.
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significantly. The cross-section of CO2 falls steadily with energy up to 2 eV with a minimum at 1.7 eV, the one of Ar has a Ramsauer minimum at 0.24 eV, while the crosssection of the mixture Ar (93%)–CO2 (7%) has a Ramsauer dip at 0.45 eV.
2
1
Fig. 14. Influence of the addition of CO2 on the drift velocity as a function of the drift path. The lowest, almost flat, curve is for pure Argon, while the following are for 0.5%, 1%, 1.5%, 2%, 2.5%, 3%, 4%, 5%, 6%, 7%, 8%, 9% and 10% CO2.
CO2 fraction [%]
Fig. 16. Maximum drift velocity as a function of the CO2 percentage.
The Ramsauer minimum in the Ar cross-section corresponds to the energy at which incoming electrons undergo an S-wave phase shift by an angle of p, while traversing the strongly attractive field around the Ar nucleus. At the minimum, the S-wave cross-section therefore vanishes. P-wave scattering does not yet have high
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Fig. 17. The electric field at which the drift velocity in Ar–CO2 mixtures, reaches its maximum increase almost linearly with the CO2.
Fig. 19. Influence of the addition of water on the drift velocity as a function of the electric field. The curves correspond from left to right to pure Ar (93%)–CO2 (7%) and water addition of 0.5%, 1%, 1.5% and 2%.
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Electron drift velocity [cm/µsec]
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Fig. 18. Maximum drift time as a function of the CO2 percentage.
Fig. 20. Influence of the addition of nitrogen in the drift velocity as a function of the electric field. The curves correspond from bottom to top to pure Ar (93%)–CO2 (7%), and nitrogen addition of 0.5%, 1%, 1.5%, 2%, 2.5% and 3%.
amplitude at these energies so the total cross-section is small and the mean free path is large. This effect is responsible for the second peak that we observe and it is very interesting as it was one of the early
pure quantum effects to be observed [14–18]. Since the electron goes through the attractive field of nucleus with inverted phase, without any further interactions, it gains energy from the electric field and increases its drift velocity.
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Fig. 21. Influence of the water addition on the double peak, which gradually disappears as the water quantity increases. The time spectra correspond from bottom to top to pure Ar (93%)–CO2 (7%) (lowest), and water addition of 0.5% and 1%.
Fig. 22. Influence of the nitrogen addition on the double peak, which gradually disappears as the nitrogen quantity increases. The time spectra correspond from bottom to top to pure Ar (93%)–CO2 (7%) (lowest), and nitrogen addition of 0.5% and 1%.
The electron drift velocity is related to the cross-sections via the energy distribution function which is determined by the electric field and the cross-sections (elastic, vibration, excitation, ionization, attachment, etc.) as well as the energy loss by electrons during collisions with gas molecules. Fig. 9 shows that the electron energy
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distribution in the Ramsauer dip (0.35–0.60 eV) is largest for E ¼ 1613 V/cm. The value of 1613 V/cm corresponds to the value of the electric field, at which the second peak of the drift velocity is observed (Fig. 3). So the explanation of the appearance of the double peak at the drift time spectra is related to the Ramsauer dip of the electron cross-section, which causes the second maximum of the drift velocity. Although pure Ar has a Ramsauer dip, the drift velocity of electrons does not show a second peak (see Section 4). The reason for this observation is that in pure Ar, electrons with energy at the Ramsauer minimum have a very long mean free path and thereby acquire rapidly energies far above the minimum. Fig. 10 shows that the average electron energy in pure Ar is 4 eV and only few electrons have energies near the Ramsauer minimum (Fig. 11). The electrons therefore have a tendency to move fast but not forward, they are scattered in all directions and the transverse diffusion coefficient is high. The addition of CO2 reduces the transverse diffusion significantly and increases the drift velocity. Figs. 12 and 13 show the effect on the transverse diffusion coefficient of the addition of different percentages of CO2 in pure Ar. 4. Drift velocity Pure noble gases have low drift velocities, especially at low electric fields and they are too slow for use at the MDT chambers as they do not satisfy the detector dead-time constraints. Adding CO2 to Argon increases dramatically the electron drift velocity. In addition CO2 acts as quencher and reduces diffusion. Moreover it does not cause ageing effects. Figs. 14 and 15 show the influence of the addition of CO2 on the drift velocity for various fractions of CO2 as a function of the distance from the anode wire and as a function of the electric field, respectively. These figures can be compared with the measurements of Zhao et al. [19]. The good agreement is not surprising since the CO2 cross-sections used in Magboltz are in part based on these measurements. Figs. 14 and 16 show that the peak velocity increases with the addition of a higher percentage of CO2. Moreover, the maximum of the velocity shifts to higher electric fields when increasing the CO2 fraction (Figs. 15 and 17). The effects of the behaviour of the drift velocity are related to the peculiarities of the electron cross-section for these components. The cross-section increases with the addition of CO2, while it shows a minimum (Ramsauer dip), which shifts to higher energies, as already mentioned above. This tendency explains the shift of the velocity maximum to higher electric fields for higher fractions of CO2. The increase of the minimum value of the crosssection and the consequent decrease of the mean free path would be expected to cause a lower peak velocity contrary to the trend which is observed. The explanation is that there is an increase in the mean electron energy due to the higher electric field strength, which dominates over the decrease due to the shorter mean free path.
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Fig. 23. Detailed cross-sections for electrons in CO2, as a function of their energy.
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Another quantity which is directly related to the electron drift velocity is the drift time. The maximum drift time decreases up to 3% of CO2 and then increases (Fig. 18). The reason for the decrease is that pure Ar is very slow and it starts to become faster with small additions of CO2. The steep decrease up to 1% of CO2 can be explained by the cross-section (Ramsauer dip) and the significant reduction of the transverse diffusion. The plot is in good agreement with the expected results from the integration of the velocity curves of Fig. 14. Moreover, the mean electron energy is high, so the drift velocity is increased and the drift time is reduced. This effect is still dominant up to 2% of CO2. For higher percentages of CO2 the cross-section goes up, the mean free path goes down and consequently the drift time increases, as this effect starts now to become dominant.
Acknowledgements
5. Applications
[1] The First Precision Drift Tube Chambers for the ATLAS Muon Spectrometer ATL-MUON-2001–2004. (MPI-PhE/2001–2003), (ATL-COM-MUON-2001–2015), F. Bauer et al., 28 Feb 2001, Paper Contributed to the Ninth Vienna Conference on Instrumentation, Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 478, No. 1–2, 1 February 2002, pp. 153–157. [2] Th. Alexopoulos, et al., IEEE Trans. Nucl. Sci. NS-49(5) (2002) 2484. [3] ATLAS, Muon Spectrometer, Technical Design Report, CERN/ LHCC/97-22, ATLAS TDR, 10, 31 May 1997. [4] Th. Alexopoulos, et al., IEEE Trans. Nucl. Sci. NS-50(6) (2003) 2420. [5] Fifth Workshop on Electronics for LHC experiments, CERN 99-09, CERN/LHCC/99-33, October 1999. [6] Seventh Workshop on Electronics for LHC experiments, CERN 2001–2005, CERN/LHCC/21–34, October 2001. [7] Automatic Synchronization of Drift-Time Spectra and Maximum Drift-Time Measurement of an MDT, O. Kortner, F. Rauscher, ATL-MUON-2005–012, Geneva, CERN, 08 Mar 2002, available in the web address: http://documents.cern.ch/cgi-bin/setlink?base= atlnot&categ=Note&id=muon-2005-012S. [8] M. Aleksa, M. Deile, N. P. Hessey, W. Riegler, MDT Performance in a High Rate Background Environment, ATL-MUON-98-258, Geneva, CERN, 22 October 1998, available in the web address: /http://preprints.cern.ch/cgi-bin/setlink?base=atlnot &categ=Note&id=muon-98-258S. [9] S. Biagi, MAGBOLTZ: Transport of electrons in gas mixtures, CERN Program Library. [10] I. Smirnov, HEED: Interactions of particles with gases, CERN Program Library W5060. [11] R. Veenhof, GARFIELD—Simulation of gaseous detectors, CERN Program Library W5050. [12] S. Biagi, Private communication. [13] S.F. Biagi, Monte Carlo simulation of electron drift and diffusion in counting gases under the influence of electric and magnetic fields, Nucl Instr. and Meth. A 421 (1999) 234. [14] Carl Ramsauer, Ann. der Phys.(Leipzig) 64 or 65 (1921) 513. [15] Carl Ramsauer, Ann. der Phys. (Leipzig) 66 (1921) 513. [16] J.S. Townsend, V.A. Bailey, Phil. Mag. 43 (1922) 593. [17] W. Blum, L. Rolandi, Particle Detection with Drift Chambers, Springer, Berlin, 1993. [18] R. Veenhof, Choosing a gas mixture for the Alice TPC, ALICE-INT2003–2029, February 13, 2003. [19] T. Zhao, Y. Chen, S. Han, J. Hersch, A study of electron drift velocity in Ar–CO2 and Ar–CO2–CF4 gas mixtures, Nucl. Instr. and Meth. A 340 (3) (1994) 485.
As already shown in Ref. [19] the second peak is sensitive to % level contaminations by water (H2O) and nitrogen (N2). Therefore, the second peak can be used as a monitoring tool for such contaminations (Figs. 19 and 20). Additional 2% of water makes the second peak vanish, while the drift velocity is reduced substantially for drift distances larger than 2 mm, while at drift distances of 5–6 mm the drift velocity is reduced by a factor of 4 (Figs. 4 and 19). The addition of nitrogen makes a second peak appear at higher fields and therefore at smaller times, as can be seen in Fig. 20. Figs. 21 and 22 show the influence of water and nitrogen addition on the drift time spectra. The detection of a global change in the gas mixture requires about 20 K events (the higher the statistics the clearer the effect). At the level of one multiplayer, the time needed to collect sufficient statistics is of the order of 1 h. This time depends on the chamber position, since the muon rate varies for the different parts of the muon spectrometer. Moreover investigating this at the level of the distribution line, we could take into account more than one multilayers, which are fed by the same line, and increase the statistics. 6. Conclusions The drift time spectra of the MDT (Monitored Drift Tube) chambers of the ATLAS Muon Spectrometer, which use a gas mixture of Ar (93%)–CO2 (7%) under a pressure of 3 bar, has a peculiarity of a double peak that is directly related to the electron drift velocity. The second peak appears at an electric field of 1613 V/cm. The origin is a dip in the cross-section for electron energies of 0.35–0.60 eV which is related to the Ramsauer effect. This effect allows the electron to increase its energy and its velocity, as the total cross-section is small and the mean free path is long.
We would like to express our thanks to Stephen Biagi, author of Magboltz program for providing us the crosssection plots and his important remarks on the content of this paper. This work has been partially supported by the project ‘‘PYTHAGORAS I’’, which is co-funded by the European Social Fund (75%) and National Resources (25%). Appendix The plots in Fig. 23 show in detail the CO2 crosssections [12]. References