- Email: [email protected]
From MARK3 to superB and ILC
ARTICLE IN PRESS
Nuclear Instruments and Methods in Physics Research A 579 (2007) 557–561 www.elsevier.com/locate/nima
From MARK3 to superB and ILC F. Grancagnolo INFN Sezione di Lecce, Via Arnesano, 73100 Lecce, Italy Available online 24 May 2007
Abstract A brief evolution of about 30 years of tracking with gas drift chambers will be presented, emphasizing the progress made in this field thanks to Abe Seiden, whom we are honoring today. r 2007 Elsevier B.V. All rights reserved. PACS: 29.40.Cs Keywords: Drift chambers; Cluster counting; Momentum resolution; Particle identification
1. Introduction We will start from the multi-wire drift cell of the MARK3 chamber at SPEAR; proceed through the need for improving the multiple scattering contribution to the momentum measurement and, therefore, through the introduction of lighter gas mixtures based on helium— the KLOE drift chamber at DAFNE will be illustrated as an example; conclude with what may be considered the ultimate resolution drift chamber, based on reading out the contribution of each individual ionization cluster to the signal. It will be shown that, by collecting on the sense wire all primary ionization and recording the drift times and amplitudes of all individual ionization electrons, spatial resolution and particle identification can be pushed to their theoretical limits of accuracy. Such a method will prove to be ideal for colliders like SuperB, where accuracies of the order of a few percent in dE=dx are required for particle identification, or like the Linear Collider, where the momentum resolution is needed at the level of a few tenths of a percent for 100 GeV=c momenta particles. 2. From single-wire to multi-wire cells After an extensive and very successful use of single sense wire cells in experiments at SPEAR and DESY, while E-mail address: [email protected] 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.05.245
preparing the proposal for the MARK3 drift chamber at SPEAR, Abe Seiden, for the purpose of solving immediately the left-right ambiguity, typical of these chambers, introduced the staggered multi-wire drift cell (see Fig. 1). Such a solution presents numerous advantages. First of all, it produces a very convenient ratio of field wires to sense wires; it facilitates track-finding since in each cell one gets, in the transverse plane, a point and a vector; it gives a good monitor of calibration constants; it gives a good estimate of geometrical parameters and of chamber performance. This last point, in particular, is evident from the analysis of the histogram of the quantity D ¼ ðd 1 þ d 3 Þ=2 d 2 , shown in Fig. 2, where the d i are the drift distances on each of three sense wires within a cell and is equivalent to D ¼ 2d, depending on which side the ionizing track crosses the cell [1]. A fit to D gives an estimate of the drift velocity by comparing the distance between the two peaks to the nominal stagger (taken into account the sense wires electrostatic repulsion); an estimate of the intrinsic position resolution, sxy , averaged over the length of the wire by fitting width of the distribution of each peak, pffiffiffiffiffiffiffithe ffi s2d ¼ 3=2 sxy ; a measurement of the electrostatic repulsion of the sense wires and of their mechanical tension by plotting D versus z; an estimate of cell systematic errors, like t0 , TDC ramp, sense-wire position offsets, by plotting D versus the cell number for each layer. During the eighties, most of the drift chambers designed and built for experiments at the PEP, PETRA, SLC, LEP, Tevatron were based on the multi-wire cell design [2].
ARTICLE IN PRESS 558
F. Grancagnolo / Nuclear Instruments and Methods in Physics Research A 579 (2007) 557–561
and 3 m length, immersed in a solenoid axial field B ¼ 1:0 T, with 60 stereo layers (average 150 mrad) of single sense wire cell, 1.5 cm wide and transverse position resolution sxy ¼ 150 mm. This can be achieved with about 13,000 hexagonal cell with 13,000 W sense wires, 20 mm diameter and fewer than 30,000 Al field wires 100 mm diameter. Assuming a gas mixture based on argon, with X 0 100 m, one obtains for the transverse momentum resolution: Dp? =p? ¼ 1:2 103 p? 5:5 103
Fig. 1. MARK3 multi-wire drift cell. The three sense wires are staggered by d ¼ 0:4 mm.
(2)
where the contribution due to the multiple scattering in the gas (5:4 103 ), folded in with that due to the wires, assumed to be uniformly distributed in the gas volume (1:1 103 ), is clearly the dominant one up to 4:6 GeV=c (the full range of momenta of interest for a ‘B factory’). It was thanks to many stimulating and inspiring discussions with Abe Seiden that the suggestion to use helium as main gas in drift chambers was proposed [4]. Helium had not been used1 because of the paucity of primary ionization produced, even though it possesses other attractive qualities: very long radiation length (X 0 ¼ 5300 m, about 50 times longer than argon); slow drift velocity (a factor 2.5 with respect pto ffiffiffiffiffiffiffiargon); moderate single electron diffusion (140 mm= cm); small photoionization cross section for photons coming from synchrotron radiation. A mixture of 90% helium–10% isobutane (X 0 ¼ 1700 m) would reduce, in the drift chamber considered as an example, the contribution due to the multiple scattering from 5:4 103 to 1:3 103 . 4. The KLOE drift chamber
Fig. 2. D ¼ ðd 1 þ d 3 Þ=2 d 2 . Distance between peaks, corrected for electrostatic repulsion, is 4d ¼ 1:6 mm.
3. The need for a lighter gas mixture The MARK3 drift chamber performed in an excellent way for many years at SPEAR. However, it was evident, in the middle eighties, when designing new drift chambers for the so-called ‘Flavor Factories’, that the dominant error contributing to momentum resolution was coming from the multiple scattering of the charged track within the gas itself. The transverse momentum resolution can, in fact, be expressed as the sum of the contributions due to the sagitta measurement error and to the multiple scattering in the active tracking media [3]: pffiffiffiffiffiffiffiffi rffiffiffiffiffiffi 320 sxy Dp? 5:4 102 ‘ ¼ pffiffiffi p? 2 X0 p? B‘ 0:3 B ‘ n
(1)
One of the first and most innovative drift chambers which makes use of a helium-based gas mixture is the KLOE drift chamber [6] at the eþ e f-factory DAFNE of INFN Laboratory in Frascati. The requirements driving the choice of the parameters were: a large tracking volume because of the long K L decay length (340 m); uniformity and isotropy because the K-decays can occur anywhere and in any direction in the tracking volume; high transparency because of multiple scattering, of K-regeneration process and of low-energy photon conversions. These requirements were met by designing the largest drift chamber ever built: 4 m diameter, 3:3 m length with a uniform single-wire cell structure throughout the active volume with 56 layers of stereo wires (from 60 to 150 mrad). The mechanical structure was entirely made in carbon fiber and, therefore, very transparent: spherical end plates made of 8 mm of C-fiber laminated with a 30 mm copper foil to ensure a good grounding of the on-site electronics (total of 0:032 X 0 ); inner cylindrical wall made of 0:7 mm of C-fiber laminated with a 30 mm aluminum foil for shielding (0:003 X 0 ); outer 1
(lengths in (m), B field in (T), momentum in (GeV/c)). As an example, let us consider a drift chamber of 2 m diameter
A successful attempt was made with the PLUTO drift chamber [5] which, however, received cautious reception for the modest resolution obtained (260 mmÞ.
ARTICLE IN PRESS F. Grancagnolo / Nuclear Instruments and Methods in Physics Research A 579 (2007) 557–561
cylindrical wall made of a sandwich of C-fiber and hex-cell (0:020 X 0 ); 90% helium–10% isobutane gas mixture (0:0012 X 0 ); 80 mm Al field wires for a total of about 40,000 and 12,600 W sense wires 20 mm thick (total of 0:001 X 0 ) (see Fig. 3). The momentum resolution for Bhabha events at 510 MeV=c is shown in Fig. 4. In the range50 pyp130 , where the projected track length is constant, the resolution is 1:4 MeV=cðffi 3:0 103 Þ. The calculated resolution Dp? =p? ¼ 2:1 103 p? 2:1 103 , where the multiple scattering contributions due to the gas and to the wires are, respectively, 1:8 103 and 1:1 103 , is in excellent agreement with the experimental measurement. 5. The ultimate resolution drift chamber It is clear that having gained a large factor by using one of the lightest gas mixture, one can only improve further by optimizing the remaining parameters in Eq. (1). However, increasing the number of measurements leads to a more complicated construction procedure for the chamber and,
Fig. 3. The KLOE drift chamber at the end of the stringing procedure. The angles at which the wires are strung are clearly visible by reflection.
Fig. 4. Momentum resolution for Bhabha events (510 MeV=c) as a function of the polar angle.
559
more important, to an increase of the multiple scattering contribution due to the wires, whereas, increasing the B field, apart from costs, decreases the trapping radius and complicates the track finding. Finally, increasing the track length, which has the double advantage of decreasing both contributions to the momentum resolution, has the disadvantage of increasing the costs of the magnet and of the external calorimeter. One can only gain by improving the spatial resolution of each measuring point. Let us consider a cylindrical drift tube of radius 2 cm, run at a reasonable gain. The time separation between consecutive ionization clusters, as a function of their drift distance from the sense wire, for any impact parameter, is, in the case of an argon-based gas mixture, of the order of a few hundredths of a nanosecond to a few nanoseconds, whereas, for a helium-based gas mixture, the same quantity goes from a few nanoseconds to a few tens of nanoseconds. This is essentially due to two effects: the higher density of ionizations per unit of track length in argon versus helium (generally a factor of 6–10) and the slower drift velocity in helium with respect to argon (roughly a factor of three). We can, then, conclude that in helium, provided the front-end electronics is such that rise time of electrons signals is below 1 ns and they are read-out at a sampling rate of at least 2 Gsa/s, single electron counting can be efficiently performed [7,8]. Of course, clusters with more than a single electron, about 23% of the total in such a gas mixture, complicate this picture, particularly for very short drift distances, where the time-spread due to single electron diffusion is comparable to the time separation between consecutive clusters. At larger drift distances, already of a few mm, instead, diffusion grows only with the square root of the distance whereas the time separation between clusters increases linearly due to the slowing down of the drift velocity. 6. Cluster counting In Fig. 5 the pulse shapes generated by a cosmic ray at both ends of a 2 cm radius drift tube, filled with a mixture of 90% helium–10% isobutane at NTP, triggered by a scintillation telescope and read out by an 8 bit, 4 GHz, 2.5 Gsa/s digital sampling scope, through a 1.8 GHz, gain10 preamplifier, are shown. The maximum drift time is 1:3 ms and the number of primary ionization clusters is 13/cm with a total number of electrons of about 20/cm. In general, by subtracting the maximum drift time, 1:3 ms, from the drift time of the last ionization electron, tlast , one determines t0 , the time corresponding to the cosmic ray crossing (the trigger time), independently from its specific ionization and from the angle between track and sense wire, which both affect, instead, the number of primary clusters. The first drifting electron after t0 , tfirst , gives a good approximation of the impact parameter b relative to the sense wire and of the length of the chord c, projection of the track segment in the plane transverse to the sense
ARTICLE IN PRESS 560
F. Grancagnolo / Nuclear Instruments and Methods in Physics Research A 579 (2007) 557–561
stability of the working parameters of the detector, like, high voltage, gas temperature and pressure variations, composition of the gas mixture; which we can conservatively estimate of the order of 30235 mm. In conclusion, we can affirm that transverse position resolutions of the order of 40 mm per sense wire can be reached and that the optimal dimension of the drift cell corresponds to an average value of about 40 primary cluster for a m.i.p. perpendicular to the sense wire. 7.2. Longitudinal position resolution
Fig. 5. Pulse shapes, taken at both ends of a drift tube, of a m.i.p. triggered by a telescope of scintillators (white trace). Horizontal scale is 250 ns/div., vertical scale is 2 mV/div. In the inset, scales are 50 ns and 5 mV/div.
wire. The expected number of primary clusters is, therefore, c (3) N cl ¼ lbg sin y where l is the mean path between two ionization acts, which depends on bg of the crossing particle, and y is the dip angle between the track and the sense wire. The total number of ionizing electrons is N ele (in average 1.6 times the number of primary clusters in this gas). In general, from the pulse shapes (left and right) alone, one can reconstruct the ordered sequences of the electrons arrival times and of their amplitudes:
By matching the left and right sequences of amplitudes fAi g, properly scaled, one easily obtains the relative timings of the two arrival time sequences fti g and, therefore, the transit time of the signals on the sense wire, one of the limiting elements of the time-to-distance conversion (for a sampling rate of 2.5 Gsa/s, this is expected to be measured with a precision of a fraction of a ns, corresponding to a few cm uncertainty on the longitudinal coordinate). Moreover, the N ele scale factors relating the left and right sequences of amplitudes will provide a measurement of the longitudinal coordinate along the sense wire, with a precision better than the ‘traditional’ 0:5% obtained with theffiffiffiffiffiffiffiffi integration of the complete signal, by a factor up to ffi p N ele , corresponding to a fraction of a mm per m of wire. On the other end, if one were to use cluster counting in a large drift chamber, like the one of KLOE, with all stereo wires, strung at angles from 100 to 200 mrad, it would be reasonable to assume sz 2002400 mm. 7.3. Transverse momentum resolution
7. Cluster counting performances
A cylindrical drift chamber 0.8 m radius, with a 90% helium–10% isobutane gas mixture in a solenoid magnetic field B ¼ 1:5 T, with 60 stereo layers at an average angle of 150 mrad, made of hexagonal cells approximately 1.2 cm wide, each one capable, by cluster counting, of a position resolution of 50 mm, is, then, able to measure the transverse momentum with a resolution:
7.1. Transverse position resolution
Dp? =p? ¼ 4:0 104 p? 1:3 103 .
fti gleft fAi gleft
and fti gright fAi gright ;
i ¼ 1;
N ele
(4)
and a probability function, based on them, which relates the probability that the ith electron belongs to the jth cluster: Pði; jÞ; i ¼ 1; N ele , j ¼ 1; N cl .
Assuming that the clusters are generated along the track with a constant linear density obtained, hit-by-hit, by the ratio between the measured N cl and the length of the measured chord and given the ordered sequences of drifting clusters, each one of them, in principle, contributes to the measurement of the impact parameter with an independent estimate. The precision on the impact parameter sb is thus reduced by a factor, in principle, equivalent to the square root of the number of primary clusters. However, sb will saturate at a value given by various contributions: mechanical tolerances, like the position of the sense wire, its gravitational sagitta and its electrostatic displacement; timing uncertainties, like trigger timing, electronics calibration, transit time along the wire; in-
(5)
Therefore, such a chamber can provide a momentum resolution of better than 0.25% for all momenta of interest at a B-factory like SuperB. Analogously, a 1.5 m radius chamber, with the same gas, in a B ¼ 5:0 T and with 100 layers of stereo wires, can reach a momentum resolution of Dp? =p? ¼ 2:6 105 p? 1:5 103
(6)
equivalent to 300 MeV/c for 100 GeV/c momenta at a generic detector for the ILC. 7.4. Dip angle estimate For a m:i:p: and an average impact parameter, from Eq. (3) one can get an estimate of the dip angle with an
ARTICLE IN PRESS F. Grancagnolo / Nuclear Instruments and Methods in Physics Research A 579 (2007) 557–561
uncertainty of approximately sy 1502200 mrad good enough to extrapolate from one stereo layer to the next with a precision of a few mm, equivalent to the measurement of charge division described in Section 7.2. This is an extremely powerful tool when approaching the track finding problem with global 3D algorithms.
561
Acknowledgments The author would like to thank Hartmut Sadrozinski and the staff of the Organizing Committee of the 6th Hiroshima Symposium and, in particular, of the Special Workshop on Tracking Honoring Abe Seiden for the kind invitation and the warm hospitality received.
7.5. Particle identification Because of the Poisson nature of the phenomenon and despite the limitations of experimental data on the relativistic rise of dN cl =dx versus bg in gas mixtures [9], as opposed to dE=dx, we can expect, for a 1.2 m long m.i.p. track, in the drift chamber illustrated in Section 3.3 for SuperB a resolution of approximately 2.5%. This corresponds to a 3 sigma p=K separation for momenta up to 870 MeV/c and from 1.7 to 30 GeV/c and 4s up to 750 MeV/c and from 2.0 to 15 GeV/c, results of extreme interest for a detector at SuperB. As an example, we will also cite the result obtained in a beam test at PSI [10,8] by applying the cluster counting method to the m=p separation at 200 MeV/c. The test was performed with an unoptimized chain of electronics and a lighter gas mixture (95% helium–5% isobutane, 10 clusters/cm) which, however, obtained a separation of 1.3 s, to be compared to a theoretically obtainable value of 2.0 s and to what could, instead, be obtained with a traditional truncated mean method applied to dE=dx, of 0.6 s.
References [1] J. Roehrig, et al., Nucl. Instr. and Meth. 226 (1984) 319. [2] F. Grancagnolo, A. Seiden, D. B. Smith, Large Drift Chambers with Multiwire Cell Design, SLC Workshop, Note # 36, Stanford, CA, December 1981, SCIPP-81-5, May 1981. [3] F. Grancagnolo, Nucl. Instr. and Meth. A 277 (1989) 110. [4] F. Grancagnolo, A Helium Drift Chamber as the Central Tracker of a B-Factory, Workshop on Heavy Quarks Factory and Nuclear Physics Facility with Superconducting Linacs, Courmayeur, Italy, December 14–18, 1987, ISBN 88-7794-011-5. [5] W. Zimmermann, et al., Nucl. Instr. and Meth. A 243 (1986) 86. [6] M. Adinolfi, et al., Nucl. Instr. and Meth. A 488 (2002) 51. [7] G. Cataldi, F. Grancagnolo, S. Spagnolo, Nucl. Instr. and Meth. A 386 (1997) 458. [8] G. Cataldi, F. Grancagnolo, S. Spagnolo, INFN/AE-96/07, March 1996. [9] A.H. Walenta, Phys. Scr. 23 (1981) 354. [10] G. Cataldi, F. Grancagnolo, S. Spagnolo, KLOE-Note-155, February 1996.
Nuclear Instruments and Methods in Physics Research A 579 (2007) 557–561 www.elsevier.com/locate/nima
From MARK3 to superB and ILC F. Grancagnolo INFN Sezione di Lecce, Via Arnesano, 73100 Lecce, Italy Available online 24 May 2007
Abstract A brief evolution of about 30 years of tracking with gas drift chambers will be presented, emphasizing the progress made in this field thanks to Abe Seiden, whom we are honoring today. r 2007 Elsevier B.V. All rights reserved. PACS: 29.40.Cs Keywords: Drift chambers; Cluster counting; Momentum resolution; Particle identification
1. Introduction We will start from the multi-wire drift cell of the MARK3 chamber at SPEAR; proceed through the need for improving the multiple scattering contribution to the momentum measurement and, therefore, through the introduction of lighter gas mixtures based on helium— the KLOE drift chamber at DAFNE will be illustrated as an example; conclude with what may be considered the ultimate resolution drift chamber, based on reading out the contribution of each individual ionization cluster to the signal. It will be shown that, by collecting on the sense wire all primary ionization and recording the drift times and amplitudes of all individual ionization electrons, spatial resolution and particle identification can be pushed to their theoretical limits of accuracy. Such a method will prove to be ideal for colliders like SuperB, where accuracies of the order of a few percent in dE=dx are required for particle identification, or like the Linear Collider, where the momentum resolution is needed at the level of a few tenths of a percent for 100 GeV=c momenta particles. 2. From single-wire to multi-wire cells After an extensive and very successful use of single sense wire cells in experiments at SPEAR and DESY, while E-mail address: [email protected] 0168-9002/$ - see front matter r 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.nima.2007.05.245
preparing the proposal for the MARK3 drift chamber at SPEAR, Abe Seiden, for the purpose of solving immediately the left-right ambiguity, typical of these chambers, introduced the staggered multi-wire drift cell (see Fig. 1). Such a solution presents numerous advantages. First of all, it produces a very convenient ratio of field wires to sense wires; it facilitates track-finding since in each cell one gets, in the transverse plane, a point and a vector; it gives a good monitor of calibration constants; it gives a good estimate of geometrical parameters and of chamber performance. This last point, in particular, is evident from the analysis of the histogram of the quantity D ¼ ðd 1 þ d 3 Þ=2 d 2 , shown in Fig. 2, where the d i are the drift distances on each of three sense wires within a cell and is equivalent to D ¼ 2d, depending on which side the ionizing track crosses the cell [1]. A fit to D gives an estimate of the drift velocity by comparing the distance between the two peaks to the nominal stagger (taken into account the sense wires electrostatic repulsion); an estimate of the intrinsic position resolution, sxy , averaged over the length of the wire by fitting width of the distribution of each peak, pffiffiffiffiffiffiffithe ffi s2d ¼ 3=2 sxy ; a measurement of the electrostatic repulsion of the sense wires and of their mechanical tension by plotting D versus z; an estimate of cell systematic errors, like t0 , TDC ramp, sense-wire position offsets, by plotting D versus the cell number for each layer. During the eighties, most of the drift chambers designed and built for experiments at the PEP, PETRA, SLC, LEP, Tevatron were based on the multi-wire cell design [2].
ARTICLE IN PRESS 558
F. Grancagnolo / Nuclear Instruments and Methods in Physics Research A 579 (2007) 557–561
and 3 m length, immersed in a solenoid axial field B ¼ 1:0 T, with 60 stereo layers (average 150 mrad) of single sense wire cell, 1.5 cm wide and transverse position resolution sxy ¼ 150 mm. This can be achieved with about 13,000 hexagonal cell with 13,000 W sense wires, 20 mm diameter and fewer than 30,000 Al field wires 100 mm diameter. Assuming a gas mixture based on argon, with X 0 100 m, one obtains for the transverse momentum resolution: Dp? =p? ¼ 1:2 103 p? 5:5 103
Fig. 1. MARK3 multi-wire drift cell. The three sense wires are staggered by d ¼ 0:4 mm.
(2)
where the contribution due to the multiple scattering in the gas (5:4 103 ), folded in with that due to the wires, assumed to be uniformly distributed in the gas volume (1:1 103 ), is clearly the dominant one up to 4:6 GeV=c (the full range of momenta of interest for a ‘B factory’). It was thanks to many stimulating and inspiring discussions with Abe Seiden that the suggestion to use helium as main gas in drift chambers was proposed [4]. Helium had not been used1 because of the paucity of primary ionization produced, even though it possesses other attractive qualities: very long radiation length (X 0 ¼ 5300 m, about 50 times longer than argon); slow drift velocity (a factor 2.5 with respect pto ffiffiffiffiffiffiffiargon); moderate single electron diffusion (140 mm= cm); small photoionization cross section for photons coming from synchrotron radiation. A mixture of 90% helium–10% isobutane (X 0 ¼ 1700 m) would reduce, in the drift chamber considered as an example, the contribution due to the multiple scattering from 5:4 103 to 1:3 103 . 4. The KLOE drift chamber
Fig. 2. D ¼ ðd 1 þ d 3 Þ=2 d 2 . Distance between peaks, corrected for electrostatic repulsion, is 4d ¼ 1:6 mm.
3. The need for a lighter gas mixture The MARK3 drift chamber performed in an excellent way for many years at SPEAR. However, it was evident, in the middle eighties, when designing new drift chambers for the so-called ‘Flavor Factories’, that the dominant error contributing to momentum resolution was coming from the multiple scattering of the charged track within the gas itself. The transverse momentum resolution can, in fact, be expressed as the sum of the contributions due to the sagitta measurement error and to the multiple scattering in the active tracking media [3]: pffiffiffiffiffiffiffiffi rffiffiffiffiffiffi 320 sxy Dp? 5:4 102 ‘ ¼ pffiffiffi p? 2 X0 p? B‘ 0:3 B ‘ n
(1)
One of the first and most innovative drift chambers which makes use of a helium-based gas mixture is the KLOE drift chamber [6] at the eþ e f-factory DAFNE of INFN Laboratory in Frascati. The requirements driving the choice of the parameters were: a large tracking volume because of the long K L decay length (340 m); uniformity and isotropy because the K-decays can occur anywhere and in any direction in the tracking volume; high transparency because of multiple scattering, of K-regeneration process and of low-energy photon conversions. These requirements were met by designing the largest drift chamber ever built: 4 m diameter, 3:3 m length with a uniform single-wire cell structure throughout the active volume with 56 layers of stereo wires (from 60 to 150 mrad). The mechanical structure was entirely made in carbon fiber and, therefore, very transparent: spherical end plates made of 8 mm of C-fiber laminated with a 30 mm copper foil to ensure a good grounding of the on-site electronics (total of 0:032 X 0 ); inner cylindrical wall made of 0:7 mm of C-fiber laminated with a 30 mm aluminum foil for shielding (0:003 X 0 ); outer 1
(lengths in (m), B field in (T), momentum in (GeV/c)). As an example, let us consider a drift chamber of 2 m diameter
A successful attempt was made with the PLUTO drift chamber [5] which, however, received cautious reception for the modest resolution obtained (260 mmÞ.
ARTICLE IN PRESS F. Grancagnolo / Nuclear Instruments and Methods in Physics Research A 579 (2007) 557–561
cylindrical wall made of a sandwich of C-fiber and hex-cell (0:020 X 0 ); 90% helium–10% isobutane gas mixture (0:0012 X 0 ); 80 mm Al field wires for a total of about 40,000 and 12,600 W sense wires 20 mm thick (total of 0:001 X 0 ) (see Fig. 3). The momentum resolution for Bhabha events at 510 MeV=c is shown in Fig. 4. In the range50 pyp130 , where the projected track length is constant, the resolution is 1:4 MeV=cðffi 3:0 103 Þ. The calculated resolution Dp? =p? ¼ 2:1 103 p? 2:1 103 , where the multiple scattering contributions due to the gas and to the wires are, respectively, 1:8 103 and 1:1 103 , is in excellent agreement with the experimental measurement. 5. The ultimate resolution drift chamber It is clear that having gained a large factor by using one of the lightest gas mixture, one can only improve further by optimizing the remaining parameters in Eq. (1). However, increasing the number of measurements leads to a more complicated construction procedure for the chamber and,
Fig. 3. The KLOE drift chamber at the end of the stringing procedure. The angles at which the wires are strung are clearly visible by reflection.
Fig. 4. Momentum resolution for Bhabha events (510 MeV=c) as a function of the polar angle.
559
more important, to an increase of the multiple scattering contribution due to the wires, whereas, increasing the B field, apart from costs, decreases the trapping radius and complicates the track finding. Finally, increasing the track length, which has the double advantage of decreasing both contributions to the momentum resolution, has the disadvantage of increasing the costs of the magnet and of the external calorimeter. One can only gain by improving the spatial resolution of each measuring point. Let us consider a cylindrical drift tube of radius 2 cm, run at a reasonable gain. The time separation between consecutive ionization clusters, as a function of their drift distance from the sense wire, for any impact parameter, is, in the case of an argon-based gas mixture, of the order of a few hundredths of a nanosecond to a few nanoseconds, whereas, for a helium-based gas mixture, the same quantity goes from a few nanoseconds to a few tens of nanoseconds. This is essentially due to two effects: the higher density of ionizations per unit of track length in argon versus helium (generally a factor of 6–10) and the slower drift velocity in helium with respect to argon (roughly a factor of three). We can, then, conclude that in helium, provided the front-end electronics is such that rise time of electrons signals is below 1 ns and they are read-out at a sampling rate of at least 2 Gsa/s, single electron counting can be efficiently performed [7,8]. Of course, clusters with more than a single electron, about 23% of the total in such a gas mixture, complicate this picture, particularly for very short drift distances, where the time-spread due to single electron diffusion is comparable to the time separation between consecutive clusters. At larger drift distances, already of a few mm, instead, diffusion grows only with the square root of the distance whereas the time separation between clusters increases linearly due to the slowing down of the drift velocity. 6. Cluster counting In Fig. 5 the pulse shapes generated by a cosmic ray at both ends of a 2 cm radius drift tube, filled with a mixture of 90% helium–10% isobutane at NTP, triggered by a scintillation telescope and read out by an 8 bit, 4 GHz, 2.5 Gsa/s digital sampling scope, through a 1.8 GHz, gain10 preamplifier, are shown. The maximum drift time is 1:3 ms and the number of primary ionization clusters is 13/cm with a total number of electrons of about 20/cm. In general, by subtracting the maximum drift time, 1:3 ms, from the drift time of the last ionization electron, tlast , one determines t0 , the time corresponding to the cosmic ray crossing (the trigger time), independently from its specific ionization and from the angle between track and sense wire, which both affect, instead, the number of primary clusters. The first drifting electron after t0 , tfirst , gives a good approximation of the impact parameter b relative to the sense wire and of the length of the chord c, projection of the track segment in the plane transverse to the sense
ARTICLE IN PRESS 560
F. Grancagnolo / Nuclear Instruments and Methods in Physics Research A 579 (2007) 557–561
stability of the working parameters of the detector, like, high voltage, gas temperature and pressure variations, composition of the gas mixture; which we can conservatively estimate of the order of 30235 mm. In conclusion, we can affirm that transverse position resolutions of the order of 40 mm per sense wire can be reached and that the optimal dimension of the drift cell corresponds to an average value of about 40 primary cluster for a m.i.p. perpendicular to the sense wire. 7.2. Longitudinal position resolution
Fig. 5. Pulse shapes, taken at both ends of a drift tube, of a m.i.p. triggered by a telescope of scintillators (white trace). Horizontal scale is 250 ns/div., vertical scale is 2 mV/div. In the inset, scales are 50 ns and 5 mV/div.
wire. The expected number of primary clusters is, therefore, c (3) N cl ¼ lbg sin y where l is the mean path between two ionization acts, which depends on bg of the crossing particle, and y is the dip angle between the track and the sense wire. The total number of ionizing electrons is N ele (in average 1.6 times the number of primary clusters in this gas). In general, from the pulse shapes (left and right) alone, one can reconstruct the ordered sequences of the electrons arrival times and of their amplitudes:
By matching the left and right sequences of amplitudes fAi g, properly scaled, one easily obtains the relative timings of the two arrival time sequences fti g and, therefore, the transit time of the signals on the sense wire, one of the limiting elements of the time-to-distance conversion (for a sampling rate of 2.5 Gsa/s, this is expected to be measured with a precision of a fraction of a ns, corresponding to a few cm uncertainty on the longitudinal coordinate). Moreover, the N ele scale factors relating the left and right sequences of amplitudes will provide a measurement of the longitudinal coordinate along the sense wire, with a precision better than the ‘traditional’ 0:5% obtained with theffiffiffiffiffiffiffiffi integration of the complete signal, by a factor up to ffi p N ele , corresponding to a fraction of a mm per m of wire. On the other end, if one were to use cluster counting in a large drift chamber, like the one of KLOE, with all stereo wires, strung at angles from 100 to 200 mrad, it would be reasonable to assume sz 2002400 mm. 7.3. Transverse momentum resolution
7. Cluster counting performances
A cylindrical drift chamber 0.8 m radius, with a 90% helium–10% isobutane gas mixture in a solenoid magnetic field B ¼ 1:5 T, with 60 stereo layers at an average angle of 150 mrad, made of hexagonal cells approximately 1.2 cm wide, each one capable, by cluster counting, of a position resolution of 50 mm, is, then, able to measure the transverse momentum with a resolution:
7.1. Transverse position resolution
Dp? =p? ¼ 4:0 104 p? 1:3 103 .
fti gleft fAi gleft
and fti gright fAi gright ;
i ¼ 1;
N ele
(4)
and a probability function, based on them, which relates the probability that the ith electron belongs to the jth cluster: Pði; jÞ; i ¼ 1; N ele , j ¼ 1; N cl .
Assuming that the clusters are generated along the track with a constant linear density obtained, hit-by-hit, by the ratio between the measured N cl and the length of the measured chord and given the ordered sequences of drifting clusters, each one of them, in principle, contributes to the measurement of the impact parameter with an independent estimate. The precision on the impact parameter sb is thus reduced by a factor, in principle, equivalent to the square root of the number of primary clusters. However, sb will saturate at a value given by various contributions: mechanical tolerances, like the position of the sense wire, its gravitational sagitta and its electrostatic displacement; timing uncertainties, like trigger timing, electronics calibration, transit time along the wire; in-
(5)
Therefore, such a chamber can provide a momentum resolution of better than 0.25% for all momenta of interest at a B-factory like SuperB. Analogously, a 1.5 m radius chamber, with the same gas, in a B ¼ 5:0 T and with 100 layers of stereo wires, can reach a momentum resolution of Dp? =p? ¼ 2:6 105 p? 1:5 103
(6)
equivalent to 300 MeV/c for 100 GeV/c momenta at a generic detector for the ILC. 7.4. Dip angle estimate For a m:i:p: and an average impact parameter, from Eq. (3) one can get an estimate of the dip angle with an
ARTICLE IN PRESS F. Grancagnolo / Nuclear Instruments and Methods in Physics Research A 579 (2007) 557–561
uncertainty of approximately sy 1502200 mrad good enough to extrapolate from one stereo layer to the next with a precision of a few mm, equivalent to the measurement of charge division described in Section 7.2. This is an extremely powerful tool when approaching the track finding problem with global 3D algorithms.
561
Acknowledgments The author would like to thank Hartmut Sadrozinski and the staff of the Organizing Committee of the 6th Hiroshima Symposium and, in particular, of the Special Workshop on Tracking Honoring Abe Seiden for the kind invitation and the warm hospitality received.
7.5. Particle identification Because of the Poisson nature of the phenomenon and despite the limitations of experimental data on the relativistic rise of dN cl =dx versus bg in gas mixtures [9], as opposed to dE=dx, we can expect, for a 1.2 m long m.i.p. track, in the drift chamber illustrated in Section 3.3 for SuperB a resolution of approximately 2.5%. This corresponds to a 3 sigma p=K separation for momenta up to 870 MeV/c and from 1.7 to 30 GeV/c and 4s up to 750 MeV/c and from 2.0 to 15 GeV/c, results of extreme interest for a detector at SuperB. As an example, we will also cite the result obtained in a beam test at PSI [10,8] by applying the cluster counting method to the m=p separation at 200 MeV/c. The test was performed with an unoptimized chain of electronics and a lighter gas mixture (95% helium–5% isobutane, 10 clusters/cm) which, however, obtained a separation of 1.3 s, to be compared to a theoretically obtainable value of 2.0 s and to what could, instead, be obtained with a traditional truncated mean method applied to dE=dx, of 0.6 s.
References [1] J. Roehrig, et al., Nucl. Instr. and Meth. 226 (1984) 319. [2] F. Grancagnolo, A. Seiden, D. B. Smith, Large Drift Chambers with Multiwire Cell Design, SLC Workshop, Note # 36, Stanford, CA, December 1981, SCIPP-81-5, May 1981. [3] F. Grancagnolo, Nucl. Instr. and Meth. A 277 (1989) 110. [4] F. Grancagnolo, A Helium Drift Chamber as the Central Tracker of a B-Factory, Workshop on Heavy Quarks Factory and Nuclear Physics Facility with Superconducting Linacs, Courmayeur, Italy, December 14–18, 1987, ISBN 88-7794-011-5. [5] W. Zimmermann, et al., Nucl. Instr. and Meth. A 243 (1986) 86. [6] M. Adinolfi, et al., Nucl. Instr. and Meth. A 488 (2002) 51. [7] G. Cataldi, F. Grancagnolo, S. Spagnolo, Nucl. Instr. and Meth. A 386 (1997) 458. [8] G. Cataldi, F. Grancagnolo, S. Spagnolo, INFN/AE-96/07, March 1996. [9] A.H. Walenta, Phys. Scr. 23 (1981) 354. [10] G. Cataldi, F. Grancagnolo, S. Spagnolo, KLOE-Note-155, February 1996.