- Email: [email protected]
High-accuracy measurement of photon position in a liquid krypton calorimeter
Nuclear Instruments and Methods in Physics Research A 419 (1998) 602—608
High-accuracy measurement of photon position in a liquid krypton calorimeter V.M. Aulchenko, G.Ya. Kezerashvili, S.G. Klimenko, V.M. Malyshev, A.L. Maslennikov, A.M. Milov, N.Yu. Muchnoi, A.P. Onuchin, V.S. Panin, S.V. Peleganchuk, G.E. Pospelov*, A.G. Shamov, Yu.A. Tikhonov Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
Abstract The new experimental results with a prototype of the liquid krypton calorimeter (LKr) for the KEDR detector are presented. The prototype (0.4t of LKr) has the strip structure with a strip width of 1.0 cm. The signals from the strips are used for measuring the coordinates of the photon conversion point. The experiment was carried out at VEPP-4M collider on a tagged photon beam with an energy of 100—1700 MeV. Spatial resolution of the order of 1.0 mm in the whole energy region was obtained which is much better than that for crystal calorimeters. The results are in good agreement with the Monte-Carlo simulation. 1998 Elsevier Science B.V. All rights reserved. Keywords: KEDR detector; Liquid krypton calorimeter; Photon splitting
1. Introduction The electromagnetic calorimeter based on liquid krypton (LKr) for the KEDR detector is under construction at the e>e\ collider VEPP-4M [1—3]. The LKr calorimeter gives the energy resolution comparable to the best crystallic calorimeters and much better spatial resolution for photons due to a possibility to measure the position of the photon conversion point. A few prototypes of the LKr calorimeter [4—6] have been built and the energy resolution of 5.7% at 130 MeV and 1.9% at 1190 MeV has been obtained. The spatial resolution of 0.4 mm was obtained in the measurement
* Corresponding author. E-mail: [email protected].
with cosmic rays [4]. In this paper we present the new results obtained with the prototype-400 (400 kg of LKr) equipped with a strip structure at the tagged photon beam. The results on energy resolution and some results on spatial resolution were published elsewhere [7]. The spatial resolution was measured in the energy region 100—1700 MeV. The results on spatial resolution with double-sided semitransparent strip structure used in the LKr calorimeter for observation of a photon splitting in Coulomb field [8] are also presented.
2. The tagged photon beam The ROKK-1M facility [9] at the VEPP-4M collider provides the tagged photon beam in the
0168-9002/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 8 7 5 - 4
V.M. Aulchenko et al. /Nucl. Instr. and Meth. in Phys. Res. A 419 (1998) 602—608
wide energy range. It includes the Nd : YAG laser, the optic system to transfer the laser light to the electron beam and the KEDR Tagging System (TS) [10]. The layout of ROKK-1M at the VEPP-4M experimental area is shown in Fig. 1. High-energy photons are produced in the backward Compton scattering of the laser photons on the colliding electron beam. The maximum energy of the scattered photons is 4uc E " ,
1#4uc/mc where u is the energy of the laser photon (2.34 eV), c is the beam relativistic factor and m is the electron mass. The scattered electrons are detected by the tagging system (TS). The tagging system includes two bending magnets (M1,M2), the doublet of
603
mini-b quadrupoles (Q1,Q2) and four drift tube hodoscopes (TS1—TS4). The energy resolution of the tagging system is mainly determined by the beam angle spread and the spatial resolution of the TS. The typical energy resolution for photons is about 1.3%. The beam energy was varied during the experiment between 1.5 and 4.5 GeV, thus the tagged photon energy range was 40—625 MeV. The Bremsstrahlung spectra were used for the measurement of position resolution in the high-energy region up to 1.7 GeV.
3. The prototype of the LKr calorimeter The prototype contains 400 kg of liquid krypton. In Fig. 2 the layout of the calorimeter is shown.
Fig. 1. The layout of the ROKK-1M and the VEPP-4M experimental area.
Fig. 2. Layout of the prototype: (1) external vessel; (2) copper shield; (3) internal vessel; (4) output cable; (5) electrodes with strips; (6) electrodes with pads, (L1—L3) cells for energy measurements.
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V.M. Aulchenko et al. /Nucl. Instr. and Meth. in Phys. Res. A 419 (1998) 602—608
Table 1 The main parameters of the prototype-400 Length of the calorimeter Diameter of the calorimeter Entrance window thickness Gap width Electrode thickness Number of cells Strip width Typical cell capacitance Liquid nitrogen consumption
76 cm (16.5X ) 42 cm 0.13X 19.5 mm 0. 5 mm G1 0 #2; 1 8 lm Cu 27 towers, 28 strips 10 mm 350 pF 50 l/day
The main parameters are listed in Table 1, a more detailed description of the cryostat and cryogenics was published elsewhere [4]. The electrodes in each gap are subdivided in pads and are connected together in the longitudinal direction in the towers for the energy measurement. There are 27 towers in total. The electrodes in the first three gaps (3X ) are used for coordinate measurement. One electrode has 8—10 strips parallel to each other. The width of the strips is 1.0 cm. The sketch of the electrode system is shown in Fig. 3a and b. A modified structure with doublesided semitransparent strip electrodes was used in the experiment on photon splitting in a Coulomb field [8]. The sketch of this structure is shown in Fig. 3c. In this case a current in one gap induces
Table 2 The noise of strips (MeV)
1 layer 2 layer 3 layer
N
R#N
C
0.19 0.15 0.15
0.24 0.21 0.27
0.31 0.04 0.06
a signal on both sides of the electrode and one can measure two coordinates in one gap. This structure was designed in order to improve a photon detection efficiency with measurement of both photon coordinates. The measurement of the collected charge is provided by the charge sensitive preamplifiers based on FE¹ NJ1800D. The preamplifiers are placed outside the cryostat and connected to the electrodes through cold and warm connectors. The signal from the preamplifier is fed to the RC-2CR shaper by a twisted pair of 40 m length. The shaping time for strips was 5 ls. The amplitudes are digitized by a 12-bit anologue-digital convertor (ADC) operating in the peak detector mode. There are three different sources of noise in the LKr calorimeter: the electronic noise (N), the LKr radioactivity (R) and coherent (peak-up) noise (C). The measured numbers for noise in different strip layers are shown in Table 2.
Fig. 3. High voltage and “grounded” electrodes: (a) high voltage electrodes; (b) electrodes with strips; (c) double-sided semitransparent strip electrodes.
V.M. Aulchenko et al. /Nucl. Instr. and Meth. in Phys. Res. A 419 (1998) 602—608
4. Calculation of the spatial resolution
can be obtained:
The simplest design for the coordinate measurements in the LKr calorimeter is a set of flat ionization chambers (Fig. 4). In the anode readout mostly only one strip is sensitive to the ionization in the gap and spatial resolution is determined by strip width (p"S/(12) [4]. In the case of cathode readout if the strip width S is comparable to the gap size the current is shared on few strips and much better spatial resolution can be obtained by weighting the signals from these strips. The accuracy of photon coordinate measurement in an LKr calorimeter is determined by the following factors:
q» I(t)" +g(x , y)!g(x , y),, 2h
E fluctuation of the center of gravity of the charge induced on a cathode due to multiple scattering and fluctuation of the ionization losses; E electronic, radioactive and coherent noise; E electronegative impurities; E Algorithm of photon reconstruction. All these factors can be taken into account using Monte-Carlo simulation if we know a current shape on each strip from point-like charge in the gap of an ionization chamber. The potential distribution from a point-like charge q, placed in a point (x , y ) has the following form [11]: q P(x, y)"! 2pe ln
cosh a(x!x )!cos a(y!y ) , a"p/2h, cosh a(x!x )#cos a(y#y )
where 2h is the gap size. From this expression in the case of cathode readout a current I(t) on each strip
Fig. 4. Flat ionization chamber.
605
sin(ay)e?V!1 g(x, y)" , 1#2e?V!2e?V sin(ay) where » is a drift speed in the LKr gap, y"h!»t time-depending y-coordinate of charge, (x , x ) — coordinates of the left and right strip edges. The currents on the strips from distributed charge in the gap can be obtained by summing the currents from point-like charges: I (t)" I (t) exp(!t/¹ ). / OG H OG The number of electrons in a gap is decreased in time by factor exp(!t/¹ ) due to electro-negative H impurities (where ¹ is the lifetime of electrons in H LKr). The shape of a signal º(t) at the input of ADC can be obtained if we know the response of the electronic chain G(t) on the d-shape current signal.
R º(t)" I(t!v)G(v) dv, t(¹ , where ¹ is a drift time of electrons. Fig. 5 shows calculated I(t), º(t), A on different G strips from minimal ionising particles at S"10 mm, 2h"20 mm, » "2 mm/ls, ¹ " 7 ls, q "5.2 ls. 5. Experimental results Several runs with a collimated photon beam were carried out for the experimental study of the spatial resolution. In these runs the lead collimator with a thickness of 80 mm and a 1 mm split parallel to the strip in the calorimeter was placed in front of the cryostat. The collimator was moved across the strip direction and its position was measured with an accuracy of 0.1 mm. During the runs, the spatial resolution was measured in 10 points of strip structure with the step of 1 mm.
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Fig. 5. Amplitude on the strips: (a) I(t); (b) º(t), 1 — the sum of signals from 11 strips, 2 — the signal from the strip with maximum amplitude, 3 — the signal from the next strip and (c) A for track position between the strips and in the middle of the strip. G
Fig. 6. (a) Center-of-gravity coordinate as a function of the photon coordinate. (Points) experiment; (lines) fit. (b) Calculated function for a minimal ionising particle, experimental function for layer of conversion and next layer.
5.1. The coordinate reconstruction The center-of-gravity method can be used for the coordinate reconstruction: a)x 1 L 1 L ½" , a ) x" a x , aN " a , L G G G n aN n G G where a is the charge induced on the strip i, x is the G G strip coordinate, n the number of strips taken in analysis. The width of charge distribution on the cathode is close to a gap size, therefore, in our case, two or three strips with maximum amplitudes are sufficient for coordinate calculation. The center-ofgravity coordinate ½ is nonlinear and a disconL tinuous function of the real coordinate X . The A functions ½ (X ) and ½ (X ) for two and three A A
strips have jumps in the middle of a strip and between strips, respectively (Fig. 6a). To make the functions smooth the “generalized” center-of-gravity coordinate was used: a !a a !a #½ , ½ "½ a !a a !a where a 'a 'a are amplitudes on the strips. The coordinate reconstruction procedure was the following: E Using the energy measurements in the towers of calorimeter the photons were subdivided in groups depending on energy (MeV): (50—150, 150—250, 350—450, 550—625) — Compton spectra, (700—900, 900—1100, 1100—1350, 1400—1700) — bremsstrahlung spectra. These groups were
V.M. Aulchenko et al. /Nucl. Instr. and Meth. in Phys. Res. A 419 (1998) 602—608
E E
E
E
used to obtain a dependence of spatial resolution on photon energy. The strip with maximum amplitude in each strip layer is found. The energy deposition E in each strip layer is calculated: it is a sum from three strips (from the strip with maximum amplitude and two neighboring strips). The number of layer N where the photon was converted is determined: for this layer E 'P, , for all preceding layers E (P, where ,\ P"3(3p#9p is the threshold on energy the deposition in a layer. p is the electronic and radioactive noise, p is the coherent noise from one strip. The coordinate of a photon is calculated in the layers N and N#1 using the “generalized” center-of-gravity method for three strips.
We used data from only the last two strip layers. Therefore, two data samples +X,X, were availA A able in each run, where X is the coordinate, meaA sured in a layer, where the first interaction of the photon took place, X is the coordinate in the next A layer. The correction function for “generalized” center of gravity was obtained in the experiment. To determine the functions ½ (X ) the average center of A gravity coordinates ½ for each position of the collimator have been measured (Fig. 6). The measured dependencies ½ on X were fitted by A smooth functions. These functions were used to determine the photon coordinate X from the A center of gravity coordinates. In Fig. 6a the centerof-gravity coordinate as a function of the photon coordinates in a layer of conversion is shown. Fig. 6b shows the experimental correction function for the layer of conversion, the next layer and the calculated function for a minimal ionizing particle. Fig. 7 shows the spatial resolution dependence across the strip. The average spatial resolution for different energies of the photons is shown in Fig. 8. The results are in good agreement with Monte-Carlo simulation. The best spatial resolution is obtained in the layer where the first conversion of a photon into an e>e\-pair takes place and it is determined by the noise. The resolution in the next layer is affected by multiple scatter-
607
Fig. 7. The space resolution depending on the coordinate across the strip: (䢇) the X data sample, (*) the X data sample, (—) A A fit.
Fig. 8. The space resolution depending on the photon energy: (䢇) X data sample, (*) X data sample, (—) fit, (夹) MC A A simulation.
ing. At energies below 300 MeV the resolution is mainly determined by multiple scattering. 5.2. The spatial resolution with semitransparent strip structure The experiment on photon splitting was carried out at the tagged photon beam of the VEPP-4M collider. In this experiment the photon splitting was observed for the first time [8]. In order to increase the efficiency of photon detection with simultaneous measurement of both coordinates in one gap the semitransparent double side strip structure has been implemented in the calorimeter. A method for calculation of the spatial resolution in this structure was developed in Ref. [12]. The efficiency of both the photon coordinate reconstruction in the layer, where the first interaction of the photon took place
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Fig. 9. The spatial resolution depending on the photon energy. (䢇) y-coordinate resolution, (*) x-coordinate resolution, (夹) MC simulation.
was found to be 70.0%. In the other 30% of events the second coordinate was taken from the next layer. The dependence of spatial resolution on photon energy is shown in Fig. 9. One can see a good agreement with Monte-Carlo simulation.
whose efforts made this work possible. We wish to thank R.G. Snopkov for help in the prototype assembling.
6. Conclusions
[1] V.M. Aulchenko et al., Proc. 24 Int. Conf. on High Energy Physics, Munich, 1988 (contrib. paper) V.V. Anashin et al., Proc. Int. Symp. on Position Detect. in High Energy Physics, Dubna, 1988, p. 58. [2] V.M. Aulchenko et al., in: F. Anderson (Ed.), Proc. Int. Conf. on Calorimetry at High Energy Physics, FNAL, 1990, World Scientific, p. 223. [3] P. Cantoni et al., Nucl. Instr. and Meth. A 315 (1992) 491. [4] V.M. Aulchenko et al., Nucl. Instr. and Meth. A 289 (1990) 468. [5] V.M. Aulchenko et al., Nucl. Instr. and Meth. A 316 (1992) 8. [6] V.M. Aulchenko et al., Nucl. Instr. and Meth. A 327 (1993) 194. [7] V.M. Aulchenko et al., Nucl. Instr. and Meth. A 394 (1997) 35. [8] Sh.Zh. Akhmadaliev et al., PHOTON’97 Egmond-aanZee, Nederlands, 10-16/05/97. [9] G.Ya. Kezerashvili et al., Proc. XXII Int. Conf. on the Accelerators of High Energy Charged Particles, Dubna, vol. 1, 1992, pp. 416—418. [10] A.E. Bondar et al., Proc. XXII Int. Conf. on the Accelerators of High Energy Charged Particles, Dubna, vol. 1, 1992, p. 309. [11] J.S. Gordon et al., Nucl. Instr. and Meth. A 227 (1984) 267. [12] G.E. Pospelov, Graduate diploma, Novosibirsk State University (in russian) (unpublished).
The LKr calorimeter for the KEDR detector at the VEPP-4M collider has a strip structure for measurement of the photon coordinate. In the experiment with the prototype at the tagged photon beam a spatial resolution of about 1.0 mm was obtained in the energy range 100—1700 MeV. Obtained spatial resolution is about five times better than that for best crystal calorimeters. A better spatial resolution improves efficiency of the nreconstruction in the calorimeter. A double-sided semitransparent strip structure was used for the experiment on photon splitting in the Coulomb field. A spatial resolution of 1.5—1.0 mm at the energies 100—300 MeV was obtained. Acknowledgements The authors would like to express their gratitude to professor A.N. Skrinsky and Professor V.A. Sidorov for support and to the VEPP-4M staff
References
High-accuracy measurement of photon position in a liquid krypton calorimeter V.M. Aulchenko, G.Ya. Kezerashvili, S.G. Klimenko, V.M. Malyshev, A.L. Maslennikov, A.M. Milov, N.Yu. Muchnoi, A.P. Onuchin, V.S. Panin, S.V. Peleganchuk, G.E. Pospelov*, A.G. Shamov, Yu.A. Tikhonov Budker Institute of Nuclear Physics, Novosibirsk 630090, Russia
Abstract The new experimental results with a prototype of the liquid krypton calorimeter (LKr) for the KEDR detector are presented. The prototype (0.4t of LKr) has the strip structure with a strip width of 1.0 cm. The signals from the strips are used for measuring the coordinates of the photon conversion point. The experiment was carried out at VEPP-4M collider on a tagged photon beam with an energy of 100—1700 MeV. Spatial resolution of the order of 1.0 mm in the whole energy region was obtained which is much better than that for crystal calorimeters. The results are in good agreement with the Monte-Carlo simulation. 1998 Elsevier Science B.V. All rights reserved. Keywords: KEDR detector; Liquid krypton calorimeter; Photon splitting
1. Introduction The electromagnetic calorimeter based on liquid krypton (LKr) for the KEDR detector is under construction at the e>e\ collider VEPP-4M [1—3]. The LKr calorimeter gives the energy resolution comparable to the best crystallic calorimeters and much better spatial resolution for photons due to a possibility to measure the position of the photon conversion point. A few prototypes of the LKr calorimeter [4—6] have been built and the energy resolution of 5.7% at 130 MeV and 1.9% at 1190 MeV has been obtained. The spatial resolution of 0.4 mm was obtained in the measurement
* Corresponding author. E-mail: [email protected].
with cosmic rays [4]. In this paper we present the new results obtained with the prototype-400 (400 kg of LKr) equipped with a strip structure at the tagged photon beam. The results on energy resolution and some results on spatial resolution were published elsewhere [7]. The spatial resolution was measured in the energy region 100—1700 MeV. The results on spatial resolution with double-sided semitransparent strip structure used in the LKr calorimeter for observation of a photon splitting in Coulomb field [8] are also presented.
2. The tagged photon beam The ROKK-1M facility [9] at the VEPP-4M collider provides the tagged photon beam in the
0168-9002/98/$19.00 1998 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 8 - 9 0 0 2 ( 9 8 ) 0 0 8 7 5 - 4
V.M. Aulchenko et al. /Nucl. Instr. and Meth. in Phys. Res. A 419 (1998) 602—608
wide energy range. It includes the Nd : YAG laser, the optic system to transfer the laser light to the electron beam and the KEDR Tagging System (TS) [10]. The layout of ROKK-1M at the VEPP-4M experimental area is shown in Fig. 1. High-energy photons are produced in the backward Compton scattering of the laser photons on the colliding electron beam. The maximum energy of the scattered photons is 4uc E " ,
1#4uc/mc where u is the energy of the laser photon (2.34 eV), c is the beam relativistic factor and m is the electron mass. The scattered electrons are detected by the tagging system (TS). The tagging system includes two bending magnets (M1,M2), the doublet of
603
mini-b quadrupoles (Q1,Q2) and four drift tube hodoscopes (TS1—TS4). The energy resolution of the tagging system is mainly determined by the beam angle spread and the spatial resolution of the TS. The typical energy resolution for photons is about 1.3%. The beam energy was varied during the experiment between 1.5 and 4.5 GeV, thus the tagged photon energy range was 40—625 MeV. The Bremsstrahlung spectra were used for the measurement of position resolution in the high-energy region up to 1.7 GeV.
3. The prototype of the LKr calorimeter The prototype contains 400 kg of liquid krypton. In Fig. 2 the layout of the calorimeter is shown.
Fig. 1. The layout of the ROKK-1M and the VEPP-4M experimental area.
Fig. 2. Layout of the prototype: (1) external vessel; (2) copper shield; (3) internal vessel; (4) output cable; (5) electrodes with strips; (6) electrodes with pads, (L1—L3) cells for energy measurements.
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Table 1 The main parameters of the prototype-400 Length of the calorimeter Diameter of the calorimeter Entrance window thickness Gap width Electrode thickness Number of cells Strip width Typical cell capacitance Liquid nitrogen consumption
76 cm (16.5X ) 42 cm 0.13X 19.5 mm 0. 5 mm G1 0 #2; 1 8 lm Cu 27 towers, 28 strips 10 mm 350 pF 50 l/day
The main parameters are listed in Table 1, a more detailed description of the cryostat and cryogenics was published elsewhere [4]. The electrodes in each gap are subdivided in pads and are connected together in the longitudinal direction in the towers for the energy measurement. There are 27 towers in total. The electrodes in the first three gaps (3X ) are used for coordinate measurement. One electrode has 8—10 strips parallel to each other. The width of the strips is 1.0 cm. The sketch of the electrode system is shown in Fig. 3a and b. A modified structure with doublesided semitransparent strip electrodes was used in the experiment on photon splitting in a Coulomb field [8]. The sketch of this structure is shown in Fig. 3c. In this case a current in one gap induces
Table 2 The noise of strips (MeV)
1 layer 2 layer 3 layer
N
R#N
C
0.19 0.15 0.15
0.24 0.21 0.27
0.31 0.04 0.06
a signal on both sides of the electrode and one can measure two coordinates in one gap. This structure was designed in order to improve a photon detection efficiency with measurement of both photon coordinates. The measurement of the collected charge is provided by the charge sensitive preamplifiers based on FE¹ NJ1800D. The preamplifiers are placed outside the cryostat and connected to the electrodes through cold and warm connectors. The signal from the preamplifier is fed to the RC-2CR shaper by a twisted pair of 40 m length. The shaping time for strips was 5 ls. The amplitudes are digitized by a 12-bit anologue-digital convertor (ADC) operating in the peak detector mode. There are three different sources of noise in the LKr calorimeter: the electronic noise (N), the LKr radioactivity (R) and coherent (peak-up) noise (C). The measured numbers for noise in different strip layers are shown in Table 2.
Fig. 3. High voltage and “grounded” electrodes: (a) high voltage electrodes; (b) electrodes with strips; (c) double-sided semitransparent strip electrodes.
V.M. Aulchenko et al. /Nucl. Instr. and Meth. in Phys. Res. A 419 (1998) 602—608
4. Calculation of the spatial resolution
can be obtained:
The simplest design for the coordinate measurements in the LKr calorimeter is a set of flat ionization chambers (Fig. 4). In the anode readout mostly only one strip is sensitive to the ionization in the gap and spatial resolution is determined by strip width (p"S/(12) [4]. In the case of cathode readout if the strip width S is comparable to the gap size the current is shared on few strips and much better spatial resolution can be obtained by weighting the signals from these strips. The accuracy of photon coordinate measurement in an LKr calorimeter is determined by the following factors:
q» I(t)" +g(x , y)!g(x , y),, 2h
E fluctuation of the center of gravity of the charge induced on a cathode due to multiple scattering and fluctuation of the ionization losses; E electronic, radioactive and coherent noise; E electronegative impurities; E Algorithm of photon reconstruction. All these factors can be taken into account using Monte-Carlo simulation if we know a current shape on each strip from point-like charge in the gap of an ionization chamber. The potential distribution from a point-like charge q, placed in a point (x , y ) has the following form [11]: q P(x, y)"! 2pe ln
cosh a(x!x )!cos a(y!y ) , a"p/2h, cosh a(x!x )#cos a(y#y )
where 2h is the gap size. From this expression in the case of cathode readout a current I(t) on each strip
Fig. 4. Flat ionization chamber.
605
sin(ay)e?V!1 g(x, y)" , 1#2e?V!2e?V sin(ay) where » is a drift speed in the LKr gap, y"h!»t time-depending y-coordinate of charge, (x , x ) — coordinates of the left and right strip edges. The currents on the strips from distributed charge in the gap can be obtained by summing the currents from point-like charges: I (t)" I (t) exp(!t/¹ ). / OG H OG The number of electrons in a gap is decreased in time by factor exp(!t/¹ ) due to electro-negative H impurities (where ¹ is the lifetime of electrons in H LKr). The shape of a signal º(t) at the input of ADC can be obtained if we know the response of the electronic chain G(t) on the d-shape current signal.
R º(t)" I(t!v)G(v) dv, t(¹ , where ¹ is a drift time of electrons. Fig. 5 shows calculated I(t), º(t), A on different G strips from minimal ionising particles at S"10 mm, 2h"20 mm, » "2 mm/ls, ¹ " 7 ls, q "5.2 ls. 5. Experimental results Several runs with a collimated photon beam were carried out for the experimental study of the spatial resolution. In these runs the lead collimator with a thickness of 80 mm and a 1 mm split parallel to the strip in the calorimeter was placed in front of the cryostat. The collimator was moved across the strip direction and its position was measured with an accuracy of 0.1 mm. During the runs, the spatial resolution was measured in 10 points of strip structure with the step of 1 mm.
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Fig. 5. Amplitude on the strips: (a) I(t); (b) º(t), 1 — the sum of signals from 11 strips, 2 — the signal from the strip with maximum amplitude, 3 — the signal from the next strip and (c) A for track position between the strips and in the middle of the strip. G
Fig. 6. (a) Center-of-gravity coordinate as a function of the photon coordinate. (Points) experiment; (lines) fit. (b) Calculated function for a minimal ionising particle, experimental function for layer of conversion and next layer.
5.1. The coordinate reconstruction The center-of-gravity method can be used for the coordinate reconstruction: a)x 1 L 1 L ½" , a ) x" a x , aN " a , L G G G n aN n G G where a is the charge induced on the strip i, x is the G G strip coordinate, n the number of strips taken in analysis. The width of charge distribution on the cathode is close to a gap size, therefore, in our case, two or three strips with maximum amplitudes are sufficient for coordinate calculation. The center-ofgravity coordinate ½ is nonlinear and a disconL tinuous function of the real coordinate X . The A functions ½ (X ) and ½ (X ) for two and three A A
strips have jumps in the middle of a strip and between strips, respectively (Fig. 6a). To make the functions smooth the “generalized” center-of-gravity coordinate was used: a !a a !a #½ , ½ "½ a !a a !a where a 'a 'a are amplitudes on the strips. The coordinate reconstruction procedure was the following: E Using the energy measurements in the towers of calorimeter the photons were subdivided in groups depending on energy (MeV): (50—150, 150—250, 350—450, 550—625) — Compton spectra, (700—900, 900—1100, 1100—1350, 1400—1700) — bremsstrahlung spectra. These groups were
V.M. Aulchenko et al. /Nucl. Instr. and Meth. in Phys. Res. A 419 (1998) 602—608
E E
E
E
used to obtain a dependence of spatial resolution on photon energy. The strip with maximum amplitude in each strip layer is found. The energy deposition E in each strip layer is calculated: it is a sum from three strips (from the strip with maximum amplitude and two neighboring strips). The number of layer N where the photon was converted is determined: for this layer E 'P, , for all preceding layers E (P, where ,\ P"3(3p#9p is the threshold on energy the deposition in a layer. p is the electronic and radioactive noise, p is the coherent noise from one strip. The coordinate of a photon is calculated in the layers N and N#1 using the “generalized” center-of-gravity method for three strips.
We used data from only the last two strip layers. Therefore, two data samples +X,X, were availA A able in each run, where X is the coordinate, meaA sured in a layer, where the first interaction of the photon took place, X is the coordinate in the next A layer. The correction function for “generalized” center of gravity was obtained in the experiment. To determine the functions ½ (X ) the average center of A gravity coordinates ½ for each position of the collimator have been measured (Fig. 6). The measured dependencies ½ on X were fitted by A smooth functions. These functions were used to determine the photon coordinate X from the A center of gravity coordinates. In Fig. 6a the centerof-gravity coordinate as a function of the photon coordinates in a layer of conversion is shown. Fig. 6b shows the experimental correction function for the layer of conversion, the next layer and the calculated function for a minimal ionizing particle. Fig. 7 shows the spatial resolution dependence across the strip. The average spatial resolution for different energies of the photons is shown in Fig. 8. The results are in good agreement with Monte-Carlo simulation. The best spatial resolution is obtained in the layer where the first conversion of a photon into an e>e\-pair takes place and it is determined by the noise. The resolution in the next layer is affected by multiple scatter-
607
Fig. 7. The space resolution depending on the coordinate across the strip: (䢇) the X data sample, (*) the X data sample, (—) A A fit.
Fig. 8. The space resolution depending on the photon energy: (䢇) X data sample, (*) X data sample, (—) fit, (夹) MC A A simulation.
ing. At energies below 300 MeV the resolution is mainly determined by multiple scattering. 5.2. The spatial resolution with semitransparent strip structure The experiment on photon splitting was carried out at the tagged photon beam of the VEPP-4M collider. In this experiment the photon splitting was observed for the first time [8]. In order to increase the efficiency of photon detection with simultaneous measurement of both coordinates in one gap the semitransparent double side strip structure has been implemented in the calorimeter. A method for calculation of the spatial resolution in this structure was developed in Ref. [12]. The efficiency of both the photon coordinate reconstruction in the layer, where the first interaction of the photon took place
VIII. CALORIMETRY
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Fig. 9. The spatial resolution depending on the photon energy. (䢇) y-coordinate resolution, (*) x-coordinate resolution, (夹) MC simulation.
was found to be 70.0%. In the other 30% of events the second coordinate was taken from the next layer. The dependence of spatial resolution on photon energy is shown in Fig. 9. One can see a good agreement with Monte-Carlo simulation.
whose efforts made this work possible. We wish to thank R.G. Snopkov for help in the prototype assembling.
6. Conclusions
[1] V.M. Aulchenko et al., Proc. 24 Int. Conf. on High Energy Physics, Munich, 1988 (contrib. paper) V.V. Anashin et al., Proc. Int. Symp. on Position Detect. in High Energy Physics, Dubna, 1988, p. 58. [2] V.M. Aulchenko et al., in: F. Anderson (Ed.), Proc. Int. Conf. on Calorimetry at High Energy Physics, FNAL, 1990, World Scientific, p. 223. [3] P. Cantoni et al., Nucl. Instr. and Meth. A 315 (1992) 491. [4] V.M. Aulchenko et al., Nucl. Instr. and Meth. A 289 (1990) 468. [5] V.M. Aulchenko et al., Nucl. Instr. and Meth. A 316 (1992) 8. [6] V.M. Aulchenko et al., Nucl. Instr. and Meth. A 327 (1993) 194. [7] V.M. Aulchenko et al., Nucl. Instr. and Meth. A 394 (1997) 35. [8] Sh.Zh. Akhmadaliev et al., PHOTON’97 Egmond-aanZee, Nederlands, 10-16/05/97. [9] G.Ya. Kezerashvili et al., Proc. XXII Int. Conf. on the Accelerators of High Energy Charged Particles, Dubna, vol. 1, 1992, pp. 416—418. [10] A.E. Bondar et al., Proc. XXII Int. Conf. on the Accelerators of High Energy Charged Particles, Dubna, vol. 1, 1992, p. 309. [11] J.S. Gordon et al., Nucl. Instr. and Meth. A 227 (1984) 267. [12] G.E. Pospelov, Graduate diploma, Novosibirsk State University (in russian) (unpublished).
The LKr calorimeter for the KEDR detector at the VEPP-4M collider has a strip structure for measurement of the photon coordinate. In the experiment with the prototype at the tagged photon beam a spatial resolution of about 1.0 mm was obtained in the energy range 100—1700 MeV. Obtained spatial resolution is about five times better than that for best crystal calorimeters. A better spatial resolution improves efficiency of the nreconstruction in the calorimeter. A double-sided semitransparent strip structure was used for the experiment on photon splitting in the Coulomb field. A spatial resolution of 1.5—1.0 mm at the energies 100—300 MeV was obtained. Acknowledgements The authors would like to express their gratitude to professor A.N. Skrinsky and Professor V.A. Sidorov for support and to the VEPP-4M staff
References